Astronomy

Are large body orbits self correcting?

Are large body orbits self correcting?


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If a rogue planet disrupts Earth's orbit slightly to cause a long winter or summer will the Earth's orbit normalize back close its original orbit over time? Could a Planet X or some other elliptical orbit large body revolving around the sun effect Earth's orbit by being inside the inner solar system?


No. Basically, there is no such thing as a stable orbit in a realistic solar system. All planetary orbits are unstable due to gravitational interactions between planets, but how long it takes the instability to make a big change in a planet's orbit varies a lot. It can be a few of the planet's years, thousands, millions or billions. (Earth's orbit has been stable, so far, for 4+ billion years.) But stability going forward can't be guaranteed beyond at most a hundred million or so years.

The main source of instability is resonances. A resonance is where two planets are in orbits where the ratio of their periods is a simple fraction like 1/2 or 2/3 or 5/3 or whatever. Because of the simple relationship between periods, planets repeat the same configuration in space repeatedly, and gravitational interactions can build up. (Without the resonance, the interactions are just as strong, but in random directions and thus mostly cancel.)

Resonances can disrupt an orbit or can stabilize it. The Hilda group of asteroids are in a stable 3:2 resonance with Jupiter, for example, and Pluto is in a 2:3 resonance with Neptune. Both of these resonances act to stabilize the orbits. But the Kirkwood Gap in the asteroid belt is a 2:1 resonance with Jupiter which tends to keep the gap empty by disrupting the orbits of any asteroids that stray into the gap.

After the interaction, Earth will be in a new orbit and that orbit may also be stable over an extended period or it may be one where interactions with other planets quickly render the new orbit unstable. There's no way to tell without detailed orbital information on the encounter.

In any event, there is no restoring force to push Earth back to its old orbit.


N-Body solver¶

One feature that FARGO3D has inherited from its ancestor FARGO is the possibility to include a number of point-like masses which can interact between themselves and which can also gravitationally interact with the gas. The set of such masses is defined in a file. This file must be defined in the parameter file with the parameter PlanetConfig . For instance, in the default parameter file of the fargo setup (that is, setups/fargo/fargo.par ), we find the line:

Throughout this chapter, we call this file the config file, or the planetary configuration file. The content of this file is strictly similar to that defined in the previous FARGO code:

Lines beginning with a ‘#’ are ignored. A line containing a valid planet definition must begin with a letter (‘a-z’ or ‘A-Z’). So far this name is not reflected in the code output, but it gives a sense of what kind of planet or planetary system is intended. The second column gives the semi-major axis in units of R0 , defined in src/fondam.h . The third column gives the planetary mass in units of MSTAR , defined also in src/fondam.h . The fourth column, relative to accretion, is not used at the present time. So far its only purpose is to allow backward compatibility with FARGO’s planetary config files. Finally, the content of the last two columns, which is self-explanatory, indicates whether the planet feels the gravity of the other planets and whether it feels the gravity of the disk.

Our N-Body solver is a simple fifth order Runge-Kutta integrator. This may seem pretty simplistic compared to way more sophisticated N-body integrators, which are tailored to follow the dynamics of a collection of point-like masses in vacuum over very long timescales. It should be remembered that our primary purpose is the study of protoplanets embedded in disks. The lifetime of the disk is 3 to 4 orders of magnitude shorter than the age of the Solar System, and the variation of total energy of planet under a disk tide is usually many orders of magnitude larger than that inherent to our scheme. The latter is therefore perfectly fine for our purpose.

The planets are initialized at (t=0) such that they lie on the (x) axis, are prograde with the disk, have all same eccentricity (defined by the parameter ECCENTRICITY , which defaults to zero). Their initial location corresponds to apoastron.

By default, a central star of mass MSTAR (defined in src/fondam.h ) is added at the mesh center. This default behavior can be superseded, for instance, to have the mesh centered on the center of gravity of the system, or to have a binary star at the center.

The value of MSTAR is used to initialize the orbits of the planets, in all cases.


Yes, New York Times, there is a scientific method

“Philosophy of science is about as useful to scientists as ornithology is to birds.” -Richard Feynman

There are lots of different ways to do science that are equally valid one scientific method does not necessarily fit all cases. In astronomy, experiments are virtually impossible, as all you can do is make observations of what the Universe gives us. In the early days of quantum physics, the results were so surprising that it took many years before it was even possible to hypothesize in a sensible fashion, as the rules defied intuition. And in many fields, there are too many variables at play to accurately model the system even when all the underlying, governing equations are 100% known. Yet the differences in the details of how science is performed in no way invalidates astronomy, quantum physics, protein-folding or climate modeling as sciences. By the same token, however, the similarities between these scientific endeavors and poetry or philosophy do not elevate the latter to the status of being considered science.

On July 4th, an opinion piece ran in the New York Times declaring that there is no scientific method. The author clarifies that he means there is no distinctly scientific method, and then goes on to describe how concepts like “justice” and “courage” are hard to define in an all-encompassing way, despite the fact that we know and recognize it when we see it. Then he takes two examples — one of Kepler’s first law (that planets move in ellipses around the Sun) and one of Galileo’s discovery of the motion of freely-falling objects — and brings up the facts that:

  • Kepler could have fit circles, circles-with-epicycles, or ovals to the data just as easily as an ellipse, and could have arrived at a totally different law as a result.
  • Galileo needed to neglect air resistance, a known force, to arrive at his result.

And therefore, the conclusion went, science is no different than any other arbitrary endeavor.

Except that science is completely different than every other endeavor, and Kepler and Galileo actually provide extraordinary examples of showing exactly how, if only James Blachowicz would have dug a little deeper. Kepler’s original model, above, was the Mysterium Cosmographicum, where he detailed his outstandingly creative theory for what determined the planetary orbits. In 1596, he published the idea that there were a series of invisible Platonic solids, with the planetary orbits residing on the inscribed and circumscribed spheres. This model would predict their orbits, their relative distances, and — if it were right — would match the outstanding data taken by Tycho Brahe over many decades.

But beginning in the early 1600s, when Kepler had access to the full suite of Brahe’s data, he found that it didn’t match his model. His other efforts at models, including oval-shaped orbits, failed as well. The thing is, Kepler didn’t just say, “oh well, it didn’t match,” to some arbitrary degree of precision. He had the previous best scientific model — Ptolemy’s geocentric model with epicycles, equants and deferents — to compare it to. In science, if you want your new idea to supersede the old model, it has to prove itself to be superior through experiments and observations. That’s what makes it science. And that’s why the ellipses succeeded, because they gave better, more accurate prediction than all the models that came before, including Ptolemy’s, Copernicus’, Brahe’s and even Kepler’s own earlier models.

The point of Galileo’s is another deep illustration of how science actually works. One of the very first science experiments of all — over 2,500 years ago — was done by Empedocles, in an attempt to answer the question of whether air takes up space. The device above is known as a clepsydra (Greek for “water-thief”), which is a gourd with one hole in the top and one-to-many holes in the bottom. You submerge the gourd into a source of water until it fills, then put your thumb over the hole at the top and carry the water everywhere. Although the Greeks didn’t know about a vacuum or the concept of air pressure, they could see that the water at the bottom wasn’t falling out, and the only thing that could be pushing “up” against it was air. Therefore, air takes up space and fills all the space around us on Earth, and when that air moves relative to an object, it exerts a force.

Galileo knew about air resistance as well, although he couldn’t quantify it. He knew that if you dropped two masses of different weights from a small height and a large height, the large drop led to a larger difference in when those two masses hit the ground, and that difference was due to air resistance. Galileo’s revolutionary advance, as I detailed here, was to determine that objects fell a distance that was proportional to the amount of time they had been falling squared, when these other effects were ignored. This was as true for balls dropped from a tower as they were for objects rolled down a ramp. When we finally made it to an airless world, we performed Galileo’s experiment exactly as it was idealized: without air resistance at all.

But other effects really do exist, and science didn’t “end” at the advances of Kepler and Galileo. Rather, these advances became the starting points for the theories that would improve upon them, in both cases by Isaac Newton. For Kepler’s problem of planetary motion, the gravitational effects of the planets on one another were the next imperfection to account for, and after we nailed that, there were no further improvements until Einstein in the 20th century. Newton also enabled us — through his development of mechanics — to account for as many additional forces as we like, including air resistance, since the F in F = ma is actually the sum of all the relevant forces on a system.

The only thing that limits how accurately we can model something if we understand the underlying dynamics is either the inherent uncertainty in how a system behaves or is set up, and how much of the actual forces in play we can practically include in our model. Science is more than a body of knowledge — although it requires those facts, that data and those results — but is also a process. It’s a self-correcting process where it must always be confronted with the real world, with what we observe and measure, with what its new predictions are and with the full suite of models and ideas that came before. What’s truly shocking, though, is that one of the earliest philosophers, Thales of Miletus, knew all of this and enunciated it quite clearly in his philosophy of naturalism. So when Blachowicz asks,

If scientific method is only one form of a general method employed in all human inquiry, how is it that the results of science are more reliable than what is provided by these other forms?

all we need to do is point his own examples — full of illustrative science — back at him to arrive at the answer.


Contents

The word theory means a contemplation or speculation, as opposed to action. It is a statement of how and why particular facts are related. Theory is especially often contrasted to "practice". While theories may address ideas and empirical phenomena which are not easily measurable, scientific theory is generally understood to refer to a proposed explanation of empirical phenomena, made in a way consistent with scientific method. Such theories are preferably described in such a way that any scientist in the field is in a position to understand and either provide empirical support ("verify") or empirically contradict ("falsify") it. A common distinction made in science is between theories and hypotheses. Hypotheses are individual empirically testable conjectures while theories are collections of hypotheses that are logically linked together into a coherent explanation of some aspect of reality and which have individually or jointly received some empirical support.

  1. a coherentstatement or set of ideas that explainsobservedfacts or phenomena, or which sets out the laws and principles of something known or observed a hypothesis confirmed by observation, experiment etc.
  2. the underlying principles or methods of a given technical skill, art etc., as opposed to its practice
  3. a field of study attempting to exhaustivelydescribe a particular class of constructs
  4. a hypothesis or conjecture
  5. a set of axioms together with all statements derivable from them. Equivalently, a formal language plus a set of axioms (from which can then be derived theorems) is called a theory.

The nomology and any effort to acquire a system of laws or knowledge focusing on any natural body in the sky especially at night constitutes the theory of astronomy.

The overall theory of astronomy consists of three fundamental parts:

  1. the derivation of logical laws,
  2. the definitions of natural bodies (entities, sources, or objects), and
  3. the definition of the sky (and associated realms).

Def. "the expanse of space that seems to be over the earth like a dome" [2] is called the sky, or sometimes the heavens.

This definition applies especially well to an individual on top of the Earth's solid crust looking around at what lies above and off to the horizon in all directions. Similarly, it applies to an individual's visual view while floating on a large body of water, where off on the horizon is still water.

The image at right shows the horizon marking the lower edge of the sky and the upper edge of the Atlantic Ocean, with a layer of cumulus clouds just above.

A more general definition of 'sky' allows for skies as seen on other worlds. At left is a 360° panarama of the horizon on Mars as perceived in the visual true-color range of the NASA Mars Exploration Rover 'Spirit' on November 23-8, 2005.

Def. an "expanse of space that seems to be [overhead] like a dome" [2] is called a sky.

Even in day light, the sky may seem absent of objects if a nearby source tends to overwhelm other luminous objects.

At top is a view of the horizon on the Moon's solid surface taken by an Apollo 16 astronaut. The image shows a black sky without stars because the sunlight coming from the left is overwhelming.

1.a: an "independent, separate, or self-contained existence", 1.b: "the existence of a thing as contrasted with its attributes", or 2. "something that has separate and distinct existence and objective or conceptual reality",

1.a: "something that is or is capable of being seen, touched, or otherwise sensed", 1.b: "something physical or mental of which a subject is cognitively aware", 2. "something that arouses an emotion in an observer", or 3. "a thing that forms an element of or constitutes the subject matter of an investigation or science"

1.a: "a mass of matter distinct from other masses" or 2.b: "something that embodies or gives concrete reality to a thing [specifically] : a sensible object in physical space"

1.a: "a separate and distinct individual quality, fact, idea, or [usually] entity", 1.b: "the concrete entity as distinguished from its appearances", 1.c: "a spatial entity", or 1.d: "an inanimate object distinguished from a living being"

1: "an observable fact or event", 2.a: "an object or aspect known through the senses rather than by though or intuition", 2.b: "an object of experience in space and time as distinguished from a thing-in-itself", or 2.c: "a fact or event of scientific interest susceptible of scientific description and explanation"

is called a phenomenon. [2]

Such words as "entity", "object", "thing", and perhaps "body", words "connoting universal properties, constitute the very highest genus or "summum genus"" of a classification of universals. [3] To propose a definition for say a plant whose flowers open at dawn on a warm day to be pollinated during the day time using the word "thing", "entity", "object", or "body" seems too general and is. But, astronomy deals with the universe, sometimes only the very local universe just above the Earth's atmosphere. These "universals" may be just the words to use.

On the basis of dictionary definitions, what is the difference between a 'body', an 'entity', an 'object', a 'thing', and a 'phenomenon'?

The categories for synonymy and most common usage place 'body' in "3. SUBSTANTIALITY" [4] , 'entity' in the same, 'object' in "651. INTENTION" [4] , 'thing' in "3. SUBSTANTIALITY" [4] , and 'phenomenon' in "918. WONDER" [4] . The more common uses of the words 'object' and 'phenomenon' are not exactly the same as may be used in a specialized endeavor like a science such as astronomy. A slightly less common use of 'phenomenon' is in category "150. EVENTUALITY" [4] . For the word 'object' a slightly less common or popular meaning is in category "543. MEANING" [4] . The closest category of meaning or synonymy for 'object' to category 1. is category "375. MATERIALITY" [4] .

Of each of these words, 'entity' uses the word 'existence', category "1. EXISTENCE" [4] in each definition. 'Entity' may be thought of as the most general of these terms because its meanings are the closest to category 1. The farthest from category 1. on the basis of conceptual meaning and synonymy is the word 'object' in category 375. A tentative order is 'entity' > 'phenomenon' > 'object' by generalness, or by preciseness (perhaps more description is needed beyond only existence) 'object' > 'phenomenon' > 'entity'.

'Thing' (category 3.) has the word 'entity' in three of four meanings and 'object' in the fourth. The second most popular meaning of 'thing' is in category 375.

'Body' (category 3.) has 'mass' and is closer to 'substantiality' in common usage than 'thing', and neither word has a synonym closer in meaning to 'existence'. The second most common meaning of 'body' is category "203. BREADTH, THICKNESS" [4] .

This suggests a hierarchy such as 'entity' > 'body' > 'thing' > 'phenomenon' > 'object' by generalness, where 'existence' is the most general word or, 'object' > 'phenomenon' > 'thing' > 'body' > 'entity' by preciseness. An 'astronomical object' may be expected to require a more detailed description in its definition to indicate meaning than an 'astronomical entity'. In astronomy, the concept of an 'astronomical body' may suggest a meaning closer to category 203. rather than a 'thing' or 'entity'.

The choice of general order is 'entity' > 'source' > 'object' > 'phenomena'. The term 'astronomical body' has much less popularity per Google scholar than 'object'. The body of astronomers in the International Astronomical Union is auspicious and here is considered an astronomical entity.

Def. the theory of the science of the biological, chemical, physical, and logical laws (or principles) with respect to any natural being, body, thing, entity, source, object, or phenomena in the sky especially at night is called theoretical astronomy.

1.a: an "independent, separate, or self-contained [astronomical] existence", 1.b: "the [astronomical] existence of a [person, place, or] thing as contrasted with its attributes", or 2. "some [astronomical] thing that has separate and distinct existence and objective or conceptual reality", [2]

is called an astronomical entity.

By generalness, 'being' > 'entity' > 'phenomenon' > 'object'. Further, 'being' > 'body' > 'something' or 'thing' > 'entity'. [4]

What are some astronomical entities?

"[V]oids [are] now considered as regular astronomical entities in their own rights, [and] are clustered." [5]

There are "a plethora of observations from heavenly bodies which did not agree with each other despite being from the same astronomical entities." [6] The observations themselves, media of recording, and the heavenly bodies are all astronomical entities. So are the observers and astronomers who make or made the records. Constellations are astronomical entities. 'Sky' is an astronomical entity. [7]

Included as astronomical entities are 'astronomical objects' and 'astronomical sources', even those with large error regions of whole degrees. Diffuse background radiations, whether gamma ray or radio, are astronomical entities.

"Astronomical named entities":

  1. "Names of telescopes and other measurement instruments,"
  2. "Names of celestial objects,"
  3. "Types of objects," and
  4. "Features that can be pointed to on a spectrum". [8]

"Gazetteers are useful for finding commonly referenced names of people, places or organisations" [9] associated with astronomy. These are astronomical entities that can be used for information processing.

Astronomical entities include some journals (such as The Astrophysical Journal, the Monthly Notices of the Royal Astronomical Society, and Astronomy & Astrphysics), articles in journals and magazines, books on astronomy that may be references or be cited for astronomy information or facts.

Named entity recognition (NER) for astronomy literature: [10] NER "involves assigning broad semantic categories to entity references in text." [10]

Types of entities for Natural Language Processing (NLP):

  1. names - person, location, organization
  2. temporal expressions - date, time
  3. numeric expressions - money, percent
  4. instrument name
  5. source name
  6. source type
  7. spectral feature and
  8. text and scientific databases. [10]

"Astronomy is a broad scientific domain combining theoretical, observational and computational research, which all differ in conventions and jargon." [10] "There is a major effort in astronomy to move towards integrated databases, software and telescopes." [10] ("The Virtual Observatory" [10] ).

Entity categories include 'galaxy', 'nebula', 'star', 'star cluster', 'supernova', 'planet', 'frequency', 'duration', 'luminosity', 'position', 'telescope', 'ion', 'survey', and 'date'. [10]

Dominant groups Edit

The term "dominant group" is used in astronomy to identify other astronomical entities of importance. The genera differentia for possible definitions of "dominant group" fall into the following set of orderable pairs:

Genera differentia for "dominant group" [4]
Synonym for "dominant" Category Number Category Title Synonym for "group" Category Number Catgeory Title
“superior” 36 SUPERIORITY "arrangement" 60 ARRANGEMENT
“influential” 171 INFLUENCE "class" 61 CLASSIFICATION
“musical note” 462 HARMONICS "assembly" 74 ASSEMBLAGE
“most important” 670 IMPORTANCE "size" 194 SIZE
“governing” 739 GOVERNMENT "painting", "grouping" 572 ART
"master" 747 MASTER "association", "set" 786 ASSOCIATION
----- --- ------- "sect" 1018 RELIGIONS, CULTS, SECTS

'Orderable' means that any synonym from within the first category can be ordered with any synonym from the second category to form an alternate term for "dominant group" for example, "superior class", "influential sect", "master assembly", "most important group", and "dominant painting". "Dominant" falls into category 171. "Group" is in category 61. Further, any word which has its most or much more common usage within these categories may also form an alternate term, such as "ruling group", where "ruling" has its most common usage in category 739, or "dominant party", where "party" is in category 74.

"A particular subject of interest is the cluster ion series (NH3)nNH4 + , since it is the dominant group of ions over the whole investigated temperature range." [11] For astrochemisty, "[t]hese studies are expected to throw light on the sputtering from planetary and interstellar ices and the possible formation of new organic molecules in CO--NH3–H2O ice by megaelectronvolt ion bombardment." [11]

All alternate terms for dominant group [relative synonyms] used in astronomy are astronomical entities. Here are some examples from the literature:

  1. "Once created, device class objects are registered with an instance of the master class." [12]
  2. "For ATIC, a possible set of defined classes would be a master class event, and sub-classes header, silicon, scintillator, bgo and track." [13]
  1. "The superior size and albedo of Venus completely turn the scale, with the result that Venus at her brightest is about 12 times brighter than Mercury at his brightest." [14]
  2. "There is no reason to question but that they are simply ordinary meteors, which from their superior size and unusually slow speed have survived to reach the earth's surface." [15]
  1. "Together with Leonard Searle, he wrote an influential set of papers which established that stellar disks are truncated at about four exponential scale-lengths, and that the vertical scale-height of disks is constant with radius." [16]
  2. "Until now Themo has been best known for an influential set of questions on Aristotle's Meteorologica, which is closely related to similar sets by Nicole Oresme and, putatively, Simon Tunsted." [17]

Def. a natural source usually of radiation in the sky especially at night is called an astronomical source.

An astronomical source may have generated or be capable of generating electromagnetic radiation, a star, or a galaxy, for example. A source reflects, generates, transmits, or fluoresces that which may be detectable.

A celestial source is any astronomical source except the Earth.

An astronomical source usually has intensity often as a spatial, temporal, or spectral profile. Such a profile may be continuous, intermittent, transient, fluctuating, aperiodic, or unpredictable.

Some astronomical objects are not detectable directly as a source but instead may be absorbers of a portion of a signal from a source further away.

The image at right is a celestial map of the astronomical sources within the original detected error circle around the first apparent astronomical X-ray source discovered in the constellation Serpens Cauda (Serpens XR-1, or Serpens X-1). The other sources within this error circle are stars, other X-ray sources, a gamma-ray burst source, and a dark nebula.

In the theory of source astronomy comes at least an attempt to answer "Where did it come from?" Is there a causality? Is it modal? Or, is it of uncountable origin?

The science of astronomy consists of three fundamental parts:

The SIMBAD reference database "contains identifications, 'basic data', bibliography, and selected observational measurements for several million astronomical objects." [18] "The specificity of the SIMBAD database is to organize the information per astronomical object". [18] "Building a reference database for . all astronomical objects outside the Solar System – has been the first goal of the CDS". [18] "The only astronomical objects specifically excluded from SIMBAD are the Sun and Solar System bodies." [18]

Def. a natural object in the sky especially at night is called an astronomical object.

As indicated above about the astronomical objects in the SIMBAD database and in the learning reference astronomy, there are many objects between the observer on the ground atop some portion of the Earth's crust and astronomical objects other than the Sun and Solar System bodies. Further, for those observers looking toward the Earth from another location such as near the Moon in the photograph at above right, it seems that the Earth is a natural object. On the Earth 384,000 km away, the sunset terminator bisects Africa.

A closer view of Earth shows some of the astronomical objects near the Earth and apparently just above the surface, where an observer may be. Some of these objects such as clouds probably by convention are more likely to be studied by planetary observers, or weather observers, rather than astronomical observers.

With perspectives other than upwards from the Earth's crustal surface, the word "sky" may seem insufficient or inappropriate, although studying the Earth as part of planetary science may leave interesting astronomical objects near the Earth that are occasionally "in the sky". The idea being that the Earth cannot be in its own sky, or can it? Perhaps, it is more a matter of whether other observers agree that what an observer is observing is astronomy or planetary science, or both.

Star by dictionary Edit

For the object, "star", a dictionary definition is

1.a: "any natural luminous body visible in the sky [especially] at night", 1.b: "a self-luminous gaseous celestial body of great mass whose shape is [usually] spheroidal and whose size may be as small as the earth or larger than the earth's orbit". [2]

This definition seems okay for a dictionary, but is it adequate for a science, and especially, astronomy?

Def. the study of the chemical composition of stars and outer space is called astrochemistry.

"An important goal for theoretical astrochemistry is to elucidate which organics are of true interstellar origin, and to identify possible interstellar precursors and reaction pathways for those molecules which are the result of aqueous alterations." [19]

Atmospheres Edit

Def. a layer of gases that may surround a material body of sufficient mass,[3] and that is held in place by the gravity of the body is called an atmosphere.

Def. the gases surrounding the Earth or any astronomical body is called an atmosphere.

Interplanetary medium Edit

Def. that part of outer space between the planets of a solar system and its star is called interplanetary space.

Def. the material which fills the solar system and through which all the larger solar system bodies such as planets, asteroids and comets move is called an interplanetary medium.

Interstellar medium Edit

Def. the matter that exists in the space between the star systems in a galaxy is called an interstellar medium.

Intergalactic medium Edit

Def. a rarefied plasma [20] that is organized in a cosmic filamentary structure [21] is called the intergalactic medium (IGM).

Ions Edit

Def. an atom or group of atoms bearing an electrical charge such as the sodium and chlorine atoms in a salt solution is called an ion.

Materials Edit

Def. matter which may be shaped or manipulated, particularly in making something is called a material.

Def. any instrument used in astronomy for observing distant objects is called a telescope.

Def. an object, usually made of glass, that focuses or defocuses the light or an electron beam that passes through it is called a lens.

Meteorites Edit

Def. a metallic or stony object that is the remains of a meteor is called a meteorite.

Shelters Edit

Def. a refuge, haven or other cover or protection from something is called a shelter.

Def. anything shaped like a common structural element of architecture that resembles the hollow upper half of a sphere, a cupola], often used as a cover is called a dome.

Astrognosy deals with the materials of celestial objects and their general exterior and interior constitution.

The theoretical constitution of the Earth is illustrated using the one-dimensional Preliminary Reference Earth Model [22] (PREM) at right. The density in kg-m -3 of radial layers is plotted against radius in km.

The geography applicable to astronomy may be designated 'astrogeography'. But, this term is often more restricted. "[T]he relationship between outer-space geography and geographic position (astrogeography), and the evolution of current and future military space strategy" [23] has been identified and evaluated. [23]

Def. the art of describing or delineating the stars a description or mapping of the heavens is called astrography.

Def. a place where stars, planets and other celestial bodies are observed is called an observatory.

From the Ebers Papyrus, a year has 360 days of twelve months of thirty days each. [24]

"A period of 360 days, comprising 12 months of 30 days each, was assigned by the Mesopotamians to the year in days and months at least by the third millennium BC." [25]

In ancient Iran (Persia), the year was 360 days with 12 months of 30 days each. [26] [27]

"All Veda [India] texts speak uniformly and exclusively of a year of 360 days [12 months of 30 days each]. Passages in which this length of the year is directly stated are found in all the Brahmanas." [28] This period dates to approximately the third millennium (

An ancient Chinese calendar had a 360 day year of twelve months of thirty days each. [30]

The Mayans had an old tradition that the year had twelve months of thirty days each, 360 days in a year. [31]

"The Peruvian year was divided into twelve Quilla, or moons, of thirty days." [32]

Apparently, with each of these locations around the globe and several others near to the Mediterranean Sea, the year had exactly 360 days of 12 months of 30 days each, then at some point near 2700 b2k the year became lengthened to today's year.

Def. (from 1945) "those parts of human interest in celestial phenomena which are amenable to mathematical treatment" are called astronomy. [33] This is Neugebauer's definition of astronomy. [34]

Def. "the search for astronomical strata whose contents could be classified" is called astronomy. [35] This is Herschel's definition of astronomy. [36]

"Mere "star ordering" is not "astronomy", so far as the modern usage of the term implies, regardless of the word's etymology". [25]

Def. (from 2000) "the accurate mapping of the heavens in order to make possible the accurate prediction of phenomena" is called astronomy. [25]

Def. "the study of objects and matter outside the Earth's atmosphere and of their physical and chemical properties" is called astronomy. [37]

Electrical Sun Edit

"[T]he solar corona is eminently variable, and therefore like our aurora borealis, which is known to be electric." [38] "This vast electric mass must have a great electric repulsion through vacant space, and it lends probability to my position that it drives away from the sun the tails of comets and our zodiacal light and aurora borealis." [38] "Electricity alone can repel electricity." [38] "[T]he direction of the comets' tails is but the interaction between the sun and the comets, the same as the action between a charged prime conductor and a charged pith ball of an electric machine." [38]

"[A] variety of geophysical and astrophysical phenomena can be explained by a net charge on the Sun of -1.5 x 10 28 e.s.u." [39] This figure was later reduced by a factor of five. [40]

"There appears to be considerable misunderstanding on the part of physicists of the nature and degree of the observational support of gravitational theory. For example, it appears to be commonly believed that the observations of planetary motion agree with computed orbits to the accuracy of the observations. On the other hand, it has long been known by the astronomers that there are sizable systematical discrepancies between computed and observed orbits". [41]

Milky Way Edit

Democritus "lived at Abdère 300 years before the Christian era [2300 b2k]. In a short fragment quoted by Plutarch, he declares that the Milky Way is an agglomeration of small stars too far away to be perceived singly." [42]

Coronal clouds Edit

"Beginning with the daguerreotype of the corona of 1851, the Reverend Lecturer had thrown on the screen pictures illustrating the form of the corona in different years. The drawings of those of 1867, 1878, and 1900 all showed long equatorial extensions with openings at the solar poles filled with beautiful rays." [43] "The intermediate years, as, for example, 1883, 1886, and 1896 showed the four groups of synclinals which mainly constitute the corona gradually descending towards the equator of the sun, with a corresponding opening of the polar regions." [43]

"Some of the theories of the solar corona were then illustrated and discussed." [43]

  1. "The corona is not of the nature of an atmosphere round the sun, for the pressure at the sun's limb would be enormous, while the thinness of the chromospheric lines show that it is not." [43]
  2. "comets, such as that of 1843, have approached the sun with enormous velocities within the region of the prominences without suffering disruption or retardation." [43]
  3. "If not an atmosphere of particles of gas, still less is it an atmosphere of solid stones or meteorites." [43]
  4. "Meteor streams do circle round the sun, but there is no reason why the positions of the orbits, or the intrinsic brightness of such streams should vary with the sun-spot period." [43]
  5. "the appearance of the corona does not seem to be such as the projection of meteor streams upon the celestial vault would give." [43]
  6. "Prof. Schaeberle has proposed a mechanical origin of the solar corona, due to the forces of ejection of particles from the solar limb, as evidenced by the prominences, and the force of gravity under the particular conditions of the solar rotation and the inclination of its axis to the earth's orbit." [43]
  7. "The electrical theory of the corona does not negative the mechanical theory, but supplements it. In addition to the forces of gravity and ejection, it takes account of the repulsive force which the sun exerts on matter which has the same electrical sign as itself, and which has been ejected from it." [43]
  8. "it would seem that the solar corona is of the nature of an electrical aurora round the sun." [43]
  9. "the coronoidal discharges in poor vacua obtained by Prof. Pupin about an insulated metal ball are exceedingly like the rays and streamers of the solar corona." [43]

Zodiacal lights Edit

"According to Gruson and Brugsch the Egyptians were acquainted with, and even worshipped, the zodiacal light from the very earliest times, as a phenomenon visible throughout the East before sunrise and after sunset. It was described as a glowing sheaf or luminous pyramid perpendicular to the horizon in summer, and inclined more or less during the winter. Indeed the Egyptians represented the zodiacal light under the form of a triangle which sometimes stood upright and at other times was inclined." [44]

The simplest description of the paths astronomical objects may take when passing each other includes a hyperbolic and parabolic pass. When capture occurs it usually produces an elliptical orbit.

Def. mathematics used in the study of astronomy, astrophysics and cosmology is called astromathematics.

The planet Mercury is especially susceptible to Jupiter's influence because of a small celestial coincidence: Mercury's perihelion, the point where it gets closest to the Sun, precesses at a rate of about 1.5 degrees every 1000 years, and Jupiter's perihelion precesses only a little slower. One day, the two may fall into sync, at which time Jupiter's constant gravitational tugs could accumulate and pull Mercury off course. This could eject it from the Solar System altogether [45] or send it on a collision course with Venus or Earth. [46]

Orbital theory Edit

Orbits come in many shapes and motions. The simplest forms are a circle or an ellipse.

The foci of an ellipse are two special points F1 and F2 on the ellipse's major axis and are equidistant from the center point. The sum of the distances from any point P on the ellipse to those two foci is constant and equal to the major axis ( PF1 + PF2 = 2a ). Each of these two points is called a focus of the ellipse.

In the gravitational two-body problem, if the two bodies are bound to each other (i.e., the total energy is negative), their orbits are similar ellipses with the common barycenter being one of the foci of each ellipse. The other focus of either ellipse has no known physical significance. Interestingly, the orbit of either body in the reference frame of the other is also an ellipse, with the other body at one focus.

Ideally, the motion of two oppositely charged particles in empty space would also be an ellipse.

A real orbit (and its elements) changes over time due to gravitational perturbations by other objects and the effects of relativity. A Keplerian orbit is merely an idealized, mathematical approximation at a particular time.

Eccentricities Edit

"Mercury's orbit eccentricity [e] varies between about 0.11 and 0.24 with the shortest time lapse between the extremes being about 4 x 10 5 yr". [47] "Smaller amplitude variations occur with about a 10 5 yr period." [47]

Inclinations Edit

"The orbital inclination [i] [of Mercury] varies between 5° and 10° with a 10 6 yr period with smaller amplitude variations with a period of about 10 5 yr." [47]

Obliquities Edit

In axial tilt, axial tilt (also called obliquity) is the angle between an object's rotational axis, and a line perpendicular to its orbital plane. The planet Venus has an axial tilt of 177.3° because it is rotating in retrograde direction, opposite to other planets like Earth. The planet Uranus is rotating on its side in such a way that its rotational axis, and hence its north pole, is pointed almost in the direction of its orbit around the Sun. Hence the axial tilt of Uranus is 97°. [48]

The obliquity of the Earth's axis has a period of about 41,000 years. [49]

Precessions Edit

The equinoxes of Earth precess with a period of about 21,000 years. [49]

Orbital poles Edit

An orbital pole is either end of an imaginary line running through the center of an orbit perpendicular to the orbital plane, projected onto the celestial sphere. It is similar in concept to a celestial pole but based on the planet's orbit instead of the planet's rotation.

Resonances Edit

An orbital resonance occurs when two orbiting bodies exert a regular, periodic gravitational influence on each other, usually due to their orbital periods being related by a ratio of two small integers. The physics principle behind orbital resonance is similar in concept to pushing a child on a swing, where the orbit and the swing both have a natural frequency, and the other body doing the "pushing" will act in periodic repetition to have a cumulative effect on the motion. Orbital resonances greatly enhance the mutual gravitational influence of the bodies, i.e., their ability to alter or constrain each other's orbits. In most cases, this results in an unstable interaction, in which the bodies exchange momentum and shift orbits until the resonance no longer exists. Under some circumstances, a resonant system can be stable and self-correcting, so that the bodies remain in resonance. Examples are the 1:2:4 resonance of Jupiter's moons Ganymede, Europa and Io, and the 2:3 resonance between Pluto and Neptune. Unstable resonances with Saturn's inner moons give rise to gaps in the rings of Saturn. The special case of 1:1 resonance (between bodies with similar orbital radii) causes large Solar System bodies to eject most other bodies sharing their orbits this is part of the much more extensive process of clearing the neighbourhood, an effect that is used in the current definition of a planet.

Orbital decays Edit

Orbital decay is the process of prolonged reduction in the altitude of a satellite's orbit. This can be due to drag produced by an atmosphere [frequent collisions between the satellite and surrounding air molecules]. The drag experienced by the object is larger in the case of increased solar activity, because it heats and expands the upper atmosphere.

“Contrary to the belief generally held by laboratory physicists, astronomy has contributed to the growth of our understanding of physics.” [1]

Def. the physical properties of celestial bodies and with the interaction between matter and radiation in celestial bodies and in the space between them is called astrophysics.

Theoretical astronomy seeks to understand what is behind cosmic events by taking the physics from the laboratory and testing it in models against the data obtained from observations. This is usually referred to as Draft:astrophysics. But, often the observations seem more than just what the physics can describe. Adding in extra tidbits may help to describe and help to produce better agreement. If these extra tidbits are physical in nature, they are part of theoretical astrophysics, if astronomical in nature, then theoretical astronomy.

Astronomical units Edit

Def. "1 day (d)" is called the astronomical unit of time. [50]

Def. "365.25 days" is called a Julian year. [50]

Def. "36,525 days" is called a Julian century. [50]

Def. "the distance from the centre of the Sun at which a particle of negligible mass, in an unperturbed circular orbit, would have an orbital period of 365.2568983 days" is called the Astronomical Unit (AU). [50]

Def. "149,597,870,700 meters" is called the Astronomical Unit. [51]

Def. "the mass of the Sun" is called the astronomical unit of mass. [50]

Def. the rate at which a star radiates energy in all directions is called luminosity.

Def. "the distance at which one Astronomical Unit subtends an angle of one arcsecond" is called the parsec (pc). [50]

Def. "the distance traveled by light in one Julian year in a vacuum" is called the light-year (ly). [50]

Auroras Edit

Computer simulations are usually used to represent auroras. The image at right shows a terrella in a laboratory experiment to produce auroras.

Fluctuating visible source Edit

Consider only that portion of the emission of the visible source at right that is a level maximum. If this is the first observation received, a reasonable theoretical explanation from physics is a constant black body visible source, like a light bulb. In a physics laboratory, a steady voltage/current power supply produces a steady intensity.

Now consider the full length observation indicated by the moving green circle. From a physics perspective, it appears the power supply is not steady. Using alternating current (AC) to power the light bulb at 60 cycles per second may trigger the detector to yield an oscillatory intensity curve if its response time is short enough to resolve the use of AC. This is a possible theoretical physics hence, theoretical astrophysics additional explanation of what may be happening.

A theoretical astronomy explanation is indicated in the colorful figure above as two visible sources, unresolved by the detector (seen only as a point source), but possibly responsible for the changes in the visible light received at the detector. Which do you think is more likely: a fluctuating power supply or an eclipsing binary?

Physics deals with forces, fields, energy, kinetics, and radiation. Astronomy has its own laws with respect to entities or bodies in motion. Application of a field to an astronomical phenomenon may clarify what is happening. That's the focus of astrophysics. Theory is needed to bring the physics in line with the magnitude of the situation and its complexity.

Luminosity Edit

The luminosity of stars is measured in two forms: apparent (visible light only) and bolometric (total radiant energy). (A bolometer is an instrument that measures radiant energy over a wide band by absorption and measurement of heating.) When not qualified, "luminosity" means bolometric luminosity, which is measured either in the SI units, watts or in terms of solar luminosities, L ⊙ > , that is, how many times as much energy the object radiates as the Sun.

Luminosity is an intrinsic measurable property independent of distance, and is appraised as absolute magnitude, corresponding to the apparent luminosity in visible light of a star as seen at the interstellar distance of 10 parsecs, or bolometric magnitude corresponding to bolometric luminosity. In contrast, apparent brightness is related to the distance by an inverse square law. In addition to this brightness decrease from increased distance there is an extra linear decrease of brightness for interstellar "extinction" from intervening interstellar dust. Visible brightness is usually measured by apparent magnitude. Both absolute and apparent magnitudes are on an inverse logarithmic scale, where 5 magnitudes increase counterparts a 100th part decrease in nonlogarithmic luminosity.

By measuring the width of certain absorption lines in the stellar spectrum, it is often possible to assign a certain luminosity class to a star without knowing its distance. Thus a fair measure of its absolute magnitude can be determined without knowing its distance nor the interstellar extinction, and instead the distance and extinction can be determined without measuring it directly through the yearly parallax. Since the stellar parallax is usually too small to be measured for many far away stars, this is a common method of determining distances.

Given a visible luminosity (not total luminosity), one can calculate the apparent magnitude of a star from a given distance:

mstar is the apparent magnitude of the star (a pure number) msun is the apparent magnitude of the Sun (also a pure number) Lstar is the visible luminosity of the star L ⊙ > is the solar visible luminosity dstar is the distance to the star dsun is the distance to the Sun

Nucleosynthesis Edit

"Our calculations show that production of [lithium] in low-energy flares [by nucleosynthesis], taking place in the surfaces of T Tauri-like stars, is energetically possible and can give the observed excesses over the interstellar abundance." [52]

"[T]here is evidence of lithium production in some stars due to some undefined mechanism. The observations show that the Li abundance on some red giants . and young stars exceeds the average abundance in the universe by 2 orders of magnitude". [53] It is "suggested that Li produced in the helium envelopes of red giants comes to the surface of the stars as the result of a strong convection." [53] For young stars, "the production of the light elements in nonthermal nuclear reactions seems the most appropriate mechanism that can be responsible for enrichment of stellar photospheres by Li." [53] "At least 0.3 metric tons of excited Li and Be nuclei were produced during the solar flare of 1991 November 15. One can estimate the equilibrium concentration of 7 Li nuclei in the solar atmosphere by assuming that they are produced only in solar flares and that a leakage of Li nuclei occurs with the solar wind." [53]

Although 7 Be is usually assumed to have been produced by the Big Bang nuclear fusion, excesses (100x) of the isotope on the leading edge [54] of the Long Duration Exposure Facility (LDEF) relative to the trailing edge suggest that "most of the sun's fusion must occur near the surface rather than the core." [55] The particular reaction

3 He + 4 He → 7 Be + γ (429 keV)

and the associated reaction chains

generate 14% and 0.1% of the α-particles, respectively, and 10.7% of the present-epoch luminosity of the Sun. [56] Usually, the 7 Be produced is assumed to be deep within the core of the Sun however, such 7 Be would not escape to reach the leading edge of the LDEF.

Stars Edit

Def. "any object forming on a dynamical timescale, by gravitational instability", is called a star. [57]

Starspots Edit

"[T]here have been three possible periods of marked solar anomaly during the last 1000 years: the Maunder Minimum, another minimum [the Spörer Minimum] in the early 16th century, and a period of anomalously high activity in the 12th and early 13th centuries." [58]

The basic causes of the solar variability and solar cycles are still under debate, with some researchers suggesting a link with the tidal forces due to the gas giants Jupiter and Saturn, [59] [60] or due to the solar inertial motion. [61] [62]

Weak equivalence principle Edit

All test particles at the alike spacetime point in a given gravitational field will undergo the same acceleration, independent of their properties, including their rest mass. [63]

"The observation of a neutrino burst within 3 h of the associated optical burst from supernova 1987A in the Large Magellanic Cloud provides a new test of the weak equivalence principle, by demonstrating that neutrinos and photons follow the same trajectories in the gravitational field of the galaxy." [64]

The astrolabe was effectively an analog calculator capable of working out several different kinds of problems in spherical astronomy.

Some form of an "astrolabe" may have been in use by the third millennium BC. [25]

Hipparcos is the first space experiment devoted to precision astrometry, the accurate measurement of the positions of celestial objects.

These measurements allow "the accurate determination of proper motions and parallaxes of stars, their distance and tangential velocity.

Planetary science (rarely planetology) is the scientific study of planets (including Earth), moons, and planetary systems, in particular those of the solar system and the processes that form them. It studies objects ranging in size from micrometeoroids to gas giants, aiming to determine their composition, dynamics, formation, interrelations and history. It is a strongly interdisciplinary field, originally growing from astronomy and earth science, [65] but which now incorporates many disciplines, including planetary astronomy, planetary geology (together with geochemistry and geophysics), atmospheric science, oceanography, hydrology, theoretical planetary science, glaciology, and the study of extrasolar planets. [65] Allied disciplines include space physics, when concerned with the effects of the Sun on the bodies of the Solar System, and astrobiology.

Planets Edit

Def. "a celestial body that

(a) is in orbit around the Sun,

(b) has sufficient mass for its self-gravity to overcome rigid body forces so that it assumes a hydrostatic equilibrium (nearly round) shape, and

(c) has cleared the neighbourhood around its orbit" is called a planet. [66]

The proposed more general definition for a planet in orbit around another star substitutes "a star" for "the Sun" in part (a), keeps part (b), does not contain part (c), and adds "is neither a star nor a satellite of a planet." [67]

Def. "a celestial body that

(a) is in orbit around the Sun,

(b) has sufficient mass for its self-gravity to overcome rigid forces so that it assumes a hydrostatic equilibrium (nearly round) shape,

(c) has not cleared the neighbourhood around its orbit, and

(d) is not a satellite" is called a dwarf planet. [66]

Def. "[a]ll other objects [not a planet or dwarf planet], except satellites, orbiting the Sun" are called collectively Small Solar-System Bodies. [66]

Def. a wanderer that is a moving light in the sky is called a planet. [66] This is the original description meant by the word "planet". [66]

From a theoretical planetary physics perspective: "The shape of objects with mass above 5 x 10 20 kg and diameter greater than 800 km would normally be determined by self-gravity, but all borderline cases would have to be established by observation." [67]

Def. a celestial body "formed by accumulation of a rocky core, on a much longer timescale, ≳ 10 7 yr, with subsequent acquisition of a gaseous envelope if the circumstances allow this, and with an initially fractionated elemental composition" is called a planet. [57]

Meta-astronomy, or metaastronomy, is the collection of approaches to theoretical astronomy that may be considered when seeking to understand an astronomical phenomenon.

In the model shown at right the Sun and regions around it are labeled. "The core of the Sun is considered to extend from the center to about 0.2 to 0.25 solar radius. [68] It is the hottest part of the Sun and of the Solar System. It has a density of up to 150 g/cm³ (150 times the density of liquid water) and a temperature of close to 15,000,000 kelvin [15 MK] The core is made of hot, dense gas in the plasmic state. The core, inside 0.24 solar radius, generates 99% of the fusion power of the Sun. It is in the core region that solar neutrinos may be produced.

The radiation zone or radiative zone is a layer of a star's interior where energy is primarily transported toward the exterior by means of radiative diffusion, rather than by convection. [69] Energy travels through the radiation zone in the form of electromagnetic radiation as photons. Within the Sun, the radiation zone is located in the intermediate zone between the solar core at .2 of the Sun's radius and the outer convection zone at .71 of the Sun's radius. [69]

The convection zone of a star is the range of radii in which energy is transported primarily by convection. Stellar convection consists of mass movement of plasma within the star which usually forms a circular convection current with the heated plasma ascending and the cooled plasma descending. This is the granular zone in the outer layer of a star.

The standard solar model (SSM) is a mathematical treatment of the Sun as a spherical ball of gas (in varying states of ionisation, with the hydrogen in the deep interior being a completely ionised plasma). This model, technically the spherically symmetric quasi-static model of a star, has stellar structure described by several differential equations derived from basic physical principles. The model is constrained by boundary conditions, namely the luminosity, radius, age and composition of the Sun, which are well determined.

As the Sun consists of a plasma and is not solid, it rotates faster at its equator than at its poles. This behavior is known as differential rotation, and is caused by convection in the Sun and the movement of mass, due to steep temperature gradients from the core outwards. This mass carries a portion of the Sun’s counter-clockwise angular momentum, as viewed from the ecliptic north pole, thus redistributing the angular velocity.

"Solar rotation is able to vary with latitude because the Sun is composed of a gaseous plasma. The rate of rotation is observed to be fastest at the equator (latitude φ=0 deg), and to decrease as latitude increases. The differential rotation rate is usually described by the equation:

where ω is the angular velocity in degrees per day, φ is the solar latitude and A, B, and C are constants. The values of A, B, and C differ depending on the techniques used to make the measurement, as well as the time period studied. [70] A current set of accepted average values [71] is:

A= 14.713 deg/day (± 0.0491) B= –2.396 deg/day (± 0.188) C= –1.787 deg/day (± 0.253)

"[B]y assuming a harmonic variation having a period of 11.13 years . the phases of such a variation [in polar diameter minus equatorial diameter of the Sun] coincide to within one-fifth of a year with the phases of the sun-spot fluctuations that, at times corresponding to minimum of sun-spottedness, the polar diameter is relatively larger that, at times of maximum sun-spottedness, the equatorial diameter is relatively larger. The amplitude of the variation is extremely small, but its reality would seem to be established. [This] at least renders the existence of such periodic fluctuations in the shape of the sun more probable than their non-existence." [72]

"Solar oblateness, the difference between the equatorial and polar diameters, reflects certain fundamental properties of the Sun. . the oblateness reflects properties of the Sun's interior, . [There is] a time varying, excess equatorial brightness [producing] a difference between the equatorial and polar limb darkening functions . at times when the excess brightness is reduced, the intrinsic visual oblateness can be obtained from the observations without detailed knowledge of the excess brightness. A period of reduced excess brightness occurred in 1973 September." [73] The period of reduced excess equatorial brightness occurred between solar cycle maximum around 1970 and minimum around 1975. Considering excess equatorial brightness and seeking to perform measurements at opportunities of reduced excess equatorial brightness has the effect of reducing solar oblateness from some 86.6 ± 6.6 milli-arcsec to 18.4 ± 12.5 milli-arcsec. [73]

The Babcock Model describes a mechanism which can explain magnetic and sunspot patterns observed on the Sun.

  1. The start of the 22-year cycle begins with a well-established dipole field component aligned along the solar rotational axis. The field lines tend to be held by the highly conductive solar plasma of the solar surface.
  2. The solar surface plasma rotation rate is different at different latitudes, and the rotation rate is 20 percent faster at the equator than at the poles (one rotation every 27 days). Consequently, the magnetic field lines are wrapped by 20 percent every 27 days.
  3. After many rotations, the field lines become highly twisted and bundled, increasing their intensity, and the resulting buoyancy lifts the bundle to the solar surface, forming a bipolar field that appears as two spots, being kinks in the field lines.
  4. The sunspots result from the strong local magnetic fields in the solar surface that exclude the light-emitting solar plasma and appear as darkened spots on the solar surface.
  5. The leading spot of the bipolar field has the same polarity as the solar hemisphere, and the trailing spot is of opposite polarity. The leading spot of the bipolar field tends to migrate towards the equator, while the trailing spot of opposite polarity migrates towards the solar pole of the respective hemisphere with a resultant reduction of the solar dipole moment. This process of sunspot formation and migration continues until the solar dipole field reverses (after about 11 years).
  6. The solar dipole field, through similar processes, reverses again at the end of the 22-year cycle.
  7. The magnetic field of the spot at the equator sometimes weakens, allowing an influx of coronal plasma that increases the internal pressure and forms a magnetic bubble which may burst and produce an ejection of coronal mass, leaving a coronal hole with open field lines. Such a coronal mass ejections are a source of the high-speed solar wind.
  8. The fluctuations in the bundled fields convert magnetic field energy into plasma heating, producing emission of electromagnetic radiation as intense ultraviolet (UV) and X-rays.

Stellar evolution is the process by which a star undergoes a sequence of radical changes during its lifetime. Depending on the mass of the star, this lifetime ranges from only a few million years for the most massive to trillions of years for the least massive, which is considerably longer than the age of the universe. All stars are born from collapsing clouds of gas and dust, often called nebulae or molecular clouds. Over the course of millions of years, these protostars settle down into a state of equilibrium, becoming what is known as a main sequence star.

Nuclear fusion powers a star for most of its life. Initially the energy is generated by the fusion of hydrogen atoms at the core of the main sequence star. Later, as the preponderance of atoms at the core becomes helium, stars like the Sun begin to fuse hydrogen along a spherical shell surrounding the core. This process causes the star to gradually grow in size, passing through the subgiant stage until it reaches the red giant phase. Stars with at least half the mass of the Sun can also begin to generate energy through the fusion of helium at their core, while more massive stars can fuse heavier elements along a series of concentric shells. Once a star like the Sun has exhausted its nuclear fuel, its core collapses into a dense white dwarf and the outer layers are expelled as a planetary nebula. Stars with around ten or more times the mass of the Sun can explode in a supernova as their inert iron cores collapse into an extremely dense neutron star or black hole.

The study of galaxy formation and evolution is concerned with the processes that formed a heterogeneous universe from a homogeneous beginning, the formation of the first galaxies, the way galaxies change over time, and the processes that have generated the variety of structures observed in nearby galaxies. It is one of the most active research areas in astrophysics.

Galaxy formation is hypothesized to occur, from structure formation theories, as a result of tiny quantum fluctuations in the aftermath of the Big Bang. The simplest model for this that is in general agreement with observed phenomena is the Λ Cold Dark Matter cosmology that is to say that clustering and merging is how galaxies gain in mass, and can also determine their shape and structure.


Yes, New York Times, There Is A Scientific Method

Scanning electron microscope image at the sub-cellular level. Public domain image by Dr. Erskine . [+] Palmer, USCDCP.

There are lots of different ways to do science that are equally valid one scientific method does not necessarily fit all cases. In astronomy, experiments are virtually impossible, as all you can do is make observations of what the Universe gives us. In the early days of quantum physics, the results were so surprising that it took many years before it was even possible to hypothesize in a sensible fashion, as the rules defied intuition. And in many fields, there are too many variables at play to accurately model the system even when all the underlying, governing equations are 100% known. Yet the differences in the details of how science is performed in no way invalidates astronomy, quantum physics, protein-folding or climate modeling as sciences. By the same token, however, the similarities between these scientific endeavors and poetry or philosophy do not elevate the latter to the status of being considered science.

Chart showing signs of the zodiac and the solar system with world at centre. From Andreas Cellarius . [+] Harmonia Macrocosmica, 1660/61. Image credit: Loon, J. van (Johannes), ca. 1611-1686.

On July 4th, an opinion piece ran in the New York Times declaring that there is no scientific method. The author clarifies that he means there is no distinctly scientific method, and then goes on to describe how concepts like "justice" and "courage" are hard to define in an all-encompassing way, despite the fact that we know and recognize it when we see it. Then he takes two examples -- one of Kepler's first law (that planets move in ellipses around the Sun) and one of Galileo's discovery of the motion of freely-falling objects -- and brings up the facts that:

  • Kepler could have fit circles, circles-with-epicycles, or ovals to the data just as easily as an ellipse, and could have arrived at a totally different law as a result.
  • Galileo needed to neglect air resistance, a known force, to arrive at his result.

And therefore, the conclusion went, science is no different than any other arbitrary endeavor.

Kepler's Platonic solid model of the Solar system from Mysterium Cosmographicum (1596). Image . [+] credit: J. Kepler.

Except that science is completely different than every other endeavor, and Kepler and Galileo actually provide extraordinary examples of showing exactly how, if only James Blachowicz would have dug a little deeper. Kepler's original model, above, was the Mysterium Cosmographicum, where he detailed his outstandingly creative theory for what determined the planetary orbits. In 1596, he published the idea that there were a series of invisible Platonic solids, with the planetary orbits residing on the inscribed and circumscribed spheres. This model would predict their orbits, their relative distances, and -- if it were right -- would match the outstanding data taken by Tycho Brahe over many decades.

Tycho Brahe's Mars data, fitted to Kepler's theory. Image credit: Wayne Pafko, 2000, via . [+] http://www.pafko.com/tycho/observe.html.

But beginning in the early 1600s, when Kepler had access to the full suite of Brahe's data, he found that it didn't match his model. His other efforts at models, including oval-shaped orbits, failed as well. The thing is, Kepler didn't just say, "oh well, it didn't match," to some arbitrary degree of precision. He had the previous best scientific model -- Ptolemy's geocentric model with epicycles, equants and deferents -- to compare it to. In science, if you want your new idea to supersede the old model, it has to prove itself to be superior through experiments and observations. That's what makes it science. And that's why the ellipses succeeded, because they gave better, more accurate prediction than all the models that came before, including Ptolemy's, Copernicus', Brahe's and even Kepler's own earlier models.

The use of a hollowed-out gourd to hold liquid. Image credit: Nick Hobgood of flickr, under a . [+] cc-by-2.0 license.

The point of Galileo's is another deep illustration of how science actually works. One of the very first science experiments of all -- over 2,500 years ago -- was done by Empedocles, in an attempt to answer the question of whether air takes up space. The device above is known as a clepsydra (Greek for "water-thief"), which is a gourd with one hole in the top and one-to-many holes in the bottom. You submerge the gourd into a source of water until it fills, then put your thumb over the hole at the top and carry the water everywhere. Although the Greeks didn't know about a vacuum or the concept of air pressure, they could see that the water at the bottom wasn't falling out, and the only thing that could be pushing "up" against it was air. Therefore, air takes up space and fills all the space around us on Earth, and when that air moves relative to an object, it exerts a force.

A member of the U.S. Army's Golden Knights demonstrates air resistance. Image credit: flickr user . [+] Gerry Dincher under a cc-by-2.0 license.

Galileo knew about air resistance as well, although he couldn't quantify it. He knew that if you dropped two masses of different weights from a small height and a large height, the large drop led to a larger difference in when those two masses hit the ground, and that difference was due to air resistance. Galileo's revolutionary advance, as I detailed here, was to determine that objects fell a distance that was proportional to the amount of time they had been falling squared, when these other effects were ignored. This was as true for balls dropped from a tower as they were for objects rolled down a ramp. When we finally made it to an airless world, we performed Galileo's experiment exactly as it was idealized: without air resistance at all.

But other effects really do exist, and science didn't "end" at the advances of Kepler and Galileo. Rather, these advances became the starting points for the theories that would improve upon them, in both cases by Isaac Newton. For Kepler's problem of planetary motion, the gravitational effects of the planets on one another were the next imperfection to account for, and after we nailed that, there were no further improvements until Einstein in the 20th century. Newton also enabled us -- through his development of mechanics -- to account for as many additional forces as we like, including air resistance, since the F in F = ma is actually the sum of all the relevant forces on a system.

There are often a great many neglected forces on a system when we model it, to make the problem . [+] tractable. Shown, above, is a selection of forces relevant to a section of a beam under static conditions. Image credit: Bpuccio of Wikimedia Commons under a c.c.a.-s.a.-3.0 license.

The only thing that limits how accurately we can model something if we understand the underlying dynamics is either the inherent uncertainty in how a system behaves or is set up, and how much of the actual forces in play we can practically include in our model. Science is more than a body of knowledge -- although it requires those facts, that data and those results -- but is also a process. It's a self-correcting process where it must always be confronted with the real world, with what we observe and measure, with what its new predictions are and with the full suite of models and ideas that came before. What's truly shocking, though, is that one of the earliest philosophers, Thales of Miletus, knew all of this and enunciated it quite clearly in his philosophy of naturalism. So when Blachowicz asks,

If scientific method is only one form of a general method employed in all human inquiry, how is it that the results of science are more reliable than what is provided by these other forms?

all we need to do is point his own examples -- full of illustrative science -- back at him to arrive at the answer.


The Nature of Science

The ultimate judge in science is always what nature itself reveals based on observations, experiments, models, and testing. Science is not merely a body of knowledge, but a method by which we attempt to understand nature and how it behaves. This method begins with many observations over a period of time. From the trends found through observations, scientists can model the particular phenomena we want to understand. Such models are always approximations of nature, subject to further testing.

As a concrete astronomical example, ancient astronomers constructed a model (partly from observations and partly from philosophical beliefs) that Earth was the center of the universe and everything moved around it in circular orbits. At first, our available observations of the Sun, Moon, and planets did fit this model however, after further observations, the model had to be updated by adding circle after circle to represent the movements of the planets around Earth at the center. As the centuries passed and improved instruments were developed for keeping track of objects in the sky, the old model (even with a huge number of circles) could no longer explain all the observed facts. As we will see in the chapter on Observing the Sky: The Birth of Astronomy, a new model, with the Sun at the center, fit the experimental evidence better. After a period of philosophical struggle, it became accepted as our view of the universe.

When they are first proposed, new models or ideas are sometimes called hypotheses. You may think there can be no new hypotheses in a science such as astronomy—that everything important has already been learned. Nothing could be further from the truth. Throughout this textbook you will find discussions of recent, and occasionally still controversial, hypotheses in astronomy. For example, the significance that the huge chunks of rock and ice that hit Earth have for life on Earth itself is still debated. And while the evidence is strong that vast quantities of invisible “dark energy” make up the bulk of the universe, scientists have no convincing explanation for what the dark energy actually is. Resolving these issues will require difficult observations done at the forefront of our technology, and all such hypotheses need further testing before we incorporate them fully into our standard astronomical models.

This last point is crucial: a hypothesis must be a proposed explanation that can be tested. The most straightforward approach to such testing in science is to perform an experiment. If the experiment is conducted properly, its results either will agree with the predictions of the hypothesis or they will contradict it. If the experimental result is truly inconsistent with the hypothesis, a scientist must discard the hypothesis and try to develop an alternative. If the experimental result agrees with predictions, this does not necessarily prove that the hypothesis is absolutely correct perhaps later experiments will contradict crucial parts of the hypothesis. But, the more experiments that agree with the hypothesis, the more likely we are to accept the hypothesis as a useful description of nature.

One way to think about this is to consider a scientist who was born and lives on an island where only black sheep live. Day after day the scientist encounters black sheep only, so he or she hypothesizes that all sheep are black. Although every observed sheep adds confidence to the theory, the scientist only has to visit the mainland and observe one white sheep to prove the hypothesis wrong.

When you read about experiments, you probably have a mental picture of a scientist in a laboratory conducting tests or taking careful measurements. This is certainly the case for a biologist or a chemist, but what can astronomers do when our laboratory is the universe? It’s impossible to put a group of stars into a test tube or to order another comet from a scientific supply company.

As a result, astronomy is sometimes called an observational science we often make our tests by observing many samples of the kind of object we want to study and noting carefully how different samples vary. New instruments and technology can let us look at astronomical objects from new perspectives and in greater detail. Our hypotheses are then judged in the light of this new information, and they pass or fail in the same way we would evaluate the result of a laboratory experiment.

Much of astronomy is also a historical science—meaning that what we observe has already happened in the universe and we can do nothing to change it. In the same way, a geologist cannot alter what has happened to our planet, and a paleontologist cannot bring an ancient animal back to life. While this can make astronomy challenging, it also gives us fascinating opportunities to discover the secrets of our cosmic past.

You might compare an astronomer to a detective trying to solve a crime that occurred before the detective arrived at the scene. There is lots of evidence, but both the detective and the scientist must sift through and organize the evidence to test various hypotheses about what actually happened. And there is another way in which the scientist is like a detective: they both must prove their case. The detective must convince the district attorney, the judge, and perhaps ultimately the jury that his hypothesis is correct. Similarly, the scientist must convince colleagues, editors of journals, and ultimately a broad cross-section of other scientists that her hypothesis is provisionally correct. In both cases, one can only ask for evidence “beyond a reasonable doubt.” And sometimes new evidence will force both the detective and the scientist to revise their last hypothesis.

This self-correcting aspect of science sets it off from most human activities. Scientists spend a great deal of time questioning and challenging one another, which is why applications for project funding—as well as reports for publication in academic journals—go through an extensive process of peer review, which is a careful examination by other scientists in the same field. In science (after formal education and training), everyone is encouraged to improve upon experiments and to challenge any and all hypotheses. New scientists know that one of the best ways to advance their careers is to find a weakness in our current understanding of something and to correct it with a new or modified hypothesis.

This is one of the reasons science has made such dramatic progress. An undergraduate science major today knows more about science and math than did Sir Isaac Newton, one of the most renowned scientists who ever lived. Even in this introductory astronomy course, you will learn about objects and processes that no one a few generations ago even dreamed existed.


Are large body orbits self correcting? - Astronomy

. Conjunctions are highlighted by brief color changes. There are two Io-Europa conjunctions (green) and three Io-Ganymede conjunctions (grey) for each Europa-Ganymede conjunction (magenta). This diagram is not to scale.]] In celestial mechanics, orbital resonance occurs when orbiting bodies exert regular, periodic gravitational influence on each other, usually because their orbital periods are related by a ratio of small integers. Most commonly, this relationship is found between a pair of objects. The physical principle behind orbital resonance is similar in concept to pushing a child on a swing, whereby the orbit and the swing both have a natural frequency, and the body doing the "pushing" will act in periodic repetition to have a cumulative effect on the motion. Orbital resonances greatly enhance the mutual gravitational influence of the bodies (i.e., their ability to alter or constrain each other's orbits). In most cases, this results in an ''unstable'' interaction, in which the bodies exchange momentum and shift orbits until the resonance no longer exists. Under some circumstances, a resonant system can be self-correcting and thus stable. Examples are the 1:2:4 resonance of Jupiter's moons Ganymede, Europa and Io, and the 2:3 resonance between Pluto and Neptune. Unstable resonances with Saturn's inner moons give rise to gaps in the rings of Saturn. The special case of 1:1 resonance between bodies with similar orbital radii causes large solar system bodies to eject most other bodies sharing their orbits this is part of the much more extensive process of clearing the neighbourhood, an effect that is used in the current definition of a planet. A binary resonance ratio in this article should be interpreted as the ''ratio of number of orbits'' completed in the same time interval, rather than as the ''ratio of orbital periods'', which would be the inverse ratio. Thus, the 2:3 ratio above means that Pluto completes two orbits in the time it takes Neptune to complete three. In the case of resonance relationships among three or more bodies, either type of ratio may be used (whereby the smallest whole-integer ratio sequences are not necessarily reversals of each other), and the type of ratio will be specified.

Since the discovery of Newton's law of universal gravitation in the 17th century, the stability of the Solar System has preoccupied many mathematicians, starting with Pierre-Simon Laplace. The stable orbits that arise in a two-body approximation ignore the influence of other bodies. The effect of these added interactions on the stability of the Solar System is very small, but at first it was not known whether they might add up over longer periods to significantly change the orbital parameters and lead to a completely different configuration, or whether some other stabilising effects might maintain the configuration of the orbits of the planets. It was Laplace who found the first answers explaining the linked orbits of the Galilean moons (see below). Before Newton, there was also consideration of ratios and proportions in orbital motions, in what was called "the music of the spheres", or ''musica universalis''. The article on resonant interactions describes resonance in the general modern setting. A primary result from the study of dynamical systems is the discovery and description of a highly simplified model of mode-locking this is an oscillator that receives periodic kicks via a weak coupling to some driving motor. The analog here would be that a more massive body provides a periodic gravitational kick to a smaller body, as it passes by. The mode-locking regions are named Arnold tongues.

semimajor axes, showing the Kirkwood gaps where orbits are destabilized by resonances with Jupiter ]] s in Rings of Saturn#A Ring|Saturn's A Ring excited by resonances with inner moons. Such waves propagate away from the planet (towards upper left). The large set of waves just below center is due to the 6:5 resonance with Janus.]] in the Columbo Gap of Saturn's Rings of Saturn#C Ring|C Ring (center) and the inclined orbits of resonant particles in the bending wave just inside it have apsidal and nodal precessions, respectively, commensurate with Titan's mean motion.]] In general, an orbital resonance may *involve one or any combination of the orbit parameters (e.g. Orbital eccentricity|eccentricity versus semimajor axis, or eccentricity versus inclination). *act on any time scale from short term, commensurable with the orbit periods, to secular, measured in 10 4 to 10 6 years. *lead to either long-term stabilization of the orbits or be the cause of their destabilization. A ''mean-motion orbital resonance'' occurs when two bodies have periods of revolution that are a simple integer ratio of each other. Depending on the details, this can either stabilize or destabilize the orbit. ''Stabilization'' may occur when the two bodies move in such a synchronised fashion that they never closely approach. For instance: *The orbits of Pluto and the plutinos are stable, despite crossing that of the much larger Neptune, because they are in a 2:3 resonance with it. The resonance ensures that, when they approach perihelion and Neptune's orbit, Neptune is consistently distant (averaging a quarter of its orbit away). Other (much more numerous) Neptune-crossing bodies that were not in resonance were ejected from that region by strong perturbations due to Neptune. There are also smaller but significant groups of resonant trans-Neptunian objects occupying the 1:1 (Neptune trojans), 3:5, 4:7, 1:2 (twotinos) and 2:5 resonances, among others, with respect to Neptune. *In the asteroid belt beyond 3.5 AU from the Sun, the 3:2, 4:3 and 1:1 resonances with Jupiter are populated by ''clumps'' of asteroids (the Hilda family, the few Thule asteroids, and the numerous Trojan asteroids, respectively). Orbital resonances can also ''destabilize'' one of the orbits. This process can be exploited to find energy-efficient ways of deorbiting spacecraft. For small bodies, destabilization is actually far more likely. For instance: *In the asteroid belt within 3.5 AU from the Sun, the major mean-motion resonances with Jupiter are locations of ''gaps'' in the asteroid distribution, the Kirkwood gaps (most notably at the 4:1, 3:1, 5:2, 7:3 and 2:1 resonances). Asteroids have been ejected from these almost empty lanes by repeated perturbations. However, there are still populations of asteroids temporarily present in or near these resonances. For example, asteroids of the Alinda family are in or close to the 3:1 resonance, with their orbital eccentricity steadily increased by interactions with Jupiter until they eventually have a close encounter with an inner planet that ejects them from the resonance. *In the rings of Saturn, the Cassini Division is a gap between the inner B Ring and the outer A Ring that has been cleared by a 2:1 resonance with the moon Mimas. (More specifically, the site of the resonance is the Huygens Gap, which bounds the outer edge of the B Ring.) *In the rings of Saturn, the Encke and Keeler gaps within the A Ring are cleared by 1:1 resonances with the embedded moonlets Pan and Daphnis, respectively. The A Ring's outer edge is maintained by a destabilizing 7:6 resonance with the moon Janus. Most bodies that are in resonance orbit in the same direction however, the retrograde asteroid 514107 Kaʻepaokaʻawela appears to be in a stable (for a period of at least a million years) 1:−1 resonance with Jupiter. In addition, a few retrograde damocloids have been found that are temporarily captured in mean-motion resonance with Jupiter or Saturn. Such orbital interactions are weaker than the corresponding interactions between bodies orbiting in the same direction. A ''Laplace resonance'' is a three-body resonance with a 1:2:4 orbital period ratio (equivalent to a 4:2:1 ratio of orbits). The term arose because Pierre-Simon Laplace discovered that such a resonance governed the motions of Jupiter's moons Io, Europa, and Ganymede. It is now also often applied to other 3-body resonances with the same ratios, such as that between the extrasolar planets Gliese 876 c, b, and e. Three-body resonances involving other simple integer ratios have been termed "Laplace-like" or "Laplace-type". A ''Lindblad resonance'' drives spiral density waves both in galaxies (where stars are subject to forcing by the spiral arms themselves) and in Saturn's rings (where ring particles are subject to forcing by Saturn's moons). A ''secular resonance'' occurs when the precession of two orbits is synchronised (usually a precession of the perihelion or ascending node). A small body in secular resonance with a much larger one (e.g. a planet) will precess at the same rate as the large body. Over long times (a million years, or so) a secular resonance will change the eccentricity and inclination of the small body. Several prominent examples of secular resonance involve Saturn. A resonance between the precession of Saturn's rotational axis and that of Neptune's orbital axis (both of which have periods of about 1.87 million years) has been identified as the likely source of Saturn's large axial tilt (26.7°). Initially, Saturn probably had a tilt closer to that of Jupiter (3.1°). The gradual depletion of the Kuiper belt would have decreased the precession rate of Neptune's orbit eventually, the frequencies matched, and Saturn's axial precession was captured into the spin-orbit resonance, leading to an increase in Saturn's obliquity. (The angular momentum of Neptune's orbit is 10 4 times that of Saturn's rotation rate, and thus dominates the interaction.) The perihelion secular resonance between asteroids and Saturn (''ν6'' = ''g'' − ''g6'') helps shape the asteroid belt (the subscript "6" identifies Saturn as the sixth planet from the Sun). Asteroids which approach it have their eccentricity slowly increased until they become Mars-crossers, at which point they are usually ejected from the asteroid belt by a close pass to Mars. This resonance forms the inner and "side" boundaries of the asteroid belt around 2 AU, and at inclinations of about 20°. Numerical simulations have suggested that the eventual formation of a perihelion secular resonance between Mercury and Jupiter (''g1'' = ''g5'') has the potential to greatly increase Mercury's eccentricity and possibly destabilize the inner Solar System several billion years from now. The Titan Ringlet within Saturn's C Ring represents another type of resonance in which the rate of apsidal precession of one orbit exactly matches the speed of revolution of another. The outer end of this eccentric ringlet always points towards Saturn's major moon Titan. A ''Kozai resonance'' occurs when the inclination and eccentricity of a perturbed orbit oscillate synchronously (increasing eccentricity while decreasing inclination and vice versa). This resonance applies only to bodies on highly inclined orbits as a consequence, such orbits tend to be unstable, since the growing eccentricity would result in small pericenters, typically leading to a collision or (for large moons) destruction by tidal forces. In an example of another type of resonance involving orbital eccentricity, the eccentricities of Ganymede and Callisto vary with a common period of 181 years, although with opposite phases.

Mean-motion resonances in the Solar System

There are only a few known mean-motion resonances (MMR) in the Solar System involving planets, dwarf planets or larger satellites (a much greater number involve asteroids, planetary rings, moonlets and smaller Kuiper belt objects, including many possible dwarf planets). * 2:3 Pluto–Neptune (also and other plutinos) * 2:4 Tethys–Mimas (Saturn's moons). Not simplified, because the libration of the nodes must be taken into account. * 1:2 Dione–Enceladus (Saturn's moons) * 3:4 Hyperion–Titan (Saturn's moons) * 1:2:4 Ganymede–Europa–Io (Jupiter's moons, ratio of ''orbits''). Additionally, Haumea is believed to be in a 7:12 resonance with Neptune, and 225088 Gonggong is believed to be in a 3:10 resonance with Neptune. The simple integer ratios between periods hide more complex relations: *the point of conjunction can oscillate (librate) around an equilibrium point defined by the resonance. *given non-zero eccentricities, the nodes or periapsides can drift (a resonance related, short period, not secular precession). As illustration of the latter, consider the well-known 2:1 resonance of Io-Europa. If the orbiting periods were in this relation, the mean motions n,! (inverse of periods, often expressed in degrees per day) would satisfy the following : n_ - 2cdot n_=0 Substituting the data (from Wikipedia) one will get −0.7395° day −1 , a value substantially different from zero. Actually, the resonance perfect, but it involves also the precession of perijove (the point closest to Jupiter), dotomega . The correct equation (part of the Laplace equations) is: : n_ - 2cdot n_ + dotomega_=0 In other words, the mean motion of Io is indeed double of that of Europa taking into account the precession of the perijove. An observer sitting on the (drifting) perijove will see the moons coming into conjunction in the same place (elongation). The other pairs listed above satisfy the same type of equation with the exception of Mimas-Tethys resonance. In this case, the resonance satisfies the equation : 4cdot n_ - 2cdot n_ - dotOmega_- dotOmega_=0 The point of conjunctions librates around the midpoint between the nodes of the two moons.

right|thumb|300px|Illustration of Io–Europa–Ganymede resonance. From the centre outwards: Io (yellow), Europa (gray) and Ganymede (dark) The Laplace resonance involving Io–Europa–Ganymede includes the following relation locking the ''orbital phase'' of the moons: : Phi_L=lambda_ - 3cdotlambda_ + 2cdotlambda_=180^circ where lambda are mean longitudes of the moons (the second equals sign ignores libration). This relation makes a triple conjunction impossible. (A Laplace resonance in the Gliese 876 system, in contrast, is associated with one triple conjunction per orbit of the outermost planet, ignoring libration.) The graph illustrates the positions of the moons after 1, 2 and 3 Io periods. Phi_L librates about 180° with an amplitude of 0.03°. Another "Laplace-like" resonance involves the moons Styx, Nix and Hydra of Pluto: : Phi=3cdotlambda_ - 5cdotlambda_ + 2cdotlambda_=180^circ This reflects orbital periods for Styx, Nix and Hydra, respectively, that are close to a ratio of 18:22:33 (or, in terms of the near resonances with Charon's period, 3+3/11:4:6 see below) the respective ratio of orbits is 11:9:6. Based on the ratios of synodic periods, there are 5 conjunctions of Styx and Hydra and 3 conjunctions of Nix and Hydra for every 2 conjunctions of Styx and Nix. As with the Galilean satellite resonance, triple conjunctions are forbidden. Phi librates about 180° with an amplitude of at least 10°.

The dwarf planet Pluto is following an orbit trapped in a web of resonances with Neptune. The resonances include: *A mean-motion resonance of 2:3 *The resonance of the perihelion (libration around 90°), keeping the perihelion above the ecliptic *The resonance of the longitude of the perihelion in relation to that of Neptune One consequence of these resonances is that a separation of at least 30 AU is maintained when Pluto crosses Neptune's orbit. The minimum separation between the two bodies overall is 17 AU, while the minimum separation between Pluto and Uranus is just 11 AU (see Pluto's orbit for detailed explanation and graphs). The next largest body in a similar 2:3 resonance with Neptune, called a ''plutino'', is the probable dwarf planet Orcus. Orcus has an orbit similar in inclination and eccentricity to Pluto's. However, the two are constrained by their mutual resonance with Neptune to always be in opposite phases of their orbits Orcus is thus sometimes described as the "anti-Pluto".

Naiad:Thalassa 73:69 resonance

Neptune's innermost moon, Naiad, is in a 73:69 fourth-order resonance with the next outward moon, Thalassa. As it orbits Neptune, the more inclined Naiad successively passes Thalassa twice from above and then twice from below, in a cycle that repeats every

21.5 Earth days. The two moons are about 3540 km apart when they pass each other. Although their orbital radii differ by only 1850 km, Naiad swings

2800 km above or below Thalassa's orbital plane at closest approach. As is common, this resonance stabilizes the orbits by maximizing separation at conjunction, but it is unusual for the role played by orbital inclination in facilitating this avoidance in a case where eccentricities are minimal.

Mean-motion resonances among extrasolar planets

While most extrasolar planetary systems discovered have not been found to have planets in mean-motion resonances, chains of up to five resonant planets and up to seven at least near resonant planets have been uncovered. Simulations have shown that during planetary system formation, the appearance of resonant chains of planetary embryos is favored by the presence of the primordial gas disc. Once that gas dissipates, 90–95% of those chains must then become unstable to match the low frequency of resonant chains observed. *As mentioned above, Gliese 876 e, b and c are in a Laplace resonance, with a 4:2:1 ratio of periods (124.3, 61.1 and 30.0 days). In this case, Phi_L librates with an amplitude of 40° ± 13° and the resonance follows the time-averaged relation: : Phi_L=lambda_ - 3cdotlambda_ + 2cdotlambda_=0^circ *Kepler-223 has four planets in a resonance with an 8:6:4:3 orbit ratio, and a 3:4:6:8 ratio of periods (7.3845, 9.8456, 14.7887 and 19.7257 days). This represents the first confirmed 4-body orbital resonance. The librations within this system are such that close encounters between two planets occur only when the other planets are in distant parts of their orbits. Simulations indicate that this system of resonances must have formed via planetary migration. *Kepler-80 d, e, b, c and g have periods in a

1.000: 1.512: 2.296: 3.100: 4.767 ratio (3.0722, 4.6449, 7.0525, 9.5236 and 14.6456 days). However, in a frame of reference that rotates with the conjunctions, this reduces to a period ratio of 4:6:9:12:18 (an orbit ratio of 9:6:4:3:2). Conjunctions of d and e, e and b, b and c, and c and g occur at relative intervals of 2:3:6:6 (9.07, 13.61 and 27.21 days) in a pattern that repeats about every 190.5 days (seven full cycles in the rotating frame) in the inertial or nonrotating frame (equivalent to a 62:41:27:20:13 orbit ratio resonance in the nonrotating frame, because the conjunctions circulate in the direction opposite orbital motion). Librations of possible three-body resonances have amplitudes of only about 3 degrees, and modeling indicates the resonant system is stable to perturbations. Triple conjunctions do not occur. *TOI-178 has 6 confirmed planets, of which the outer 5 planets form a similar resonant chain in a rotating frame of reference, which can be expressed as 2:4:6:9:12 in period ratios, or as 18:9:6:4:3 in orbit ratios. In addition, the innermost planet b with period of 1.91d orbits close to where it would also be part of the same Laplace resonance chain, as a 3:5 resonance with the planet c would be fulfilled at period of

1.95d, implying that it might have evolved there but pulled out of resonance, possibly by tidal forces. * TRAPPIST-1's seven approximately Earth-sized planets are in a chain of near resonances (the longest such chain known), having an orbit ratio of approximately 24, 15, 9, 6, 4, 3 and 2, or nearest-neighbor period ratios (proceeding outward) of about 8/5, 5/3, 3/2, 3/2, 4/3 and 3/2 (1.603, 1.672, 1.506, 1.509, 1.342 and 1.519). They are also configured such that each triple of adjacent planets is in a Laplace resonance (i.e., b, c and d in one such Laplace configuration c, d and e in another, etc.). The resonant configuration is expected to be stable on a time scale of billions of years, assuming it arose during planetary migration. A musical interpretation of the resonance has been provided. *Kepler-29 has a pair of planets in a 7:9 resonance (ratio of 1/1.28587). *Kepler-36 has a pair of planets close to a 6:7 resonance. *Kepler-37 d, c and b are within one percent of a resonance with an 8:15:24 orbit ratio and a 15:8:5 ratio of periods (39.792187, 21.301886 and 13.367308 days). :*And *Of Kepler-90's eight known planets, the period ratios b:c, c:i and i:d are close to 4:5, 3:5 and 1:4, respectively (4:4.977, 3:4.97 and 1:4.13) and d, e, f, g and h are close to a 2:3:4:7:11 period ratio (2: 3.078: 4.182: 7.051: 11.102 also 7: 11.021). f, g and h are also close to a 3:5:8 period ratio (3: 5.058: 7.964). Relevant to systems like this and that of Kepler-36, calculations suggest that the presence of an outer gas giant planet facilitates the formation of closely packed resonances among inner super-Earths. *HD 41248 has a pair of super-Earths within 0.3% of a 5:7 resonance (ratio of 1/1.39718). *K2-138 has 5 confirmed planets in an unbroken near-3:2 resonance chain (with periods of 2.353, 3.560, 5.405, 8.261 and 12.758 days). The system was discovered in the citizen science project Exoplanet Explorers, using K2 data. K2-138 could host co-orbital bodies (in a 1:1 mean-motion resonance). Resonant chain systems can stabilize co-orbital bodies and a dedicated analysis of the K2 light curve and radial-velocity from HARPS might reveal them. Follow-up observations with the Spitzer Space Telescope suggest a sixth planet continuing the 3:2 resonance chain, while leaving two gaps in the chain (its period is 41.97 days). These gaps could be filled by smaller non-transiting planets. Future observations with CHEOPS will measure transit-timing variations of the system to further analyse the mass of the planets and could potentially find other planetary bodies in the system. *K2-32 has four planets in a near 1:2:5:7 resonance (with periods of 4.34, 8.99, 20.66 and 31.71 days). Planet e has a radius almost identical to that of the Earth. The other planets have a size between Neptune and Saturn. *V1298 Tauri has four confirmed planets of which planets c, d and b are near a 1:2:3 resonance (with periods of 8.25, 12.40 and 24.14 days). Planet e only shows a single transit in the K2 light curve and has a period larger than 36 days. Planet e might be in a low-order resonance (of 2:3, 3:5, 1:2, or 1:3) with planet b. The system is very young (23±4 Myr) and might be a precursor of a compact multiplanet system. The 2:3 resonance suggests that some close-in planets may either form in resonances or evolve into them on timescales of less than 10 Myr. The planets in the system have a size between Neptune and Saturn. Only planet b has a size similar to Jupiter. *HD 158259 contains four planets in a 3:2 near resonance chain (with periods of 3.432, 5.198, 7.954 and 12.03 days, or period ratios of 1.51, 1.53 and 1.51, respectively), with a possible fifth planet also near a 3:2 resonance (with a period of 17.4 days). The exoplanets were found with the SOPHIE échelle spectrograph, using the radial velocity method. *Kepler-1649 contains two Earth-size planets close to a 9:4 resonance (with periods of 19.53527 and 8.689099 days, or a period ratio of 2.24825), including one ("c") in the habitable zone. An undetected planet with a 13.0-day period would create a 3:2 resonance chain. *Kepler-88 has a pair of inner planets close to a 1:2 resonance (period ratio of 2.0396), with a mass ratio of

22.5, producing very large transit timing variations of

0.5 days for the innermost planet. There is a yet more massive outer planet in a

1400 day orbit. Cases of extrasolar planets close to a 1:2 mean-motion resonance are fairly common. Sixteen percent of systems found by the transit method are reported to have an example of this (with period ratios in the range 1.83–2.18), as well as one sixth of planetary systems characterized by Doppler spectroscopy (with in this case a narrower period ratio range). Due to incomplete knowledge of the systems, the actual proportions are likely to be higher. Overall, about a third of radial velocity characterized systems appear to have a pair of planets close to a commensurability. It is much more common for pairs of planets to have orbital period ratios a few percent larger than a mean-motion resonance ratio than a few percent smaller (particularly in the case of first order resonances, in which the integers in the ratio differ by one). This was predicted to be true in cases where tidal interactions with the star are significant.

Coincidental 'near' ratios of mean motion

300px|thumb|right|Depiction of the Earth:[[Venus 8:13 near resonance. With Earth held stationary at the center of a nonrotating frame, the successive [[inferior conjunction]]s of Venus over eight Earth years trace a [[pentagram]]mic pattern (reflecting the difference between the numbers in the ratio).]] A number of near-integer-ratio relationships between the orbital frequencies of the planets or major moons are sometimes pointed out (see list below). However, these have no dynamical significance because there is no appropriate precession of perihelion or other libration to make the resonance perfect (see the detailed discussion in the section above). Such near resonances are dynamically insignificant even if the mismatch is quite small because (unlike a true resonance), after each cycle the relative position of the bodies shifts. When averaged over astronomically short timescales, their relative position is random, just like bodies that are nowhere near resonance. For example, consider the orbits of Earth and Venus, which arrive at almost the same configuration after 8 Earth orbits and 13 Venus orbits. The actual ratio is 0.61518624, which is only 0.032% away from exactly 8:13. The mismatch after 8 years is only 1.5° of Venus' orbital movement. Still, this is enough that Venus and Earth find themselves in the opposite relative orientation to the original every 120 such cycles, which is 960 years. Therefore, on timescales of thousands of years or more (still tiny by astronomical standards), their relative position is effectively random. The presence of a near resonance may reflect that a perfect resonance existed in the past, or that the system is evolving towards one in the future. Some orbital frequency coincidences include: The least probable orbital correlation in the list is that between Io and Metis, followed by those between Rosalind and Cordelia, Pallas and Ceres, Jupiter and Pallas, Callisto and Ganymede, and Hydra and Charon, respectively.

Possible past mean-motion resonances

A past resonance between Jupiter and Saturn may have played a dramatic role in early Solar System history. A 2004 computer model by Alessandro Morbidelli of the Observatoire de la Côte d'Azur in Nice suggested that the formation of a 1:2 resonance between Jupiter and Saturn (due to interactions with planetesimals that caused them to migrate inward and outward, respectively) created a gravitational push that propelled both Uranus and Neptune into higher orbits, and in some scenarios caused them to switch places, which would have doubled Neptune's distance from the Sun. The resultant expulsion of objects from the proto-Kuiper belt as Neptune moved outwards could explain the Late Heavy Bombardment 600 million years after the Solar System's formation and the origin of Jupiter's Trojan asteroids. An outward migration of Neptune could also explain the current occupancy of some of its resonances (particularly the 2:5 resonance) within the Kuiper belt. While Saturn's mid-sized moons Dione and Tethys are not close to an exact resonance now, they may have been in a 2:3 resonance early in the Solar System's history. This would have led to orbital eccentricity and tidal heating that may have warmed Tethys' interior enough to form a subsurface ocean. Subsequent freezing of the ocean after the moons escaped from the resonance may have generated the extensional stresses that created the enormous graben system of Ithaca Chasma on Tethys. The satellite system of Uranus is notably different from those of Jupiter and Saturn in that it lacks precise resonances among the larger moons, while the majority of the larger moons of Jupiter (3 of the 4 largest) and of Saturn (6 of the 8 largest) are in mean-motion resonances. In all three satellite systems, moons were likely captured into mean-motion resonances in the past as their orbits shifted due to tidal dissipation (a process by which satellites gain orbital energy at the expense of the primary's rotational energy, affecting inner moons disproportionately). In the Uranian system, however, due to the planet's lesser degree of oblateness, and the larger relative size of its satellites, escape from a mean-motion resonance is much easier. Lower oblateness of the primary alters its gravitational field in such a way that different possible resonances are spaced more closely together. A larger relative satellite size increases the strength of their interactions. Both factors lead to more chaotic orbital behavior at or near mean-motion resonances. Escape from a resonance may be associated with capture into a secondary resonance, and/or tidal evolution-driven increases in orbital eccentricity or inclination. Mean-motion resonances that probably once existed in the Uranus System include (3:5) Ariel-Miranda, (1:3) Umbriel-Miranda, (3:5) Umbriel-Ariel, and (1:4) Titania-Ariel. Evidence for such past resonances includes the relatively high eccentricities of the orbits of Uranus' inner satellites, and the anomalously high orbital inclination of Miranda. High past orbital eccentricities associated with the (1:3) Umbriel-Miranda and (1:4) Titania-Ariel resonances may have led to tidal heating of the interiors of Miranda and Ariel, respectively. Miranda probably escaped from its resonance with Umbriel via a secondary resonance, and the mechanism of this escape is believed to explain why its orbital inclination is more than 10 times those of the other regular Uranian moons (see Uranus' natural satellites). Similar to the case of Miranda, the present inclinations of Jupiter's moonlets Amalthea and Thebe are thought to be indications of past passage through the 3:1 and 4:2 resonances with Io, respectively. Neptune's regular moons Proteus and Larissa are thought to have passed through a 1:2 resonance a few hundred million years ago the moons have drifted away from each other since then because Proteus is outside a synchronous orbit and Larissa is within one. Passage through the resonance is thought to have excited both moons' eccentricities to a degree that has not since been entirely damped out. In the case of Pluto's satellites, it has been proposed that the present near resonances are relics of a previous precise resonance that was disrupted by tidal damping of the eccentricity of Charon's orbit (see Pluto's natural satellites for details). The near resonances may be maintained by a 15% local fluctuation in the Pluto-Charon gravitational field. Thus, these near resonances may not be coincidental. The smaller inner moon of the dwarf planet Haumea, Namaka, is one tenth the mass of the larger outer moon, Hiiaka. Namaka revolves around Haumea in 18 days in an eccentric, non-Keplerian orbit, and as of 2008 is inclined 13° from Hiiaka. Over the timescale of the system, it should have been tidally damped into a more circular orbit. It appears that it has been disturbed by resonances with the more massive Hiiaka, due to converging orbits as it moved outward from Haumea because of tidal dissipation. The moons may have been caught in and then escaped from orbital resonance several times. They probably passed through the 3:1 resonance relatively recently, and currently are in or at least close to an 8:3 resonance. Namaka's orbit is strongly perturbed, with a current precession of about −6.5° per year.


If this were the Earth or Mars, the placement of the red material would not be an enigma at all as it lies underneath the snow-covered peaks. On the earth, the snow is ice, on Mars it is mostly CO2 ice. On Pluto it could be water, ice, methanol or even methane (IR images should tell us which). But on Pluto, it is the underlying strata that is vexing mission planetary scientists: It should not be red because there is not sufficient mass budget in Pluto for the surface to be dominated by Earth or Mars-like regoth.

So what is the red stuff? Mission scientists are speculating that it is 'tholins' - thin layers of nitrated hydrocarbons synthesized in the thin atmosphere. These organics are red in appearence but only if it is found in very thin layers. (The natural synthesis process of 'tholins' yields many hydrocarbons, and more than a thin layer of 'tholins' becomes predominately black).

Of course, much of the strata elsewhere on Pluto is red, and if the thin-layer hypothesis is correct we should see patterns where the underlying strata appear white with a thin red vale. As more color and broad spectrum images are streamed down and analyzed, the picture could become more clear or more clouded.

My hand is betting entirely on more clouded or to be more specific: Evidence that points to very thick layers of red materials with snowy caps and likewise for Charon.


Are Planetary Systems Filled to Capacity?

Steven Soter is a research associate in the Department of Astrophysics at the American Museum of Natural History in New York City, and scientist-in-residence at New York University, where he teaches on subjects ranging from life in the universe to geology and antiquity in the Mediterranean region. His research interests include planetary astronomy and geoarchaeology. He collaborated with Carl Sagan and Ann Druyan to create the acclaimed Cosmos television series in 1980.

In part one of this two-part essay, Soter explains how computer simulations suggest that planetary systems, including our own, contain as many planets as they can hold without becoming unstable. He says that observations of extrasolar systems should provide the ultimate test of this hypothesis.

This essay also appears in the September/October edition of American Scientist magazine.

Breakdown of the Clockwork Solar System
In 1605, Johannes Kepler discovered that the orbits of the planets are ellipses rather than combinations of circles, as astronomers had assumed since antiquity. Isaac Newton was then able to prove that the same force of gravity that pulls apples to the ground also keeps planets in their elliptical orbits around the Sun. But Newton was worried that the accumulated effects of the weak gravitational tugs between neighboring planets would increase their orbital eccentricities (their deviations from circularity) until their paths eventually crossed, leading to collisions and, ultimately, to the destruction of the solar system. He believed that God must intervene, making planetary course corrections from time to time so as to keep the heavens running smoothly.

By 1800, the mathematician Pierre-Simon Laplace had concluded that the solar system requires no such guiding hand but is, in fact, naturally self-correcting and stable. He calculated that the gravitational interactions between the planets would forever produce only small oscillations of their orbital eccentricities around their mean values. When asked by his friend Napoleon why he did not mention God in his major work on celestial mechanics, Laplace is said to have replied, &ldquoSir, I had no need for that hypothesis.&rdquo

Laplace also thought that, given the exact position and momentum of every object in the solar system at any one time, it would be possible to calculate from the laws of motion precisely where everything would be at any future instant, no matter how remote.

Laplace was correct to reject the need for divine intervention to preserve the solar system, but not for the reasons he thought. His calculations of stability were in fact incorrect. In the late 19th century, Henri Poincaré showed that Laplace had simplified some of his equations by removing terms he wrongly assumed to be superfluous, leading him to overlook the possibility of chaos in the solar system. Calculations with modern high-speed computers have finally provided evidence that the solar system is only marginally stable and that its detailed behavior is fundamentally unpredictable over long time periods.

Here I will outline some of the discoveries that led to current ideas about instability in the evolution of the solar system. Now is an especially promising time to consider the subject. Theorists are using powerful computer simulations to explore the formation of planetary systems under a wide range of starting conditions, while observers are rapidly discovering planetary systems around many other stars. The evidence suggests that such systems may be filled nearly to capacity. The abundance of observational data from the newly found planetary systems will stimulate and test our ideas about the delicate balance between order and chaos among the worlds.

Gaps in Understanding

In 1866, the American astronomer Daniel Kirkwood produced the first real evidence for instability in the solar system in his studies of the asteroid belt, which lies between the orbits of Mars and Jupiter. At the time, only about 90 asteroids were known (the orbits of more than 150,000 have since been charted), but that meager population was sufficient for Kirkwood to notice several &ldquogaps&rdquo in the distribution of their orbital periods or, equivalently, in their orbital sizes. (The orbital periods of planets, asteroids and comets increase with orbital size in a well-defined way.) Kirkwood found that no asteroid had a period near 3.9 years, which, he noted, is one-third that of Jupiter.

An asteroid that orbits the Sun exactly three times while Jupiter goes around just once would make every close approach to the giant planet at the same point in its own orbit and get a similar gravitational kick from its massive celestial neighbor each time. The repeated tugs Jupiter exerted would tend to add up, or resonate, from one passage to the next. Hence astronomers would refer to such an asteroid as being in a 3:1 mean-motion resonance. Other gaps in the asteroid belt correspond, for example, to where the orbital period of Jupiter would have a ratio of 5:2 or 7:3 to that of an asteroid.

A simple way to understand resonance is to push someone on a swing. If you push at random phases in the swing&rsquos motion, not much happens. But if you push each time the swing returns to you, the forces add up and the swing goes higher and higher. You could also push at the same phase but less frequently, say only every 2 or 3 swing periods the swing would then take longer to reach a given height, because such resonances are weaker.

An asteroid in such a resonant orbit can have its eccentricity increased until the body either collides with the Sun or a planet, or encounters a planet closely enough to be tossed into another part of the solar system. Asteroids that had been orbiting stably in the main belt are sometimes nudged into one of the resonant Kirkwood gaps, from which Jupiter eventually ejects them. These gaps are like holes through which the asteroid population is slowly draining away. Many of the meteorites that strike Earth are fragments that were ejected from the asteroid belt after straying into one of the resonant gaps.

Something similar takes place in the outer solar system. Gravitational tugs from the giant planets gradually remove icy worlds from the Kuiper belt, which lies beyond the orbit of Neptune. This process supplies the short-period comets, which enter the inner solar system for a brief time and return to it at regular intervals. In the early solar system, close encounters of small icy bodies with the growing giant planets populated the distant Oort cloud with hundreds of billions of cometary nuclei.

Such interactions also caused the orbits of the major planets to migrate. Because the growing planets Saturn, Uranus and Neptune tossed more small bodies inward toward the orbit of Jupiter than out of the solar system, those planets migrated outward, to conserve the total angular momentum. But the much more massive planet Jupiter ejected most of the small bodies it encountered into the outer solar system and beyond, and it consequently migrated inward. When the solar system was forming, the Kuiper belt contained hundreds of times more mass than it does today. The objects now in the belt represent only the small fraction that managed to survive. The same is true of the asteroid belt. Gravitational sculpting by the planets has severely depleted both populations, leaving the Kuiper and asteroids belt remnants of the primordial planetesimal disk.

Whereas some mean-motion resonant orbits in the solar system are highly unstable, others are quite resistant to disruption. (The difference depends on subtle details of the configuration of the interacting bodies.) Many of the objects in the Kuiper Belt have their orbits locked in a stable 2:3 mean-motion resonance with Neptune. They orbit the Sun twice for every three orbits of this planet. Such objects are called plutinos, after Pluto, the first one discovered. Some of them, including Pluto, cross inside the orbit of Neptune, but the geometry of their resonant orbits keeps them from making close approaches to the planet and accounts for their survival.

Thousands of small worlds called Trojan asteroids share Jupiter&rsquos orbit around the Sun, leading or following the planet by about 60 degrees. These bodies are trapped in a so-called 1:1 mean-motion resonance, the planet and asteroid having the same orbital period. This configuration inhibits close approaches to Jupiter and is relatively stable. Similar families of co-orbital asteroids accompany both Neptune and Mars around the Sun.

Gravitational tugs of the planets on one another produce cyclical motions in the spatial orientation of their orbits, causing another kind of resonance. The rotation of the orientation of an elliptical orbit takes many times longer than the orbital period of the planet itself. These slow gyrations of an entire orbit produce so-called secular resonances, which can strongly distort the orbits of smaller bodies&mdashand not just those in the asteroid belt. The solar system is crowded with potential orbits on which objects would be subjected to secular or mean-motion resonances. Many resonant orbits overlap, and wherever that happens, small orbiting bodies are especially prone to chaotic behavior, which is fundamentally unpredictable.

Despite its orderly appearance, the solar system actually includes many elements of what mathematicians call chaos. A defining feature of chaos is the extreme sensitivity of a system to its initial conditions. The most trivial disturbance in such a system can profoundly change its large-scale configuration at a later time. A pool table provides a familiar example: Microscopic variations in the trajectory of a billiard ball, especially one involved in multiple collisions, can completely alter the outcome of the game. Chaotic systems are deterministic, in that they follow precisely the laws of classical physics, but they are fundamentally unpredictable. The nature of chaos was not well understood until recently, when increasing computer power allowed mathematicians to explore it in sufficient detail. No one in Laplace&rsquos day imagined that the solar system, then taken as the paradigm of clockwork stability, is actually vulnerable to chaos.

Cleaning Up the Solar System

Jacques Laskar, of the Bureau des longitudes in Paris, has carried out the most extensive calculations to investigate the long-term stability of the solar system. He simulated the gravitational interactions between all eight planets over a period of 25 billion years (five times the age of the solar system). Laskar found that the eccentricities and other elements of the orbits undergo chaotic excursions, which make it impossible to predict the locations of the planets after a hundred million years. Does Laskar&rsquos result mean that the Earth might eventually find itself in a highly elliptical orbit, taking it much closer to and farther from the Sun, or that the solar system could lose a planet?

No. Even chaos has to operate within physical limits. For example, although meteorologists cannot predict the weather (another chaotic system) as far as a month in advance, they can be quite confident that conditions will fall within a certain range, because external constraints (such as the Sun&rsquos brightness and the length of the day) set limits on the overall system.

Laskar found that, despite the influence of chaos on the exact locations of the planets, their orbits remain relatively stable for billions of years. That is, whereas the long-term configuration is absolutely unpredictable in detail, the orbits remain sufficiently well behaved to prevent collisions between neighboring planets. An external constraint in this case is imposed by the conservation of angular momentum in the system, which limits the excursions of orbital eccentricity for bodies of planetary mass.

The orbits of the massive outer planets are the most stable. The smaller terrestrial planets, particularly Mars and Mercury, are more vigorously tossed about. The simulations show that over millions of years the terrestrial planets undergo substantial excursions in their eccentricities&mdashlarge enough for those planets to clear out any debris from the intervening orbital space, but not large enough to allow collisions between them. However, Laskar found one possible exception: Mercury, the lightest planet, has a small but finite chance of colliding with Venus on a timescale of billions of years. He concluded that the solar system is &ldquomarginally stable.&rdquo

Such results suggested to Laskar that the solar system is dynamically &ldquofull&rdquo or very nearly so. That is, if you tried to squeeze another planet in between the existing ones, the resulting gravitational disturbances would dynamically excite the system, leading to a collision or ejection before the system could settle down again.

Laskar surmised that the solar system, at each stage of its evolution, was always near the edge of instability, as it appears to be today. To maintain its marginal stability, the solar system has been eliminating objects on a timescale comparable with its age at every epoch. It follows that the solar system billions of years ago may have contained more planets that it does now.

According to this view, as the solar system matured, it managed to remain stable against the breakout of large-scale chaos by reducing the number of planets and increasing the spacing between them. The present number must be about as large (and their spacing about as small) as allowed by the system&rsquos long-term stability. The solar system has increased its internal order by exporting disorder&mdashentropy&mdashto the rest of the Galaxy, which receives the chaotically ejected objects.

This process, called dynamical relaxation, operates in star clusters and in entire galaxies as well as in evolving planetary systems. As such systems expel their most unstable members, the orbits of the remaining objects become more compact and well organized.

Extensive computer simulations show that the eight planets greatly disturb the motions of test particles placed on circular orbits at most locations in the solar system. Such particles are sent into close encounters with the planets, which remove them in only a few million years, a small fraction of the age of the solar system. But these simulations also identify several regions where objects can survive for far longer times. One such region is a broad zone centered about halfway between the orbits of Mars and Jupiter&mdashthe asteroid belt. Computer simulations by Jack Lissauer and colleagues at NASA Ames Research Center and at Queen&rsquos University, Ontario, showed that if an Earth-sized planet had formed there, it could remain in a stable orbit for billions of years. This result is not too surprising, because the zone of the asteroid belt is well-populated and must therefore be relatively immune to disturbance. The same study found however that a giant planet in the asteroid belt would soon become unstable.

The Kuiper belt is another region of stability, as there are no more planets to stir up the neighborhood beyond the orbit of Neptune. The Trojan asteroids of Mars, Jupiter and Neptune occupy other protected interplanetary niches.

Aside from such islands of stability, interplanetary space is remarkably empty. Most of the small objects orbiting between the planets (such as Earth-crossing asteroids and short-period comets) are transient interlopers, which recently leaked into the neighborhood from the asteroid and Kuiper belts. The planets will soon eject them or sweep them up in collisions. Indeed, a planet is now defined by the requirement that the object has cleared its orbital neighborhood of other material. Were it not for the leaky reservoirs that supply a steady trickle of debris to their vicinity, the planets would have thoroughly cleaned out most of the orbital space between them.

Read Steven Soter’s other Astrobiology Magazine essay:


Evolution: It's Only a Theory, But One Worth Teaching

My prior column was composed at 35,000 feet above North America as I surveyed the landscape from the air. The patterns etched by geological evolution are visible at altitude. Closer up, fossils tell the story of earlier life upon our continent. Gazing to the heavens, astronomers gather evidence of the evolution of planets, stars, galaxies--the whole universe evolves. Natural history museums host large collections of extant and extinct life that document biological evolution. Yet, as I noted, teaching evolution remains controversial in America.

A flood of email ensued. Many were supportive some asked questions. Several negative and hostile emails were openly critical of my assertion that American schools should teach evolution in science classrooms to "leave no child behind". In addition to rejecting evolution for religious reasons, several people claimed that there was not sufficient evidence, that scientists could not all agree, or that evolution is "only a theory" which they equate with an unfounded idea.

Evolution is supported by evidence. There are several thousand peer-reviewed scientific journals where the evidence is presented in article after article. Natural history museums house large collections of fossils that document the history of life. Geologists and astronomers have a massive amount of observational evidence of the long-term change in physical systems: stars, galaxies, planets, interstellar dust, asteroids, etc. Biologists observe and document the patterns of the evolution of life: for example, the fossil record, DNA, and the observation of evolution in action such as the adaptive evolution of antibiotic-resistant strains of bacteria that now pose a serious threat to human health. Selective breeding in agriculture generated our crops and domestic animals over thousands of years agriculture is evolution in action.

Certainly, there are continuing debates among scientists about the particulars of cosmic, planetary, and biological evolution. The nature of science requires continual questioning of ideas, evidence and theories. Theoretical scientists consider what we know, and pose new ideas and models to explain the natural world. New models and ideas generate new scientific tests of theory: observational experiments at Earth and space-based observatories, high-energy collisions of particle physics, deep-sea dives at the plate boundaries, and lab experiments in molecular biology to cite a few. Science is based upon observational and experimental evidence. Concepts that don't match observations are altered or tossed out. It's an iterative cycle. Likewise, if a scientist makes an observation or does an experiment that cannot be replicated, the results are suspect. Scientific explanations of the natural world are tested against nature, and discarded if they do not work. Consider cold fusion. Science is a self-correcting system that provides humans with powerful descriptions that allow us to understand and predict how the natural world works.

Consider Johannes Kepler, a mathematician who is often cited as one of the first modern astronomers. He took observational data collected by Tycho Brahe who was a terrific observer and had mounds of measurements for Mars. Brahe challenged Kepler to make sense of these Mars data. Tycho had his own ideas, but he didn't have Kepler's mathematical skills. Kepler spent months trying to fit the Mars data to the circular epicycles and deferents that explained planetary orbits in the astronomical tradition of his day. The data just didn't fit. Unlike his predecessors, Kepler took a leap toward modern science. He elected to trust the data, and abandoned the ancient model of circles upon circles for a new description of planetary motion. His ideas can be condensed into three statements which we call Kepler's laws. In their simplest form, they are: planets orbit on elliptical paths with the Sun at one focus the period of a planet's orbit is proportional to it's distance from the Sun and a planet's speed in orbit is proportional to its distance from the Sun (equal areas are swept out in equal time). Kepler didn't know why the planets orbited as they did, but he could describe their orbits and make accurate predictions about future positions. The next big step came with Isaac Newton who explained that why planets orbit the Sun: gravity. Only Mercury didn't behave as predicted by Newton's physics. Einstein remodeled physics once again with special and general relativity, and was able to explain Mercury's motion.

The theory of gravitation is a powerful explanation of how objects interact in space-time. Its heritage goes back to Kepler's description of planetary motion based upon Brahe's observational data. It's funny how no one argues that gravity is "only a theory," yet many dismiss evolution as "only a theory."

At a fundamental level, popular English and scientific usage are at odds here. In popular culture, a "theory" is understood to be a guess or speculation that may or may not be based upon evidence and analysis. In science, a theory is "a well-substantiated explanation of some aspect of the natural world that can incorporate facts, laws, inferences, and tested hypotheses." (Teaching About Evolution and the Nature of Science,National Academy of Sciences, 1998: 7). A scientific theory is the larger explanation of how the well-tested "laws" fit together to describe the natural world.

Dismissing evolution as "only a theory" is, at the simplest level, a misunderstanding of the meaning of "theory" in science. But, in the current controversy, discounting evolution as "only a theory" is more than a semantic debate. It's a political statement at the heart of the attack upon teaching evolution in science classrooms in America.

Science is a powerful tool for understanding the natural world, and has a dominant role in modern economics and culture. Scientific theories are at the heart of the enterprise. In the science classroom, children should learn about major scientific theories such as gravitation and evolution.

Science is a way of knowing, but not the only way of knowing. There are things that science does not address. For example, music, art, emotion, and religious beliefs are all outside the domain of what science can address. I find it unfortunate that the controversy over the theory of evolution continues as science offers all humans a way to know about the natural world and how it works.