Astronomy

Why aren't planet orbits circular?

Why aren't planet orbits circular?

Please forgive the simplicity of my question. I have only had basic science courses. Common sense seems to indicate that planetary orbits should be very close to circular, any perturbations having been eliminated over the ages. Could it be that the composition of the planet be influencing the pull of gravity to produce a different gravitational attraction due to its mass? I mean that if a planet were composed all of one substance, would the planetary orbit be perfectly circular? I think about earth having constantly shifting water and gasses and even solids that affect its own rotation. Might these shifts also affect the orbit of the planet around the sun, or does the total mass of the earth and moon together determine the orbit?


They are close to circular, although we might quibble about the meaning of "close". Except for Mercury, all planetary orbits have eccentricities below 0.1. That's close enough to a circle to actually pass for a circle at a superficial examination.

Mercury 0.2056 Venus 0.0068 Earth 0.0167 Mars 0.0934 Jupiter 0.0484 Saturn 0.0542 Uranus 0.0472 Neptune 0.0086

Check out these ellipses. The first one has an ecc. of 0.1. Looks like a circle, doesn't it? Even the second one (ecc = 0.2) kind of looks like a circle, too, if you don't examine it too long.

As for why they are not exactly circular, down to the last digit? There will always be perturbations that will squish perfect circles a little. Planets interact with each other, and pull each other off perfect circular orbits. It's very unlikely that in a complex system like ours you'll find highly circular planetary orbits.

But, again, the differences between the current planetary orbits and perfect circles are for the most part quite tiny, and you should think of them as "basically circles", unless you're an astronomer or a NASA engineer.

Comets, OTOH, those do tend to move on narrow elliptic orbits.


While this has been answered before, I'll touch on a few of your specific questions.

Common sense seems to indicate that planetary orbits should be very close to circular, any perturbations having been eliminated over the ages.

This seemed logical to a lot of people including some big brains throughout history like Aristotle, Ptolomy, even Copernicus and Kepler himself thought circles were neater than ellipses, but he couldn't deny that the carefully detailed planet charts and the mathematical calculations worked so much better with ellipses.

It wasn't until Newton that they knew why. Newton worked it out that ellipses are stable orbits, and in fact a circle is a type of ellipse with zero eccentricity. Somebody said once, and I'm repeating, setting a dial exactly at zero is very hard because you're always going to be off by a tiny fraction. Setting the dial between 0 and 1 is easy. That's why all orbits are ellipses.

Now when you say perturbations, that usually refers to a 3rd body in the system. For example, Earth-Sun, the Earth orbits the sun in an ellipse. If you have Earth and Venus orbiting the Sun, Venus and earth perturb each other's ellipse.

Could it be that the composition of the planet be influencing the pull of gravity to produce a different gravitational attraction due to its mass? I mean that if a planet were composed all of one substance, would the planetary orbit be perfectly circular?

Gravity does change a bit at different points in an orbit for the reasons you say, planets aren't uniform. The Moon is especially unbalanced for example so this is more apparent with orbits around the moon, but all planets have some degree of non uniform mass and that has some tiny effects but that's not the cause for ellipses though, in fact, non-uniform mass will slightly warp an elliptical orbit.

I think about earth having constantly shifting water and gasses and even solids that affect its own rotation. Might these shifts also affect the orbit of the planet around the sun, or does the total mass of the earth and moon together determine the orbit?

We think of water as sloshing around and causing drag cause that's our experience when we spin or move something with water in it, but that's not what happens in orbit. The Earth in orbit around the sun, for example, everything on the earth including the oceans are all falling around the sun together, so there's no "shifting" going on, in the sense that I think you mean. There are tidal bulges, but the effect of the tidal bulges on the shape of an orbit is pretty small. In fact, there's a curious side effect to tidal bulges, they tend to circularize orbits, over time. They actually have the opposite effect of what you suggest.

I tried to cover this at a basic science level. Corrections / clarifications welcome.


Why aren't planet orbits circular? - Astronomy

Why are stars and planets spherical? Why aren't they cubes or ovals?

The shape of small objects (like people and houses and mountains and small asteroids) are determined by their mechanical properties. You can take a rock and cut it into a particular shape and it will pretty much stay that way.

The larger the object, though, the stronger its gravitational field. Imagine that you want to build a really tall building. You have to make sure it has a really strong foundation, or the foundation will be crushed by the weight of the building and the building will fall. If there was anything really big sticking up on a planet or a star, gravity would pull it down.

If a planet was like a cube, the corners of the cube would be higher than the rest of the planet. Since planets and stars are so big, you cannot build a "foundation" strong enough to hold up those corners! Anything you built it out of would be too weak to hold them up. Gravity would eventually pull them down.

Even solid rock will flow like a liquid, although very slowly, if it is pulled by a very strong gravitational force for a very long time. Corners on a cubical planet or star would eventually just squish down.

Since gravity pulls toward the center of the planet or star, everything gets pulled down into a sphere. However, planets and stars are not really perfect spheres. They spin, so they bulge out a little around the equator.

This page updated on June 27, 2015

About the Author

Britt Scharringhausen

Britt studies the rings of Saturn. She got her PhD from Cornell in 2006 and is now a Professor at Beloit College in Wisconson.


The solar system follows the galactic standard—but it is a rare breed

Illustration showing an artist’s interpretation of what the TRAPPIST-1 solar system could look like. The seven planets of TRAPPIST-1 are all Earth-sized and terrestrial, and could potentially harbor liquid water, depending on their compositions. Credit: NASA/JPL-Caltech

Researchers at the Niels Bohr Institute, University of Copenhagen, have investigated more than 1000 planetary systems orbiting stars in our own galaxy, the Milky Way, and have discovered a series of connections between planetary orbits, number of planets, occurrence and the distance to their stars. It turns out that our own solar system in some ways is very rare, and in others very ordinary.

It is rare to have eight planets, but the study shows that the solar system follows exactly the same, very basic rules for the formation of planets around a star that they all do. The question about what exactly makes it so special that it harbors life is still a good question. The study is now published in MNRAS

Eccentric planet orbits are the key to determining the number of planets

There is a very clear correlation between the eccentricity of the orbits and the number of planets in any given solar system. When the planets form, they begin in circular orbits in a cloud of gas and dust. But they are still relatively small in size, up to sizes comparable to the moon. On a slightly longer time scale they interact via gravitation and acquire more and more eccentric or elliptic orbits. This means they start colliding because elliptical orbits cross one another—and so the planets grow in size due to the collisions. If the end result of the collisions is that all the pieces become just one or a few planets, then they stay in elliptical orbits. But if they end up becoming many planets, the gravitational pull between them makes them lose energy—and so they form more and more circular orbits.

The researchers have found a very clear correlation between the number of planets and how circular the orbits are. "Actually, this is not really a surprise," professor Uffe Gråe Jørgensen explains. "But our solar system is unique in the sense that no other solar systems with as many planets as ours are known. So perhaps it could be expected that our solar system doesn't fit into the correlation. But it does—as a matter of fact, it is right on."

The only solar systems that don't fit into this rule are systems with only one planet. In some cases, the reason is that in these single-planet systems, the planet is orbiting the star in very close proximity, but in others, the reason is that the systems may actually hold more planets that initially assumed. "In these cases, we believe that the deviation from the rule can help us reveal more planets that were hidden up until now," Nanna Bach-Møller, first author of the scientific article, explains. If we are able to see the extent of eccentricity of the planet orbit, then we know how many other planets must be in the system—and vice versa, if we have the number of planets, we now know their orbits. "This would be a very important tool for detecting planetary systems like our own solar system, because many exoplanets similar to the planets in our solar system would be difficult to detect directly, if we don't know where to look for them."

The Earth is among the lucky 1%

No matter which method is used in the search for exoplanets, one reaches the same result. So, there is basic, universal physics at play. The researchers can use this to say: How many systems possess the same eccentricity as our solar system? – which we can then use to assess how many systems have the same number of planets as our solar system. The answer is that there are only 1% of all solar systems with the same number of planets as our solar system or more. If there are approximately 100 billion stars in the Milky Way, this is, however, still no less than one billion solar systems. There are approximately 10 billion Earth-like planets in the habitable zone, i.e. in a distance from their star allowing for the existence of liquid water. But there is a huge difference between being in the habitable zone and being habitable or having developed a technological civilization, Uffe Gråe Jørgensen stresses. "Something is the cause of the fact that there aren't a huge amount of UFOs out there. When the conquest of the planets in a solar system has begun, it goes pretty quickly. We can see that in our own civilization. We have been to the moon and on Mars we have several robots already. But there aren't a whole lot of UFOs from the billions of Earth-like exo-planets in the habitable zones of the stars, so life and technological civilizations in particular are probably still fairly scarce."

The Earth is not particularly special—the number of planets in the system is what it is all about

What more does it take to harbor life than being an Earth-size planet in the habitable zone? What is really special here on Earth and in our solar system? Earth is not special—there are plenty of Earth-like planets out there. But perhaps it could be the number of planets and the nature of them. There are many large gas planets in our solar system, half of all of them. Could it be that the existence of the large gas planets are the cause of our existence here on Earth? A part of that debate entails the question of whether the large gas planets, Saturn and Jupiter, redirected water-bearing comets to Earth when the planet was a half-billion years old, enabling the forming of life here.

This is the first time a study has shown how unique it is for a solar system to be home to eight planets, but at the same time, shows that our solar system is not entirely unique. Our solar system follows the same physical rules for forming planets as any other solar system, we just happen to be in the unusual end of the scale. And we are still left with the question of why, exactly, we are here to be able to wonder about it.


The Curious Case Of Planetary Orbits

The planets of our solar system move in ellipses. We've known this, so we are told, ever since Johannes Kepler devised his laws of planetary motion in the early 1600s. While it's true that orbits are (approximately) ellipses, they aren't as elliptical as you might think, and that's largely due to the way the solar system is typically presented. Take, for example, a figure showing the space missions currently active in our solar system.

Like many such figures, the solar system is shown with a tilted perspective, and so the orbits appear highly elliptical. In reality, the orbits of most planets are extremely circular. If we were to draw Earth's orbit as a perfect circle 100 meters (328 ft) across, it would be accurate to Earth's actual orbit to with 14 millimeters (0.5 inches). When Kepler proposed his model, only the orbits of Mercury and Mars were known to be non-circular. Whether they were true ellipses was still a matter of debate. This is part of the reason why Kepler's model wasn't fully accepted until Newton developed his theory of universal gravity in the late 1600s.

While ancient astronomers thought planetary orbits were circular, they didn't think they were simple circles. One of the consequences of elliptical orbits is that planets orbit not about the center of the ellipse, but about a point off-center known as the focus. This offset is far more noticeable than a slightly elliptical shape. So early astronomers proposed circular orbits known as deferents that were shifted off center. Since most early models of the solar system placed the Earth at the center, a single circular path didn't agree well with observed planetary motion. In the third century BC Apollonius of Perga proposed the addition of epicycles, which moved along an off-center deferent.

Originally it was proposed that the deferent and epicycle rotated at constant rates. This explained why planets would appear to move more quickly at some points in its orbit and more slowly in others. But by the second century AD observations had become accurate enough that they couldn't explain the variation in speed. So Claudius Ptolemy introduced an idea as the equant. Basically the equant of an orbit is a point from which a planet would appear to move along the deferent at a constant speed. Since the equant was not the center of the deferent, the planet would vary in speed along its orbit.

Calculating the motion of planets using deferents, equants and epicycles may have been complex, but it was accurate. When Copernicus proposed a Sun-centered model of the solar system in the mid 1500s, it wasn't more accurate than earlier geocentric models, but it did make the calculations simpler. A heliocentric circular orbit of Mars with an equant to describe its varying speed is extremely close to the actual motion. Even astronomers who didn't think the Earth actually orbited the Sun began to use the Copernican model for its computational advantages.

While Kepler's introduction of ellipses was an elegant solution for planetary motion, it was still merely an approximate description. Newton showed that a single planet orbiting the Sun would have an elliptical orbit, but in the real solar system planets tug upon each other gravitationally, and their orbits are perturbed slightly from a perfect ellipse. In reality no planet has a truly elliptical orbit. Kepler's laws, as they've come to be known, are a beautiful but approximate consequence of a deeper gravitational truth.


Discovery

The planet was first announced in September 2010 by a team led by Steven Vogt at the University of California, Santa Cruz. Using 11 years of observational data from the W.M. Keck Observatory in Hawaii, the teams announced two planets around the star Gliese 581: Gliese 581f and Gliese 581g. Results were published in the Astrophysical Journal and also made available in pre-print version on Arxiv.

The planet was believed to be within the habitable zone of its parent star, which is a red dwarf. This type of star is cooler than our own sun, which means planets need to huddle close to receive enough warmth for water to flow on their surface. While astronomers generally define habitability by whether the planet can support liquid water, it is acknowledged that there are many factors that can influence it. This includes the planet's atmosphere and how variable its parent star is in terms of emitting energy.

In a press release announcing the discovery, the researchers acknowledged Gliese 581 "has a somewhat checkered history of habitable-planet claims". Two planets found in the system before, Gliese 581c and Gliese 581d, were later believed to be at the edge of the habitable zone. (In future years, Gliese 581d's existence was also called into question). Historical estimates for number of planets in the system range from about 3 to 6 planets, depending on the method used.

As for Gliese 581g, the researchers said that the planet always has one side facing its parent star, and the other always in darkness. The region of habitability would likely be on the line between shadow and light.

Gliese 581g was found by detecting the gravitational wobbles it induced in its parent star, but the researchers said it was subtle more than 200 observations were required at a precision of 1.6 meters per second. The data from Keck was combined with that of another famous planet-hunting instrument, the HARPS (High Accuracy Radial velocity Planetary Search project) at the European Southern Observatory's La Silla 3.6-meter telescope in Chile. Brightness measurements of the star were also confirmed with a Tennessee State University robotic telescope.


Why aren't planet orbits circular? - Astronomy

Around five billion years ago the Sun was a dizzy young thing. It was rotating on its axis, and an enormous dusty disk revolved around it. The planets, moons, asteroids and other objects formed from the disk material. Although the disk no longer exists, the plane that it occupied is still marked by the orbits of Solar System bodies. It's called the ecliptic plane. The orbits aren't circular, they are somewhat squashed circles known as ellipses. The eccentricity of an orbit tells us how squashed its shape is.

The ecliptic
As the Earth journeys around the Sun each year, we see the Sun's position changing against the background of fixed stars. The path that it seems to take is called the ecliptic. The constellations that lie along this path served as a sort of calendar and were of religious significance to ancient peoples. They are the zodiac constellations.

Instead of just thinking about the ecliptic as a path, try to imagine it as a flat surface, a plane. It would stretch from the Sun out into the Solar System. The planets orbit on the ecliptic plane. The eight planets are pretty much in the same plane. However Pluto's orbit is tilted to the ecliptic by 17 degrees.

So the ecliptic is where the planets are, and it's the center line of the zodiac. But why is it called the ecliptic? It's because it's related to eclipses. Although the Moon is also on the ecliptic, its orbit is slightly tilted – about 5 degrees – to Earth's orbit. There are two points where the orbits cross, and these are called nodes. If there's a new Moon or a full Moon when the Moon is at a node, then the Sun, Earth and Moon are lined up for an eclipse.

Ellipse
For centuries people assumed that orbits were circular and that Earth was at the center of the cosmos. Circles and spheres, being perfect shapes, were a feature of the heavens, and a contrast to our imperfect Earth. In fact, the planetary orbits in the Solar System are close enough to being circular that it takes a lot of careful observation and measurement to detect that they aren't.

However, if you assume the orbits are circular, predictions about planetary motion will not be accurate, nor will forecasts of events such as a transit of Venus. In order to make the model fit the observations, Ptolemy (90-168) had the planets moving on complicated system of circles. It actually worked fairly well in terms of prediction, but over a long period of time the errors became noticeable.

There was some improvement when Copernicus put the Sun in the center of the system. Yet it still wasn't accurate because Copernicus kept the circular orbits. The breakthrough came with the work of Johannes Kepler (1571-1630). Kepler, who was a mathematician, used the meticulous observations over a period of years by Tycho Brahe (1546-1601) to make sense of planetary motions. It was only when he got the idea that perhaps the orbits weren't circular that he was able to make theory and observation match.

Kepler found that the orbits were ellipses. This matched Brahe's data, and Kepler was able to describe them mathematically.

An ellipse is a squashed circle, with two focal points called foci. In terms of the Solar System, the orbits of the planets are ellipses and the Sun is at one focus. A circle is a special case of an ellipse, in which both foci are in the same place.

Eccentricity
Eccentricity is a term that tells us how rounded an ellipse is, on a scale of 0 to 1. A circle has an eccentricity of 0 (e=0). An ellipse can't have an eccentricity of 1, but a very long narrow ellipse could be close to 1. The Solar System planets don't have highly eccentric orbits. Venus has the most rounded orbit with e=0.0068. Dwarf planet Pluto has the most eccentric orbit (e=0.2488), and as we saw in an earlier diagram, its orbit is also notably tilted with respect to the ecliptic. It's a feature of many of the most distant objects that they have eccentric and tilted orbits.

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Stars don't obliterate their planets (very often)

Stars have an alluring pull on planets, especially those in a class called hot Jupiters, which are gas giants that form farther from their stars before migrating inward and heating up.

Now, a new study using data from NASA's Kepler Space Telescope shows that hot Jupiters, despite their close-in orbits, are not regularly consumed by their stars. Instead, the planets remain in fairly stable orbits for billions of years, until the day comes when they may ultimately get eaten.

"Eventually, all hot Jupiters get closer and closer to their stars, but in this study we are showing that this process stops before the stars get too close," said Peter Plavchan of NASA's Exoplanet Science Institute at the California Institute of Technology, Pasadena, Calif. "The planets mostly stabilize once their orbits become circular, whipping around their stars every few days."

The study, published recently in the Astrophysical Journal, is the first to demonstrate how the hot Jupiter planets halt their inward march on stars. Gravitational, or tidal, forces of a star circularize and stabilize a planet's orbit when its orbit finally become circular, the migration ceases.

"When only a few hot Jupiters were known, several models could explain the observations," said Jack Lissauer, a Kepler scientist at NASA's Ames Research Center, Moffet Field, Calif., not affiliated with the study. "But finding trends in populations of these planets shows that tides, in combination with gravitational forces by often unseen planetary and stellar companions, can bring these giant planets close to their host stars."

Hot Jupiters are giant balls of gas that resemble Jupiter in mass and composition. They don't begin life under the glare of a sun, but form in the chilly outer reaches, as Jupiter did in our solar system. Ultimately, the hot Jupiter planets head in toward their stars, a relatively rare process still poorly understood.

The new study answers questions about the end of the hot Jupiters' travels, revealing what put the brakes on their migration. Previously, there were a handful of theories explaining how this might occur. One theory proposed that the star's magnetic field prevented the planets from going any farther. When a star is young, a planet-forming disk of material surrounds it. The material falls into the star -- a process astronomers call accretion -- but when it hits the magnetic bubble around it, called the magnetosphere, the material travels up and around the bubble, landing on the star from the top and bottom. This bubble could be halting migrating planets, so the theory went.

Another theory held that the planets stopped marching forward when they hit the end of the dusty portion of the planet-forming disk.

"This theory basically said that the dust road a planet travels on ends before the planet falls all the way into the star," said co-author Chris Bilinski of the University of Arizona, Tucson. "A gap forms between the star and the inner edge of its dusty disk where the planets are thought to stop their migration."

And yet a third theory, the one the researchers found to be correct, proposed that a migrating planet stops once the star's tidal forces have completed their job of circularizing its orbit.

To test these and other scenarios, the scientists looked at 126 confirmed planets and more than 2,300 candidates. The majority of the candidates and some of the known planets were identified via NASA's Kepler mission. Kepler has found planets of all sizes and types, including rocky ones that orbit where temperatures are warm enough for liquid water.

The scientists looked at how the planets' distance from their stars varied depending on the mass of the star. It turns out that the various theories explaining what stops migrating planets differ in their predictions of how the mass of a star affects the orbit of the planet. The "tidal forces" theory predicted that the hot Jupiters of more massive stars would orbit farther out, on average.

The survey results matched the "tidal forces" theory and even showed more of a correlation between massive stars and farther-out orbits than predicted.

This may be the end of the road for the mystery of what halts migrating planets, but the journey itself still poses many questions. As gas giants voyage inward, it is thought that they sometimes kick smaller, rocky planets out of the way, and with them any chance of life evolving. Lucky for us, our Jupiter did not voyage toward the sun, and our Earth was left in peace. More studies like this one will help explain these and other secrets of planetary migration.

NASA Ames manages Kepler's ground system development, mission operations and science data analysis. NASA's Jet Propulsion Laboratory in Pasadena, Calif., managed Kepler mission development. Ball Aerospace & Technologies Corp. in Boulder, Colo., developed the Kepler flight system and supports mission operations with JPL at the Laboratory for Atmospheric and Space Physics at the University of Colorado in Boulder. The Space Telescope Science Institute in Baltimore archives, hosts and distributes the Kepler science data. Kepler is NASA's 10th Discovery Mission and is funded by NASA's Science Mission Directorate at the agency's headquarters in Washington.

NASA's Exoplanet Science Institute at Caltech manages time allocation on the Keck telescope for NASA. JPL manages NASA's Exoplanet Exploration program office. Caltech manages JPL for NASA.


Why aren't planet orbits circular? - Astronomy

After studying this section you should be able to:

  • describe the forces acting on planets, moons and satellites
  • explain how charged particles are accelerated in a cyclotron

This section cover the following topics

Movement in the Solar System

All planetary movement in the Solar System is anticlockwise, when viewed from above the North Pole. The further a planet is from the Sun, the slower the speed in its orbit. Although the orbits of the planets are ellipses, for most planets they are so close to circles that our understanding of circular motion can be applied.

Planets can be considered to be:

  • moving at constant speed in a circle around the Sun
  • accelerating towards the Sun with centripetal acceleration v 2 /r.

Mercury and Pluto have highly elliptical orbits, the other planets follow paths that are very close to being circles.

In space there are no resistive forces since the planets move through a vacuum. The only forces acting on them are gravitational. Gravitational attraction between a planet and the Sun provides the unbalanced force required to cause the centripetal acceleration.

The diagram shows the attractive forces between the Sun and a planet.

This diagram shows that the gravitational force on a planet acts at its centre of mass and is directed towards the Sun’s centre of mass.

The force on the planet is:

  • equal in size and opposite in direction to that on the Sun
  • at right angles to its direction of motion
  • the unbalanced, centripetal force required to maintain circular motion.

By equating the gravitational force to mv 2 /r, it emerges that the orbital speed depends only on the orbital radius and not on the mass of the planet.

Asteroids in the asteroid belt, between Mars and Jupiter, have a wide range of masses but similar orbit times.

KEY POINT - The centripetal force required to keep a planet in a circular orbit is the gravitational force between the planet and the Sun: so v 2 r = GM s where M s is the mass of the Sun and Mp is the mass of the planet.

The relationship between the orbital speed and radius of a planet can be applied to the orbit of a satellite around the Earth by replacing the mass of the Sun, Ms, with that of the Earth, ME. This enables the speed of a satellite to be calculated at any orbital radius.

The relationship also applies to the Earth’s natural satellite, the Moon.

Some communications satellites occupy geo-synchronous orbits . A satellite in a geo-synchronous orbit:

  • orbits above the equator
  • remains in the same position relative to the Earth’s surface
  • has an orbit time of 24 hours.

The radius of a geo-synchronous orbit can be calculated from v 2 r = GME. As there are two unknowns in this equation, v can be written as 2πr/t to work out the value
of r.

Circular orbits in magnetic fields

When a charged particle moves at right angles to a magnetic field, the magnetic force on the particle is perpendicular to both its direction of motion and the magnetic field. This can result in circular motion.

The diagram shows the path and the force on an electron moving in a magnetic field directed into the paper.

When applying Fleming’s rule to electrons, remember that the direction of the current is opposite to that of the electrons’ motion.

The electron follows a circular path, the magnetic force being the unbalanced force required to cause acceleration towards the centre of the circle. The radius of the circular path is proportional to the speed of the electron.

KEY POINT - When a charge Q moves in a circular path in a magnetic field of strength B:

BQv=mv 2 /r so BQ = mv/r

For an electron, Q = e, so the relationship is Be = mv/r

The cyclotron

A cyclotron uses a magnetic field to force charged particles to move in a circular path, and an electric field to accelerate them as they travel around the circle. As the charged particles accelerate, the increase in speed results in an increase in the radius of the circle, so they spiral outwards.

A cyclotron consists of two D-shaped halves called dees. A magnetic field acting at right angles to the plane of the dees causes a beam of charged particles to follow a circular path. Particles such as protons and alpha particles are both suitable for use in cyclotrons.

Particles accelerated in a cyclotron are used to probe atomic nuclei and for treating some cancers.

The diagram shows the path of protons produced at the centre of the cyclotron.

  • the beam of charged particles is accelerated as it passes from one dee into the other
  • this occurs because of the alternating electric field which changes polarity so that it attracts the particles as they enter a dee
  • the frequency of the alternating voltage must be equal to the frequency of rotation of the particles
  • the radius of orbit increases as the particles accelerate.

The frequency of rotation of the charged particles in a cyclotron matches that of the accelerating voltage and does not depend on the speed of the particles. The value of the magnetic field strength can be adjusted to achieve the desired frequency.

If the frequency of the accelerating voltage is fixed, each orbit takes the same time. With an increase in the radius of successive orbits, the particles travel increasing distances in a given time period.

KEY POINT - The frequency of rotation of a charged particle in a cyclotron, f, is related to the magnetic field strength, B, by the expression:

f = BQ / 2πm where Q is the charge on a particle of mass m.


Do planets orbit the sun in perfect circles?

All planets in our solar system follow an elliptical path. This path is known as an orbit. Earth's orbit is not a perfect circle. If we were to draw the Earth's orbit on a sheet of paper as a perfect circle, the width of the line would be larger than the elliptical path of the Earth.

Furthermore, why do planets orbit around the sun? Anyway, the basic reason why the planets revolve around, or orbit, the Sun, is that the gravity of the Sun keeps them in their orbits. Just as the Moon orbits the Earth because of the pull of Earth's gravity, the Earth orbits the Sun because of the pull of the Sun's gravity.

Similarly, you may ask, is the Earth's orbit around the sun a perfect circle?

Earth's orbit is not a perfect circle. It is elliptical, or slightly oval-shaped. This means there is one point in the orbit where Earth is closest to the Sun, and another where Earth is farthest from the Sun. The closest point occurs in early January, and the far point happens in early July (July 7, 2007).


Why do the planets orbit the sunny on a relatively horizontal plane?

If gravity is an inwards force towards a mass, there's no reason I can think of why our solar system's planets orbit the sun on such a relatively horizontal plane, why aren't some planet's orbits perpendicular to ours? Is it just chance? is this the case for all known stars?

All the planets are believed to have been formed from the same accreting disk of gas and dust that surrounded the Sun. Same accreting disk=same orbital plane.

OK, but space is 3-D (without the glasses). Why does the gas and dust tend to form in a disc, as opposed to a spherical shell, around a sun?

Related question: why is Pluto in a different plane than the solar system's planets?

Bingo! From ye olde wikipedia: "The currently accepted method by which the planets formed is known as accretion, in which the planets began as dust grains in orbit around the central protostar."

With the exception of comets whose orbits originate from the Oort Cloud, which is why they're generally considered a lot more dangerous than asteroids because they can come from absolutely anywhere in the sky.

Basically it's left over momentum from the disk of dust/gas that formed the sun and then the planets.

Because of conservation of angular momentum.

The Sun and the planets were formed from the same contracting cloud of gas. This gas cloud was rotating very slightly when it started out, and the speed of rotation increased as the cloud was collapsing due to gravity, in the same way figure skaters can rotate faster in the air by pulling their arms in to their sides. The fast rotation caused the gas cloud to take the shape of a disc, from which the planets were eventually formed. This video explains it very well: http://youtu.be/tFLOsRSuW0E

A slight correction, though: It is not entirely correct to say that the gas cloud was stretched into a disc shape, since the solar system is much smaller than the original gas cloud. It is more correct to say that particles positioned along the rotational axis fell straight towards the center of what would later become the center of the Sun, thus clearing that area of matter. Particles positioned more off-center had a certain velocity relative to the axis, and could thus start to maintain an orbit around the proto-sun. A lot of collisions and mayhem later, and things settled down into most of the particles going in almost circular orbits in the disc.

An interesting aside: When the center of the disc eventually became hot and dense enough to sustain a fusion process, the Sun was born. All this new energy production caused a massive outflux of light and matter, which is what we call the Solar Wind and is still ongoing. This wind pushed all the matter in the disc outwards, with the lighter elements such as hydrogen and helium being pushed fartest away. This is why you find the rocky planets such as The Earth and Mars close to the Sun, while the giant gas planets such as Jupiter and Saturn (which both consist mostly of hydrogen) are located further away.