# Why aren't new stars in Earth's relative proximity constantly discovered?

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Okay, bear with me. In layman's terms:

The estimates vary, but on a clear night, away from big cities, one can see up to 5000 stars in the sky. All those are in the Milky Way, but they're hardly equidistant from Earth, which would mean that they revolve around the galactic center at different orbits. According to some sources, some are positioned very closely to us while others hang out as far as 1000 light year away.

Now by astronomical standards, 5000 stars is not a great number. It's still pretty impressive, though.

Some stars are larger, and others are smaller. It stands to reason that some of them might be "hiding" behind others. Because they all orbit the galactic center at different speeds, using different orbits, wouldn't it follow that from time to time, over the centuries, decades, or even years (months?) a "new" star would emerge from behind another one? Shouldn't this be happening often; or are they so sparsely distributed around the galaxy that no "new" stars have appeared out there over the past three thousand years or so?

To the naked eye, the answer is almost certainly no because of the enormously slow movement of stars across the sky and because 5,000 stars may be a lot but only a tiny percentage of the sky is covered by visible stars.

To Hubble, which can see perhaps tens of millions of stars, maybe more, the link here, has a picture of two stars that are approaching crossing each other's path from our point of view. With a big enough telescope it probably happens from time to time, though I wouldn't want to try to calculate how often, but to the naked eye, I'm comfortable saying no, in fact, it was often assumed that stars didn't move and were fixed in the sky (contrary to what Macrobius said). That was the popular point of view prior to Halley's observation.

There was also Tycho Brahe's "De Nova Stella" or "new star" which we now know to be a super-nova, and that was quite the surprise at the time. Nobody thought a new star could appear because they thought the stars were fixed and permanent, but that appearance wasn't by the method you suggest.

Consider how small stars are from our point of view. Alpha Centauri A, the larger one, it's about 1.7 million KM across and it's about 4.3 light years away, or, 41 trillion KM. It's diameter is 23 million times smaller than it's distance from us. That's the equivalent of looking at a golf ball from nearly 200 miles away. Now if you scatter 5000 golf balls each 200 miles away across the sky and you let them move around very very slowly, how often do you think one golf ball passes in-front of another? Not very often. Granted, that's not quite right as the atmosphere spreads stars out a bit so each golf ball is smudged to maybe the size of a basketball, but they almost never pass infront of one another, at least, not if we only take into account 5,000 visible stars.

Now, binary stars, it happens more often if they are lined up right, then they can pass infront of each other and this has certainly been observed by telescope but not to the Naked Eye, we can't visibly tell that Alpha Centauri is 2 stars (3 with the more distant Proxima but that can't be seen by the eye). They are on average about a billion miles apart but that can't be seen by the naked eye. It was observed by telescope in 1689.

There simply aren't enough visible stars (and taking HDE's point that most of the 5,000 visible stars weren't cataloged until recently), there's essentially zero chance that it was ever observed that a star appeared "new" by passing from behind another star.

Using Hubble, it can happen, but not to human sight.

## Why can’t we feel Earth’s spin?

Earth spins on its axis once in every 24-hour day. At Earth’s equator, the speed of Earth’s spin is about 1,000 miles per hour (1,600 km per hour). The day-night has carried you around in a grand circle under the stars every day of your life, and yet you don’t feel Earth spinning. Why not? It’s because you and everything else – including Earth’s oceans and atmosphere – are spinning along with the Earth at the same constant speed.

It’s only if Earth stopped spinning, suddenly, that we’d feel it. Then it would be a feeling similar to riding along in a fast car, and having someone slam on the brakes!

Think about riding in a car or flying in a plane. As long as the ride is going smoothly, you can almost convince yourself you’re not moving. A jumbo jet flies at about 500 miles per hour (about 800 kph), or about half as fast as the Earth spins at its equator. But, while you’re riding on that jet, if you close your eyes, you don’t feel like you’re moving at all. And when the flight attendant comes by and pours coffee into your cup, the coffee doesn’t fly to the back of the plane. That’s because the coffee, the cup and you are all moving at the same rate as the plane.

Now think about what would happen if the car or plane wasn’t moving at a constant rate, but instead speeding up and slowing down. Then, when the flight attendant poured your coffee … look out!

If you’re drinking coffee in a steadily moving car or airplane, no problem. But if the car or plane speeds up or slows down, your coffee sloshes and maybe spills. Likewise, as long as Earth spins steadily, we can’t feel it move. Image via H.C. Mayer and R. Krechetnikov.

Earth is moving at a fixed rate, and we’re all moving along with it, and that’s why we don’t feel Earth’s spin. If Earth’s spin were suddenly to speed up or slow down, you would definitely feel it.

The constant spin of the Earth had our ancestors pretty confused about the true nature of the cosmos. They noticed that the stars, and the sun and the moon, all appeared to move above the Earth. Because they couldn’t feel Earth move, they logically interpreted this observation to mean that Earth was stationary and “the heavens” moved above us.

With the notable exception of the early Greek scientist Aristarchus, who first proposed a heliocentric (sun-centered) model of the universe hundreds of years B.C., the world’s great thinkers upheld the geocentric (Earth-centered) idea of the cosmos for many centuries.

It wasn’t until the 16th century that the heliocentric model of Copernicus began to be discussed and understood. While not without errors, Copernicus’ model eventually convinced the world that Earth spun on its axis beneath the stars … and also moved in orbit around the sun.

A time exposure of the northern sky, revealing the apparent motion of all the stars around Polaris. In fact, this apparent motion is due to Earth’s spin. Image via Shutterstock.

Bottom line: We don’t feel Earth rotating on its axis because Earth spins steadily – and moves at a constant rate in orbit around the sun – carrying you as a passenger right along with it.

## Why The Discovery Of An Earth-Like Planet Is Such A Big Deal

An artist imagines what the surface of the planet Proxima b, orbiting the red dwarf star Proxima Centauri, might look like.

Revolutionary discoveries don't always breakthrough the hustle of daily life.

After all, when the Wright Brothers lifted their rickety plane off the sands of Kitty Hawk, the rest of the world was just out buying their eggs, milk and toilet paper. On that day who knew — or could imagine — that decades into the future millions of people would be sitting in giant jet-planes watching Direct TV and soaring five miles above the planet's surface.

I'm telling you this because two weeks ago a threshold of discovery was crossed when astronomers announced they found a planet orbiting Proxima Centauri — the sun's closest neighbor.

Now, you may have heard that news — but did you really hear the news?

As an astronomer, I can tell space really is crazy big. A light-year is the distance light crosses in one year — that's almost 6 trillion miles. But our galaxy, the Milky Way, is a city of stars stretching 100,000 light-years across. The vast scale of the Milky Way means most of its stars are many thousands of light-years away from us. That's a very long way away, indeed, considering the fastest thing we've ever made would take a few hundred thousand years to cross just one light-year.

But Proxima Centauri, that's as close as it gets.

It's the star next door (Proxima is actually part of a triple star system called Alpha Centauri). Proxima's proximity matters a lot because, as Albert Einstein told us, nothing can travel faster than the speed of light, and that locks distance and time together. Even if you had some kind of super-technology blasting your spaceship to 10 percent of light-speed, it would still take centuries, millennia or more to reach most stars.

But not Proxima Centauri. Lying just about four light-years away, that hypothetical super-technology could get you there in 40 years — less than a human lifetime. If you could get closer to the speed of light then you might reach Proxima in under 10 years.

That's why finding a planet orbiting any of Alpha Centauri's stars has been the stuff of science fiction for decades (go watch Avatar again if you don't believe me). The fact that Proxima's planet is rocky and in an orbit that might allow water (and therefore life) to exist on its surface makes last week's discovery even more epic.

Now, here's the thing: This new planet — it's not an escape valve for our own planetary climate crisis. We don't have anything like that super-technology, so we aren't sending any human beings there anytime soon. And even if we could, we still have no idea if this new world even has an atmosphere or just a nasty barren rock.

But because Proxima is so close to us, the new telescopes we're building now will soon give us an unprecedented view of this freshly discovered world and help us unveil its secrets. That's important on its own.

But even more important is the future — the deep future.

There didn't have to be a rocky world in the habitable zone of our nearest star. Nature could have played things differently.

Instead, this world is out there. It's waiting.

And regardless of what it looks like today, perhaps 5,000 years from now we will not only have reached it but reshaped it, too, making it home for billions of people — making it our first true step outwards.

That is why, perhaps, 5,000 years from now when all the details of our age and all the names of our politicians are long forgotten — the discovery announced two weeks ago will be still be remembered and will still be a cause for celebration.

Adam Frank is a co-founder of the 13.7 blog, an astrophysics professor at the University of Rochester, a book author and a self-described "evangelist of science." You can keep up with more of what Adam is thinking on Facebook and Twitter: @adamfrank4

##### Correction Sept. 12, 2016

A previous version of this post misspelled Proxima Centauri and Alpha Centauri as Centuri.

## Why Aren’t ALL SR Effects Cumulative?

Summary:: Example: the Lorentz Contraction goes away when v—>0 but Time Dilation does not.

Why aren’t all the SR effects cumulative like Time Dilation? Why should the Space dimensional effect become null when v—>0 while the Time dimension does not revert back to the 2 frames being in sync if Space and Time are treated on an equal footing. Clearly, Space and Time are not treated on an equal footing or the times in both frames would snap back in sync just like the lengths do. I’m referring to 2 frames in relative motion v and comparing the Lorentz Contraction and Time Dilation. Thank you.

If you have a clock that ticks but doesn't record anything permanent, then it does the same as a ruler in the sense that its measured tick rate is varies with its relative velocity.

The difference between a clock and a ruler is that most clocks record something permanent.

The difference between time and space is the sign in the spacetime distance: $ds^2 = c^2 dt^2 - dx^2 - dy^2 -dz^2$ Time is not, therefore, just another spatial dimension. That's the trouble with phrases like "equal footing".

Summary:: Example: the Lorentz Contraction goes away when v—>0 but Time Dilation does not.

Why aren’t all the SR effects cumulative like Time Dilation? Why should the Space dimensional effect become null when v—>0 while the Time dimension does not revert back to the 2 frames being in sync if Space and Time are treated on an equal footing.

I'm not sure what you mean. You seem to be pointing out that a device with a memory does not behave like a device without a memory. We're aware of that. If you use the devices in the same way (ignoring their memories) they are equivalent, at least in 1+1d. It gets a bit more complex in more dimensions, but then there's more than one spacelike dimension and still only one timelike dimension, so describing them as "equivalent" would be a stretch.

I'm not sure what you think is "dogma" here. I suspect you've been reading popsci sources, which don't necessarily reflect scientific theories terribly well. It's best to treat them with the same caution as an "inspired by a true story" movie.

I'm not sure what you mean. You seem to be pointing out that a device with a memory does not behave like a device without a memory. We're aware of that. If you use the devices in the same way (ignoring their memories) they are equivalent, at least in 1+1d. It gets a bit more complex in more dimensions, but then there's more than one spacelike dimension and still only one timelike dimension, so describing them as "equivalent" would be a stretch.

I'm not sure what you think is "dogma" here. I suspect you've been reading popsci sources, which don't necessarily reflect scientific theories terribly well. It's best to treat them with the same caution as an "inspired by a true story" movie.

But that is not time dilation. That is differential aging. That is something you can only detect because the clock has a memory which the ruler does not. You can detect "differential distance" with an odometer (which has a memory) - and that will be non-reversible.

You don't seem to be catching the distinction that is being made by us.

But you keep trying to support the claim by comparing the readings on devices with a memory to the readings on devices without memories. The latter cannot remember their history of movement. The former can. So of course their behaviour is different. If you replace the clocks with metronomes (as @Sagittarius A-Star suggests) or the rulers with odometers (as I suggest) then the different behaviours disappear.

There are differences between space and time, but they have to do with space having three dimensions and time only one. This is not something you can analyse with a single clock and a ruler.

There is an analogous non-reversible effect on distances. Say we have a car instead of a spaceship, so that we can install an odometer that ticks off one kilometer for every kilometer of road that passes under the wheels (note that in the spirit of special relativity, this description works whether we consider the car to be at rest while the road moves, or the car to be moving over a stationary road). We will also dispense with the dashboard clock on the car and instead use the twins' heartrate as a clock (assume their hearts beat once per second according to them - if it is not clear to you that this assumption is unaffected by time dilation we'll have to back up and address a more basic but very common misunderstanding) so that we can have a direct connection between our time measurements and the age of the twins.

At the end of the trip, the car's odometer, measuring the spatial distance of the journey, will read fewer kilometers than the spatial length of the journey according to the stay-at-home twin's measurement of the distance traveled. The travelling twin's heart will have beaten fewer times than the stay-at-home twin's heart, so the temporal length of the journey was less also for the traveller than for the stay-at-home twin. Both effects are non-reversible - "too few" heartbeats and "too few" kilometers under the wheels, and once the twins are back at rest relative to one another both the "missing" heartbeats and the "missing" kilometers are missing forever.

## 8 The Star With Spiral Arms

When we think of spiral arms, we envision galaxies like the Milky Way. However, star SAO 206462 is here to prove us wrong because it has two spiral arms. SAO 206462 is in the Lupus (&ldquoWolf&rdquo) constellation about 460 light-years away from Earth. The star is surrounded by a very wide circumstellar disk made of dust and gas. [3]

This broad disk is almost two times the width of Pluto&rsquos orbit. Astronomers know that spiral arms can develop around a star when new planets are materializing inside its disk. In fact, they think that the two spiral arms were formed by two new planets developing inside the disk.

## Why don't we see eclipses of external stars?

The question is pretty much the title. Why don't we see a constantly changing night sky with stars popping in and out of our view through let's say star bound planets crossing our path of vision? Shouldn't there be a significant amount of stellar eclipses happening all the time, visible to the naked eye?

I'm looking forward to being educated and thanks in advance, all input is appreciated :)

We do, that's how exoplanets are detected. But they're not visible to the naked eye, the drops in brightness are every few days (more more) and are typically less than a percent of the star's total brightness. The human eye can't detect that, it can't even see most stars.

One fascinating thing I read a long time ago is that the human perceptual apparatus generally does not register differences in magnitude below 2% unless a simultaneous comparison is possible. The examples given were weights and temperatures.

To illustrate: you hand someone an object that weighs 100 lbs. Then you take it back and give them an object weighing 101 lbs. They will not be able to tell you which item is heavier, unless they are permitted to hold both objects at the same time.

I don't have a source. I read this so long ago, I can't even remember when I read it, let alone where. But I've never forgotten the number: 2% is the threshold.

Not just exoplanets, but all sorts of things in our own solar system too.

I see, but isn't there a single star or similar cosmic constillation, small enough (think neutron stars) that the entirety of it's emitted visible light can be blocked by an orbiting planet (or similar), but still bright enough for me to see with my admittedly inferior eyes? Or are the masses and sizes they would need to have too extreme? Or cause effects like the poisson spot which would technically allow continuous vision according to my limited understanding of the process? Are these cosmic objects blocking our view even detectible as Objects or do they just cause a decrease of the overall brightness of the star?

What we see as an eclipse is a matter or perspective. Planets and moons are much smaller than stars, so if you're far away from the body moving in front of the star/sun it only blocks out a small percentage of the star's light. We only see it as an eclipse because we are close to the planet/moon so we are able to stand completely in it's shadow.

Remember that the only reason we see (solar) eclipses here on Earth is because the Moon is 400 times closer to us than the Sun is. Venus is a little over three times larger than the Moon. Venus (and Mercury) passes in front of the Sun on a semi-regular basis. But because it's a hundred times further away we barely notice it.

The only eclipse-like thing you can see are stellar occultations by objects in our Solar System. Everything else is too small to block all the light. Occultations of major stars are rare, but if you have binoculars you have a reasonable chance to see one from your home at some point.

We do. But stars are big, and planets are small, so the brightness doesn't dip by much.

Here is an example of an "eclipse" of an external star.

The brightness dipped by like. 1%.

As for stars eclipsing other stars? Yeah. space is. REALLY big, and everything is getting further away from everything else.

The brightness dipped by like. 1%.

In your example plot, the brightness dipped from an average of 1.000 to 0.9995, so more like. 0.05%.

On earth we are in range of the moons "core shadow"

That means we can see a full eclipse (rarely). For external stars we are WAY out of reach of this region since the light traveling from that star is almost parallel when it reaches us. So the tiny planet will only obscure a tiny bit of light, which the human eye cant detect

One thing nobody else appears to have mentioned is that there is a term for what you're describing: transit.

Exoplanets are often discovered either because of their impact on the motion of their star, or because they transit the star.

The reason we see Solar Eclipses is that our Moon is very very close to us compared to the sun, even though the sun is very very much bigger than the moon. Coincidentally the have almost identical apparent sizes, so when all the wobbles and angles line up, bam, solar eclipse.

Now, even the furthest sizable bodies within our solar system are only 0.000625 light years away (pluto). We usually measure this in AU (Astronomical Units, 1AU is the average distance from Earth to the Sun) which is better equated to light-hours, not light years.

The closest stars are light years away. So the distance from us to the star we see and the distance between us and any planets that might be in their star system are practically the same to us, differing only by a few light hours perhaps, when the overall distance is light years (or hundreds of light years) away.

Therefore, the apparent size of a star and any planets in its system are largely decided by the actual size of the objects in the system, because their distance to us is practically the same, whereas our Moon is so much significantly closer to us than our own sun, that it can have a drastically exaggerated apparent size.

Extra: we do see complete Eclipses of other stars, they are called occultations I believe, but itɽ only ever be with bodies in our own solar system. The moon moves in front of other stars all the time. As does Jupiter, Saturn, etc. It's just not a cool eclipse because the apparent size of the stars are so much smaller than these bodies that you don't get the cool effect we get from Solar Eclipses here on Earth. We do see other planets in our system "eclipse" our sun, but they don't cover it completely from our perspective and we call them transits.

Our Moon is ridiculously close and that's the only reason it can look the same size as our star to us. Planets in other systems light years away are only at most a few light hours from their star, and the difference between a light year and a light hour is so much, that we can basically pretend the light hours don't exist at all. So real size is the only thing that matters, and no exoplanet will ever be larger than its parent star.

## Ask Ethan: Why Aren't Spiral Galaxies More Wound Up?

Think about the grandest objects you've ever seen pictures of in the night sky. Sure, there are a whole slew of targets to choose from, including dying stars, supernova remnants, star-forming nebulae and clusters of stars both new and old, but nothing compares to the beauty of a spiral galaxy. Containing between billions and trillions of stars, these "island universes" display a unique structure all their own. A structure, mind you, that's puzzling if you think about it, as our questioner Greg Rogers did:

One thing that has always bothered me about spiral galaxies is that you only see the arms wrapping around about half-way or so. Since the outside is spinning around the core more slowly, I would expect that we should see some galaxies with arms wrapping many times around the core. Is the universe simply not old enough for these more tightly wound spiral galaxies to have formed?

You can look at any number of spiral galaxies, but they all have the same apparent structure in common.

#### Gallery: Seven Amazing And Classic Spiral Galaxies From The Messier Catalog

Radiating out from the central nucleus come any number of spiral arms -- usually between two and four -- that wrap around the galaxy as they spiral outward. One of the fantastic discoveries we made in the 1970s, quite contrary to our expectations, is that the stars don't move slower in their orbital speed around the galaxy as you move outward, the way planets orbit our central star more slowly the farther out you go. Instead, the speed remains constant, which is another way of saying that the galactic rotation curves have flat profiles.

Image credit: Wikimedia Commons user Stefania.deluca.

The way we measured this is by looking at edge-on spirals, and seeing how much redshift or blueshift the individual stars displayed relative to their distance from the galactic center. But even though the velocities of the individual stars are roughly constant, a star that's twice as far from the center as another takes twice as long to go around, while one ten times as distant takes ten times as long to orbit.

Given that this is the case, we can do a little math: for a galaxy like our Milky Way, based on how fast the Sun and the other stars appear to move, it takes the Sun about 220 million years to make a single orbit around the galaxy. At our distance of roughly 26,000 light years from the galactic center, we're a little less than halfway to the outskirts. This means that for a

12 billion year old galaxy like our own: the outer stars should have completed only around 25 orbits stars where our Sun are should have completed approximately 54 orbits stars in the inner 10,000 light years should have completed more than 100 orbits. In other words, we'd expect galaxies to "wind up" over time, as the video below shows.

But as our images of galaxies show, they don't wrap around dozens of times the arms in most cases don't even wrap around one time! When we first realized this property of galaxies, it meant one thing was for certain: these spiral arms aren't material, they're simply a visual effect. This remains true whether galaxies are in isolation or not. But there's another hint these galaxies offer, if we look closely.

Image credit: ESO, taken with the EFOSC instrument, attached to the 3.58-metre New Technology . [+] Telescope at ESO's La Silla Observatory in Chile.

Do you notice how there are "pink" spots dotted all along the spiral arms here? These appear whenever we have active regions of new star formation the pink signature is actually an excess of emitted light at a very precise wavelength: 656.3 nanometers. This emission occurs when hot, new stars burn brightly enough to ionize gaseous material, and then when the electrons recombine with the protons, the newly formed hydrogen atoms emit light at very particular frequencies, including the one that turns these regions pink.

What this indicates to us is that these spiral arms are actually made out of regions where the density of material is higher than the other locations in the galaxy, and that stars are free to move in-and-out of these arms as time goes on.

The idea that explains this has been around since 1964, and is known as density wave theory. The theory holds that the arms themselves appear to stay in the same exact spots as time goes on, the same way that traffic jams stay in the same spots. Even though the individual objects (stars in the arms cars in a traffic jam) are free to move through, the same rough number remain in the "jam" at any given time. This results in the dense pattern maintaining itself over time.

The physics behind it is even simpler: stars at different radii all exert the gravitational forces we're accustomed to, and those forces are what maintain the spiral shape. In other words, if you start with a region where the gas is overdense and you allow your "disk" to rotate, you'll get an initial series of regions where stars first form: the proto-arms. As the galaxy evolves over time, these arms -- and the overdense regions -- are maintained by the effects of gravity alone.

What's remarkable is that this effect works equally well whether there's dark matter in a giant halo surrounding your galaxy (below, right) or none at all (below, left).

Image credit: Wikimedia Commons user Ingo Berg, turned into a GIF by Forbes staff.

Even though the premise of your question, Greg, was flawed, since the outer stars in a galaxy move just as fast (speed-wise) as the inner stars, it's true that the arms will never wind up, no matter how old a galaxy gets, simply due to the physics of galaxies themselves. Much like a traffic jam, the stars, gas and dust that find themselves in the spiral arms at any given time will be in a much busier neighborhood, and once they move out again, they'll find a great distance from themselves to any other star, just like our Sun experiences today.

So Greg, contact me with your address, because you just won a Year In Space 2016 Calendar ! For your chance to win, submit your questions and suggestions for the next Ask Ethan here selections for the rest of the year are all winners!

## Contents

During a year the equation of time varies as shown on the graph its change from one year to the next is slight. Apparent time, and the sundial, can be ahead (fast) by as much as 16 min 33 s (around 3 November), or behind (slow) by as much as 14 min 6 s (around 11 February). The equation of time has zeros near 15 April, 13 June, 1 September, and 25 December. Ignoring very slow changes in the Earth's orbit and rotation, these events are repeated at the same times every tropical year. However, due to the non-integral number of days in a year, these dates can vary by a day or so from year to year. [n 1] [4] : 277

The graph of the equation of time is closely approximated by the sum of two sine curves, one with a period of a year and one with a period of half a year. The curves reflect two astronomical effects, each causing a different non-uniformity in the apparent daily motion of the Sun relative to the stars:

• the obliquity of the ecliptic (the plane of the Earth's annual orbital motion around the Sun), which is inclined by about 23.44 degrees relative to the plane of the Earth's equator and
• the eccentricity of the Earth's orbit around the Sun, which is about 0.0167.

The equation of time is constant only for a planet with zero axial tilt and zero orbital eccentricity. On Mars the difference between sundial time and clock time can be as much as 50 minutes, due to the considerably greater eccentricity of its orbit. The planet Uranus, which has an extremely large axial tilt, has an equation of time that makes its days start and finish several hours earlier or later depending on where it is in its orbit.

The United States Naval Observatory states "the Equation of Time is the difference apparent solar time minus mean solar time", i.e. if the sun is ahead of the clock the sign is positive, and if the clock is ahead of the sun the sign is negative. [5] [6] The equation of time is shown in the upper graph above for a period of slightly more than a year. The lower graph (which covers exactly one calendar year) has the same absolute values but the sign is reversed as it shows how far the clock is ahead of the sun. Publications may use either format — in the English-speaking world, the former usage is the more common, but is not always followed. Anyone who makes use of a published table or graph should first check its sign usage. Often, there is a note or caption which explains it. Otherwise, the usage can be determined by knowing that, during the first three months of each year, the clock is ahead of the sundial. The mnemonic "NYSS" (pronounced "nice"), for "new year, sundial slow", can be useful. Some published tables avoid the ambiguity by not using signs, but by showing phrases such as "sundial fast" or "sundial slow" instead. [7]

In this article, and others in English Wikipedia, a positive value of the equation of time implies that a sundial is ahead of a clock.

The phrase "equation of time" is derived from the medieval Latin aequātiō diērum, meaning "equation of days" or "difference of days". The word aequātiō (and Middle English equation) was used in medieval astronomy to tabulate the difference between an observed value and the expected value (as in the equation of the centre, the equation of the equinoxes, the equation of the epicycle). Gerald J. Toomer uses the medieval term "equation" from the Latin aequātiō, [n 2] for Ptolemy's difference between the mean solar time and the apparent solar time. Johannes Kepler's definition of the equation is "the difference between the number of degrees and minutes of the mean anomaly and the degrees and minutes of the corrected anomaly." [8] : 155

The difference between apparent solar time and mean time was recognized by astronomers since antiquity, but prior to the invention of accurate mechanical clocks in the mid-17th century, sundials were the only reliable timepieces, and apparent solar time was the generally accepted standard. Mean time did not supplant apparent time in national almanacs and ephemerides until the early 19th century. [9]

### Early astronomy Edit

The irregular daily movement of the Sun was known to the Babylonians. [ citation needed ]

Based on Ptolemy's discussion in the Almagest, values for the equation of time (Arabic taʿdīl al-ayyām bi layālayhā) were standard for the tables (zij) in the works of medieval Islamic astronomy. [12]

### Early modern period Edit

A description of apparent and mean time was given by Nevil Maskelyne in the Nautical Almanac for 1767: "Apparent Time is that deduced immediately from the Sun, whether from the Observation of his passing the Meridian, or from his observed Rising or Setting. This Time is different from that shewn by Clocks and Watches well regulated at Land, which is called equated or mean Time." He went on to say that, at sea, the apparent time found from observation of the Sun must be corrected by the equation of time, if the observer requires the mean time. [1]

The right time was originally considered to be that which was shown by a sundial. When good mechanical clocks were introduced, they agreed with sundials only near four dates each year, so the equation of time was used to "correct" their readings to obtain sundial time. Some clocks, called equation clocks, included an internal mechanism to perform this "correction". Later, as clocks became the dominant good timepieces, uncorrected clock time, i.e., "mean time", became the accepted standard. The readings of sundials, when they were used, were then, and often still are, corrected with the equation of time, used in the reverse direction from previously, to obtain clock time. Many sundials, therefore, have tables or graphs of the equation of time engraved on them to allow the user to make this correction. [ citation needed ]

The equation of time was used historically to set clocks. Between the invention of accurate clocks in 1656 and the advent of commercial time distribution services around 1900, there were three common land-based ways to set clocks. Firstly, in the unusual event of having an astronomer present, the sun's transit across the meridian (the moment the sun passed overhead) was noted the clock was then set to noon and offset by the number of minutes given by the equation of time for that date. Secondly, and much more commonly, a sundial was read, a table of the equation of time (usually engraved on the dial) was consulted and the watch or clock set accordingly. These calculated the mean time, albeit local to a point of longitude. The third method did not use the equation of time instead, it used stellar observations to give sidereal time, exploiting the relationship between sidereal time and mean solar time. [13] : 57–58

The first tables to give the equation of time in an essentially correct way were published in 1665 by Christiaan Huygens. [14] Huygens, following the tradition of Ptolemy and medieval astronomers in general, set his values for the equation of time so as to make all values positive throughout the year. [14] [n 3]

Another set of tables was published in 1672–73 by John Flamsteed, who later became the first Astronomer Royal of the new Royal Greenwich Observatory. These appear to have been the first essentially correct tables that gave today's meaning of Mean Time (previously, as noted above, the sign of the equation was always positive and it was set at zero when the apparent time of sunrise was earliest relative to the clock time of sunrise). Flamsteed adopted the convention of tabulating and naming the correction in the sense that it was to be applied to the apparent time to give mean time. [15]

The equation of time, correctly based on the two major components of the Sun's irregularity of apparent motion, [n 4] was not generally adopted until after Flamsteed's tables of 1672–73, published with the posthumous edition of the works of Jeremiah Horrocks. [16] : 49

Robert Hooke (1635–1703), who mathematically analyzed the universal joint, was the first to note that the geometry and mathematical description of the (non-secular) equation of time and the universal joint were identical, and proposed the use of a universal joint in the construction of a "mechanical sundial". [17] : 219

### 18th and early 19th centuries Edit

The corrections in Flamsteed's tables of 1672–1673 and 1680 gave mean time computed essentially correctly and without need for further offset. But the numerical values in tables of the equation of time have somewhat changed since then, owing to three factors:

• general improvements in accuracy that came from refinements in astronomical measurement techniques,
• slow intrinsic changes in the equation of time, occurring as a result of small long-term changes in the Earth's obliquity and eccentricity (affecting, for instance, the distance and dates of perihelion), and
• the inclusion of small sources of additional variation in the apparent motion of the Sun, unknown in the 17th century, but discovered from the 18th century onwards, including the effects of the Moon, [n 5] Venus and Jupiter. [18]

From 1767 to 1833, the British Nautical Almanac and Astronomical Ephemeris tabulated the equation of time in the sense 'add or subtract (as directed) the number of minutes and seconds stated to or from the apparent time to obtain the mean time'. Times in the Almanac were in apparent solar time, because time aboard ship was most often determined by observing the Sun. This operation would be performed in the unusual case that the mean solar time of an observation was needed. In the issues since 1834, all times have been in mean solar time, because by then the time aboard ship was increasingly often determined by marine chronometers. The instructions were consequently to add or subtract (as directed) the number of minutes stated to or from the mean time to obtain the apparent time. So now addition corresponded to the equation being positive and subtraction corresponded to it being negative.

As the apparent daily movement of the Sun is one revolution per day, that is 360° every 24 hours, and the Sun itself appears as a disc of about 0.5° in the sky, simple sundials can be read to a maximum accuracy of about one minute. Since the equation of time has a range of about 33 minutes, the difference between sundial time and clock time cannot be ignored. In addition to the equation of time, one also has to apply corrections due to one's distance from the local time zone meridian and summer time, if any.

The tiny increase of the mean solar day due to the slowing down of the Earth's rotation, by about 2 ms per day per century, which currently accumulates up to about 1 second every year, is not taken into account in traditional definitions of the equation of time, as it is imperceptible at the accuracy level of sundials.

### Eccentricity of the Earth's orbit Edit

The Earth revolves around the Sun. As seen from Earth, the Sun appears to revolve once around the Earth through the background stars in one year. If the Earth orbited the Sun with a constant speed, in a circular orbit in a plane perpendicular to the Earth's axis, then the Sun would culminate every day at exactly the same time, and be a perfect time keeper (except for the very small effect of the slowing rotation of the Earth). But the orbit of the Earth is an ellipse not centered on the Sun, and its speed varies between 30.287 and 29.291 km/s, according to Kepler's laws of planetary motion, and its angular speed also varies, and thus the Sun appears to move faster (relative to the background stars) at perihelion (currently around 3 January) and slower at aphelion a half year later. [19] [20] [21]

At these extreme points this effect varies the apparent solar day by 7.9 s/day from its mean. Consequently, the smaller daily differences on other days in speed are cumulative until these points, reflecting how the planet accelerates and decelerates compared to the mean. As a result, the eccentricity of the Earth's orbit contributes a periodic variation which is (in the first-order approximation) a sine wave with an amplitude of 7.66 min and a period of one year to the equation of time. The zero points are reached at perihelion (at the beginning of January) and aphelion (beginning of July) the extreme values are in early April (negative) and early October (positive).

### Obliquity of the ecliptic Edit

Even if the Earth's orbit were circular, the perceived motion of the Sun along our celestial equator would still not be uniform. This is a consequence of the tilt of the Earth's rotational axis with respect to the plane of its orbit, or equivalently, the tilt of the ecliptic (the path the Sun appears to take in the celestial sphere) with respect to the celestial equator. The projection of this motion onto our celestial equator, along which "clock time" is measured, is a maximum at the solstices, when the yearly movement of the Sun is parallel to the equator (causing amplification of perceived speed) and yields mainly a change in right ascension. It is a minimum at the equinoxes, when the Sun's apparent motion is more sloped and yields more change in declination, leaving less for the component in right ascension, which is the only component that affects the duration of the solar day. A practical illustration of obliquity is that the daily shift of the shadow cast by the Sun in a sundial even on the equator is smaller close to the solstices and greater close to the equinoxes. If this effect operated alone, then days would be up to 24 hours and 20.3 seconds long (measured solar noon to solar noon) near the solstices, and as much as 20.3 seconds shorter than 24 hours near the equinoxes. [19] [22] [21]

In the figure on the right, we can see the monthly variation of the apparent slope of the plane of the ecliptic at solar midday as seen from Earth. This variation is due to the apparent precession of the rotating Earth through the year, as seen from the Sun at solar midday.

In terms of the equation of time, the inclination of the ecliptic results in the contribution of a sine wave variation with an amplitude of 9.87 minutes and a period of a half year to the equation of time. The zero points of this sine wave are reached at the equinoxes and solstices, while the extrema are at the beginning of February and August (negative) and the beginning of May and November (positive).

The two above mentioned factors have different wavelengths, amplitudes and phases, so their combined contribution is an irregular wave. At epoch 2000 these are the values (in minutes and seconds with UT dates):

## Tatooine's Two Stars? That's Cute&mdashThis System Has Five

Just about 250 light years from Earth, there's a most unusual and just recently discovered star system. We've found binary systems before &ndash that is, two stars orbiting each other. We know of triple star systems the Alpha / Proxima Centauri system is one such example. But the new system has five stars, which isn't completely unknown, but is exceedingly rare.

It was discovered by the SuperWASP program, which normally hunts for planets. A pre-print of the paper, just presented to the UK National Astronomy Meeting, is available on Arxiv.

The system involves two sets of binary stars. In one binary pair, the stars orbit around each other close enough to trade off gasses. The other binary has a little bit more room to breathe, with about 1.86 million miles of separation. This is smaller than the 35.97 million miles between the Sun and Mercury, and accounts for about the diameter of the sun plus a little extra padding. But it prevents the two suns from coming into contact.

Then there's the star that's off on its own. It orbits one of the other binary pairs, with all five on the same relative plane. There's roughly a distance of 13 billion miles between them. That's around 140 astronomical units. By comparison, Voyager 1 is now about 132 AU out and has traveled beyond our sun's heliosheath. So that's a pretty big separation.

This also means that, theoretically, a planet could safely exist in the system, as the stars aren't all gravitationally bound to one other. While it's unlikely to orbit the stars individually, planets that orbit both stars in a binary are known to exist.

The system, called 1SWASP J093010.78+533859.5, now joins the ranks of only a handful of other quintuple star systems. Of course, it could always grab a couple more and become a seven-star system.

## Cycles and Epicycles: Hipparchus and Ptolemy

A new way of combining circular motions to account for the movements of the sun, moon and planets was introduced by Hipparchus (second century BC) and realized fully by Ptolemy (around AD 150). Hipparchus was aware the seasons weren’t quite the same length, so he suggested that the sun went around a circular path at uniform speed, but that the earth wasn’t in the center of the circle. Now the solstices and equinoxes are determined by how the tilt of the earth’s axis lines up with the sun, so the directions of these places from the earth are at right angles. If the circle is off center, though, some of these seasons will be shorter than others. We know the shortest season is fall (in our hemisphere).

Another way of using circular motions was provided by Hipparchus’ theory of the moon. This introduced the idea of the “epicycle”, a small circular motion riding around a big circular motion. (See below for pictures of epicycles in the discussion of Ptolemy.) The moon’s position in the sky could be well represented by such a model. In fact, so could all the planets. One problem was that to figure out the planet’s position in the sky, that is, the line of sight from the earth, given its position on the cycle and on the epicycle, needs trigonometry. Hipparchus developed trigonometry to make these calculations possible.

Ptolemy wrote the “bible” of Greek (and other ancient) astronomical observations in his immense book, the “Almagest”. This did for astronomy at the time what Euclid’s Elements did for geometry. It gave huge numbers of tables by which the positions of planets, sun and moon could be accurately calculated for centuries to come. We cannot here do justice to this magnificent work, but I just want to mention one or two significant points which give the general picture.

To illustrate the mechanism, we present here a slightly simplified version of his account of how the planets moved. The main idea was that each planet (and also, of course, the sun and moon) went around the earth in a cycle, a large circle centered at the center of the earth, but at the same time the planets were describing smaller circles, or epicycles, about the point that was describing the cycle. Mercury and Venus, as shown in the figure, had epicycles centered on the line from the earth to the sun. This picture does indeed represent fairly accurately their apparent motion in the sky—note that they always appear fairly close to the sun, and are not visible in the middle of the night.

The planets Mars, Jupiter and Saturn, on the other hand, can be seen through the night in some years. Their motion is analyzed in terms of cycles greater than the sun’s, but with epicycles exactly equal to the sun’s cycle, and with the planets at positions in their epicycles which correspond to the sun’s position in its cycle—see the figure below.

This system of cycles and epicycles was built up to give an accurate account of the observed motion of the planets. Actually, we have significantly simplified Ptolemy’s picture. He caused some of the epicycles to be not quite centered on the cycles, they were termed eccentric. This departure from apparent perfection was necessary for full agreement with observations, and we shall return to it later. Ptolemy’s book was called the Almagest in the Middle Ages, the Arabic prefix al with the Greek for “the greatest” the same as our prefix mega.

## What do the stars have in store for NASA?

Currently the planet Uranus is slap-bang on NASA’s natal Moon. The planet of innovation, invention, upheavals and revolutions could be hitting NASA’s funding or structure, but also lead to big breakthroughs and discoveries. What NASA was involved in 19 years ago is going to come full circle as the North Node swings back through Gemini and the South will hit NASA’s Saturn in Sagittarius.

In roughly two years’ time the North Node will reach NASA’s natal Mars. Watch for big, bold leaps forward at this point. This could kick-start a new cycle of exploration and discovery. In fact, Mars could be the destination for this.

There we go NASA. A free prediction for you. Only time will tell how correct it is. But seems just like in the old days, when we examine the data, astronomers and astrologers aren’t light years apart after all.