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Imagine two identical planets planet A and planet B, orbiting the same star.

Is it possible that these two planets follow the exact same "route" as they orbit their sun, but are just distant enough from one another, that their star is effectively always between the two, so that a hypothetical person sitting on planet A would not be able to see planet B due to it being behind the star?

Sample drawing of the orbit (proportions gloriously inaccurate)

I assumed, based on the limited knowledge I have on the subject, that all star systems have ellipsoidal orbits (the star being in one of the two focal points) just like our own.

If I'm wrong, though, and perhaps a stellar system with circular orbits is possible (and I assume it would make my idea more feasible) please do point it out.

If this is at all possible, what are the "requirements" to make it work?

Note that this doesn't necessarily have to last indefinitely (e.g. maybe the orbit screws itself up after, say, 1000 years)

Also, what is the approximate minimum level of technology that a civilization inhabiting planet A would need to have good chances of finding out about planet B's existence?

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  • $\begingroup$ Comments are not for extended discussion; this conversation has been moved to chat. $\endgroup$ – James Jan 25 '18 at 18:04

12 Answers 12

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I assumed, based on the limited knowledge I have on the subject, that all star systems have ellipsoidal orbits (the star being in one of the two focal points) just like our own

You are right, this is one of Kepler's law, the first. Another one, the second, states that the line connecting the star and the planet swipes equal areas in equal times, or, to put it in picture

Kepler's law picture

As you can you see from the image, when one of the two planets is in the "slower" region, the other will be in the "faster" one, meaning that the apparent alignment between the two planets and the star won't last too long. Let's assume for simplicity that the area is covered in one month. One planet will see the other planet disappear for a fraction of that month, and the it will appear again in the sky.

The only way to escape this is to have perfectly circular orbits (at the end, a circle is just an ellipse with eccentricity = 0 ) if you approximate the star as a point in the sky.

Taking into account the apparent size of the star in the sky, if the orbit is not excessively eccentric and the planets orbit not too far from the star, it is still possible that they are constantly hidden from each other, with the star continuously covering the view line.

In this case, to find out the existence of the other planet, it is probably needed to have the capability of sending satellites out of the orbital plane, to look at the stellar system from above (or below).

It is also possible that relativistic bending of the light close to the edge of the star can make the planet visible during eclipses, when its apparent position in the sky is close to the edge of the star itself.

Though I doubt such a system would be stable over the time span needed for such a civilization to evolve.

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  • $\begingroup$ Comments are not for extended discussion; this conversation has been moved to chat. $\endgroup$ – James Jan 25 '18 at 18:04
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Circular orbits are not practically possible

From Astronomy.SE, there are a variety of reasons why orbits are not circular. There is relativity, there is planetary flexing with gravity, there is unequal radiation from the planet's surface (the sunny side reflects and radiates more energy into space, generating net thrust). Then there are the effects of any other planets. Having a Jupiter around pretty much ensures that no other planet will have a circular orbit.

If the orbits are not perfectly circular, then the planets would periodically be able to see each other.

Formation on of planets in 'opposite' orbits is not possible

Notwithstanding the fact that the orbits won't be circular anyways, if two co-orbital planets were able to form, they would form as Trojans of each other, not opposites. Trojan planets exist in the same orbit where each planet would be in the other planet's L4/L5 Lagranian points, off by 60 degrees. I don't believe any Trojan planets have been discovered yet, but there are computer simulations of Trojan formation and stability out to a billion years (e.g. Cresswell and Nelson, 2008)

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    $\begingroup$ I don't understand the second part of your answer: in the heading you say that 'opposite' orbits are not possible, but then in the paragraph you say that there are computer simulations of trojan formation and stability out to a billion years. What do you mean? $\endgroup$ – Hankrecords Jan 19 '18 at 20:10
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    $\begingroup$ @Hankrecords Hopefully that is clearer. Trojan planets are not opposite each other, they are in each other's L4/L5 spots, so they are off by 60 degrees. $\endgroup$ – kingledion Jan 19 '18 at 20:21
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    $\begingroup$ @Hankrecords For reference, Lagrange points 1, 2, and 3 are "peaks" or "ridges" while L4 and L5 are "valleys." Resting a ball on a peak isn't stable, even though there's 0 net change due to gravity, but as soon as any other force nudges the ball off the perfectly balanced tip, it rolls away. Whereas in a valley, perturbations won't shift it out of orbit, because they'd be pushing the ball uphill: it'll just roll back down again. As for the word "trojan," it has to do with celestial naming. en.wikipedia.org/wiki/Trojan_(astronomy) $\endgroup$ – Draco18s Jan 19 '18 at 20:25
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    $\begingroup$ Earth's orbit is very close to circular. $\endgroup$ – jpmc26 Jan 19 '18 at 23:57
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    $\begingroup$ @kingledion Nonsense. All of physics relies on close counting. And in particular, if there's a close to circlular orbit that would prevent a body on the opposite side of the star from being detected, that would probably be just fine with the OP. I haven't checked if that's possible, but the idea that the elliptical nature of planetary orbits automatically rules the question's scenario is pretty off base. $\endgroup$ – jpmc26 Jan 20 '18 at 3:09
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Second opinion: Yes, this is possible

But King! You posted another answer saying it wasn't possible. Well, for a two planet system, I argue that it is not, in fact, possible. But remember what I said about Trojan planets, they have to be 60 degrees apart in each other's L4/L5 points.

So the solution is: twelve planets! Put six planets in one orbit, and have each of the six be a Trojan of the two planets on either side of each other. Then, add another six planets that are either larger or smaller in a more or less distant orbit. This 'rosette' configuration can be stable with a sun in the center of it.

A lot of the problems that I mentioned in my previous post with circular orbits actually dissipate in this case as well; instead of just being in orbit around the sun, the twelve planets are constantly correcting each other's orbits to maintain the Trojan positions. The effects of radiation are balanced out by the several planets all at different orientations to the sun.

Now, this setup seems incredibly unlikely to happen naturally, so we will have to assume that this is an artificially created solar system. So in this case, the Progenitors will remove everything from the solar system, build twelve planets of two masses and set them around the sun in perfectly circular orbits. That system should be stable for a few million years at least.

So an ancient astronomer on any of the world's will see ten other worlds, but not the eleventh, opposite world. As far as discovery of the last world, well the first person to make a heliocentric model of the solar system would probably have a good idea that there is a missing planet hidden behind the sun, just due to symmetry. I argue that Ptolomey's spheres would make no sense in this kind of system, so the heliocentric model would probably be accepted by Ancient Greek times if not earlier. If that didn't happen, the mathematics of Lagrangian points were published in 1772; so by that time there should be proof that there needed to be a twelfth planet in order for orbits to be stable.

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    $\begingroup$ "the six planets are constantly correcting each other's orbits to maintain the Trojan positions" [citation needed]. Trojans work with the typical mass hierarchy $m_{Trojan} \ll m_{Planet} \ll m_{Star}$. I'm pretty sure with 6 equal mass planets one would have an instable system. With 6 unequal mass planets the project is doomed anyway. $\endgroup$ – AtmosphericPrisonEscape Jan 19 '18 at 22:59
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    $\begingroup$ A Klemperer rosette is unstable, though the six-body rosette is the least unstable of the options. Incidentally, they can't be of equal mass: you need three "heavy" planets and three "light" planets. $\endgroup$ – Mark Jan 20 '18 at 0:19
  • $\begingroup$ @Mark I read the relevant paper, Some Properties of Rosette Configurations of Gravitating Bodies in Homographic Equilibrium. Firstly, the calculations do not imply instability. Secondly, there are several solutions involving elliptical orbits and an oscillating sun at the barycenter. Finally, "rosette configurations are capable of rotary equilibrium and periodic motion." I did refine my position to match the information in the paper. $\endgroup$ – kingledion Jan 20 '18 at 3:04
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    $\begingroup$ Funny thing: this is also impossible due to the "definition" of a planet: A planet has to has to clear it's neighbourhood from similar sized objects (making its gravity dominant in it's orbit). -- This has all to do with stability as @AtmosphericPrisonEscape explained. $\endgroup$ – paul23 Jan 20 '18 at 13:38
  • $\begingroup$ I couldn't accept this as the answer because twelve planets isn't really what I was going for, but it's a really cool idea nonetheless. Thank you! $\endgroup$ – Hankrecords Jan 24 '18 at 8:25
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If you are prepared to be less strict, there is a configuration that can mask two co-planar satellites from each other:

enter image description here

Satellites are not in the same orbit. But they are in the same plane. The orbits could be elliptical as much as you want, but they maintain a symmetry: The periapsis/apoapsis are directly opposite at each side of the star.

This makes the two satellites maintain the same orbital velocities at the same time, and avoids being seen. Planets can also be slightly different in mass, but the orbits will have to be exactly the same size. I don't know a lot about orbital mechanics to determine if the two orbits will also precess in the same rate. If they do, the configuration can last indefinitely.

Admittedly, this sort of system is very improbable to form in the nature. But I guess this is a very good chance to use the artistic license.

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  • $\begingroup$ One thing that makes this more improbable is that the presence of any other large body in the system (a Jupiter) would inevitably induce an asymmetry. But! Life could evolve during the period in which the orbits were as you suggest, even if they were not symmetric before or after. $\endgroup$ – Phil H Jan 22 '18 at 11:03
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    $\begingroup$ @PhilH: That is possible. Then again, the orbits need not to be symmetric over billions of years. It would be enough to have the symmetry for 2000-5000 years in which the civilization is advanced enough to keep records of stargazing. :) $\endgroup$ – sampathsris Jan 22 '18 at 12:17
  • $\begingroup$ Yes, exactly. Also, it seems likely that life would evolve during a period of stability rather than one where frequent near misses induced volatile environments. $\endgroup$ – Phil H Jan 23 '18 at 14:08
  • $\begingroup$ So this is improbable, but is it at all possible? I thought all planets in a system had the star in roughly the same focal point of their orbital ellipsis $\endgroup$ – Hankrecords Jan 24 '18 at 8:14
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    $\begingroup$ @Hankrecords: An ellipse has two foci. In any set of orbits, one focus will coincide with the star. There is no rule to make other focus to lie in the same direction for all orbits. In fact, aphelions of different planets lie in different directions. $\endgroup$ – sampathsris Jan 24 '18 at 8:44
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You are talking about the Counter Earth Theory first proposed by Philolaus (c. 470 – c. 385 BC).

While mathematically possible, the statistical liklihood of it occuring naturally are so remote as to be sensibly described as impossible. Note also that the orbit is intrinsically unstable as you can never have perfectly balanced gravitational forces. Eventually something would change, and then it would fall apart.

A short answer, I know, but I'm being called away. My apologies.

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No.

To be able to "never see each other" (sort of like the twin worlds of Beta and Delta) they'd need to be on an almost circular orbit, or you would get a libration effect making one planet "peek" behind the star at the other every year. If the planet wanders too far from the star, it becomes visible (otherwise, it could not be seen against the glare of the star).

But you couldn't have just two planets - that configuration is too unstable.

Granted that there are no stable configurations, you could do something with a Klemperer's Rosette. Each planet only sees four others, but opposite planets are not identical.

To beat the instability, you'd need some kind of force keeping the planets apart, but it would need to act only on the planets, and be stronger (at that distance) than gravitation. In that case you would not need a rosette to keep things stable. Electric charge would seem a feasible candidate, but it actually isn't.

To discover the other planet, the inhabitants of either of them would need space probe technology - they need something to go out and get a look back. Mathematically, they might deduce it from the orbits of other planets.

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  • $\begingroup$ As far as we know most planets (earth included) have a almost circular orbit! I know orbits are eliptical but has you checked actual eccentricit? Earth 0.0167, Venus 0.0068. Of course to have two planets of equivalent mass in the same stable orbit circulating a big (red nova maybe) star is unlikely $\endgroup$ – jean Jan 19 '18 at 22:53
  • $\begingroup$ @jean A significant fraction of detected exo-planets have non-trivial eccentricities. Our solar system may be unusual in having so nearly circular orbits. $\endgroup$ – dmckee Jan 20 '18 at 21:17
  • $\begingroup$ @dmckee Exoplanets are detected mainly because orbit pertubations they cause on his sol. Little planets don't disturbing his star, like earth, cannot be detectec by current tech $\endgroup$ – jean Jan 21 '18 at 10:03
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Is it possible? Yes, why not. Will there always be Sun in the way? No or at least not for Earth or any planet in our system. Does it matter? No and here is why.

I simplified a few things, I'm using Kepler Laws (assuming elliptical orbits and none interference from other bodies) and round some things and completely disregard relativity. Relativity would not play that big role anyway, becasue the time lag to the other planet would be about 17 minutes for light.

I ran the calculations for Earth and assuming we would be at aphelion (farthest from sun) when the other planet were at perihelion (closest to sun), the sun would not be in our way to see each other for some portion of the year (here is where the calculation gets complicated because of calculation of areas of parts of ellipses, but there could be some iterative ways to calculate it. It is not the main point of the question so I won't).

Somewhere in mid-spring/mid-fall (best day would be the fall solistice or two days after or during the spring solistice or two days before, because two days are about the time difference between exactly half orbit of our ellipse on aphelion and perihelion halves) when you would look up, you would see the planet. Except you would have to look up at day. And the planet would be about one degree from the sun. In astronomy one degree is often approximated by outstretching your hand and extending your pinky. That's about the distance you would be able to see the planet from the sun.

Now that all was based on Earth, which has eccentricity of about 0.0167 and because of our distance to sun the distance between the two foci of our orbit are about 5 million kilometers apart. But let's take a look at a different planet of our system, Venus.

With eccentricity of only 0.0067 and considerably smaller orbit, its foci are only about 1,4 million kilometers apart, which is about the diameter of Sun (it's important to point out that Sun's center is in one of the foci, so the Sun almost touches the center of Venus' orbit). That would mean that when the Sun would not be directly in the way, it would be so close that it would not mostly matter and the path would be there for only brief time, about 12 hours if we make some approximations.

That would mean there would be a window for 12 hours twice a year in which you would have the chance to see the other planet, assuming you have some means to completely shut out the luminosity of the Sun. Based on our civilization, we would probably find our neighbor by accident when investigating other places in our Solar system, which gets us to another rather interesting astronomical phenomenon and that is...

Lagrangian points. Those are basically five points where in a system of two large bodies (e.g. Sun and Earth) a small enough object stays stationary or orbits around the Lagrangian point (see Halo orbits). Yes you guessed it, the third one is exactly oposite to the smaller object behind the bigger (for Sun and Earth it would be exactly your scenario).

The drawback is the great instability of the third point and the size of the objects, we know about some, but for Earth they are usually asteroids of size about 1 km or smaller. I have not heard about a planet forming in a Lagrangian point of another one, but then again, I've never researched that, but it would surelly mean that one of them would be a giant and the other a dwarf. And it is important to note here, that the two bodies would actaully not share the exact same orbit, so it would not hold for this question either.

All in all, it would be possible and for it to happen there are three main parameters: the planets' eccentricity, the stars diameter and the planets' orbital distance to the star.

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  • $\begingroup$ "there would be a window for 12 hours twice a year in which you would have the chance to see the other planet" interesting, but not "never". Making your own artificial solar eclipse by putting a suitably-sized disk in front of your sun-viewer would make the contra-planet visible. $\endgroup$ – RonJohn Jan 21 '18 at 2:06
  • $\begingroup$ yes, for Venus the planet would be visible with the right technology. But if we had a planet that orbited closer/with smaller eccentricity or we had a bigger Sun, it would be possible $\endgroup$ – Ordoshsen Jan 21 '18 at 13:24
  • $\begingroup$ Of course, there would be no intelligent life (and probably no life at all) in such a scenario. $\endgroup$ – RonJohn Jan 21 '18 at 16:48
  • $\begingroup$ thats hard to tell cause we know of only one planet that has life so we really have no idea what conditions must be met. And we know even less about conditions for evolving intelligent life. Eccentricity would probably not affect it at all so planet like that probably could exist even with conditions for Earth-like life $\endgroup$ – Ordoshsen Jan 21 '18 at 20:01
  • $\begingroup$ We "know" very little, but we can make damned accurate guesses based on chemistry and physics. (Which is why "search for life on Mars continues!" makes me so sad.) $\endgroup$ – RonJohn Jan 21 '18 at 22:35
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If two planets were in this configuration, they might stay stable for a time, possibly even as long as the thousand years that you need. But there's no way for them to get into this configuration, since if they had such similar orbits then they would billions of years ago have interacted in some way that would either have resulted in a collision or a drastic change of orbit for one or both of them.

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The Condon Report (1968) had an appendix that investigated the possibility of an antichthon in Earth orbit. Please note an "antichthon" is essentially a Counter-Earth. They concluded that an antichthon could not remain completely hidden. by the Sun, as there would be times in the orbital periods of two planet -- Earth and the Counter-Earth -- when each would be visible to the other.

This finding about planets sharing the same orbit was an incidental full note in their deliberations, but it was nice to discover that the topic of antichthonal planets had been researched.

A copies of the full Condon Report or going by its formal title of Scientific Study of Unidentified Flying Objects can be found here and here

In conclusion, could two planets follow the same orbit and never seen see each other? No. There will be times when both planets will be visible to each other. .

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No

If the orbits are highly elliptical, then as one planet moves near the sun it speeds up, and the sun doesn't stay between them.

What if the orbits are nearly circular?

Still no. Orbits with two point sized bodies are elliptical. Real orbits around the sun, with two or more planets are nearly elliptical, but actually they are perturbed by the gravity of the other planets. If two planets are in orbit about the sun, then there is not only the gravitational between the planet and the sun, there is also the much smaller gravitational attraction between the planets. Over time this will tend to move the two planets out of sync.

What about Lagrange points?

There are 5 points that (ignoring other perturbations) could allow for another body to orbit the sun with the same period as the Earth. Two are close to the Earth. L1 is between the Earth and the sun L2 is opposite the sun. L3 is just where you want your "counter-earth" to be, unfortunately L3 is unstable. To remain at L3 requires "station keeping". L4 and L5 are 60 degrees from the Earth-sun axis. They are pseudo-stable, provided the other body is small enough. An Earth-sized planet could not orbit at L4.

What if the planet was put in exactly the right place

Placing a body exactly at L3 won't work, because there are lots of other perturbations that will shift it a little from L3, and then Earth's gravity will work to move it further and further from L3, until it becomes visible.

The number of types highly stable orbits that are possible is (unfortunately) rather limited. You can have planets going around a star in well-separated orbits. You have moons. You are allowed circumbinary orbits. Interesting orbits like those of Saturn's moons Janus and Epimetheus are not stable for long enough for life to develop.

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The planets could orbit each other and each have an opaque cloud layer in their atmosphere; that's about the only way I can think of for this to be made possible. (Barring a Big Beautiful Wall in space)

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  • $\begingroup$ Welcome to Worldbuilding! It's true that this would mean the planets couldn't see each other, but could you explain how they wouldn't be able to see each other due to being "behind the star"? $\endgroup$ – Mithrandir24601 Jan 19 '18 at 21:18
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Of course it is possible

Many other answers are trying to deal with the 3 body system.

But if both your planets have a neglectable mass, any "simple" orbit is stable.

It is difficult to explain how such a system could come to existance, but if you have 1 massive sun and 2 dwarf planets (moon size) orbiting 10 UA (near circular orbit) from the sun they can be stable for billion of years. Simply because for each of them, this is extremely close to a 2 body system.

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