Would two Earth-like planets on opposite sides of a Sol-like star at about 1 AU be a stable configuration?

Question

Would two Earth-like planets on opposite sides of a Sol-like star at about 1 AU be a relatively stable configuration? I understand that there are tadpole-like orbits and the two planets may not stay exactly opposite each other, but oscillate around those position.

But given perturbations from other planets, say a Jupiter-like one at say 5 AU, might they eventually crash into each other, or would one end up moving to a higher orbit and the other to a lower orbit?

@MikeG rather than have the question closed, I've modified it to stay on-topic. — uhoh, Sep 12 '19 at 15:34
Note, some probes already checked, what is on the other side of the Sun. The answer is: nothing. Just empty space. Interplanetar gas. Nearly empty vacuum. — peterh, Sep 12 '19 at 16:04
@peterh that reminds me! Why would Hollywood's Planet X (at earth's L3) be unstable?. Also see Have any co-orbital exoplanet pairs been discovered (and not subsequently retracted)? as well as In “The Man from Planet X” was Planet X ever directly behind the sun w/ same orbit as earth? and while we're at it, Wikipedia's Co-orbital configuration — uhoh, Sep 12 '19 at 16:23
@peterh Sorry, I didn't realize it was a dupe, I searched and didn't find anything. Sorry this was outside my area and didn't know, I will delete
Nevermind can't delete, sorry — throwaway, Sep 12 '19 at 17:56
I don't think it's a duplicate. A modified version of your original question would be OK. — Mike G, Sep 12 '19 at 18:13
Still was wrong place for question as was hypothetical, I should have done more research before posting, my apologies — throwaway, Sep 12 '19 at 18:16
Possible duplicate of Have any co-orbital exoplanet pairs been discovered (and not subsequently retracted)? — peterh, Sep 12 '19 at 20:48
@throwaway don't worry too much. Some more info: 1) to be considered a duplicate your question would have to be answered there, 2) it takes five votes to close (vtc) to put the question on hold, 3) there's nothing wrong with an occasional question being closed. In this case it would have been hard for you to have found a question about co-orbital planets not knowing the specific term ahead of time. 4) Don't be hasty to delete things unless they start collecting down votes. When an answer is posted, it becomes nearly impossible to delete a question. Welcome to Stack Exchange! — uhoh, Sep 12 '19 at 22:35
This is a useful question with a clear, useful answer, it makes a worthwhile addition to our site library and it’s certainly not a duplicate of the other Astronomy.SE question. It should neither be closed nor deleted! :-) — Chappo Hasn't Forgotten, Sep 12 '19 at 23:11

score 5 · Answer 1 · answered Sep 12 '19 at 16:31

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It would not be a stable configuration, but it wouldn't be too far from the stability.

The are 5 points where a third body could have a semi-stable orbit in a 2-body system:

The Earth is the blue point. The "anti-Earth" on the other side would be in the third Lagrange point ($\rm{L}_3$).

However, this is not a stable orbit. Any small deviation, including the effect of possible fourth bodies, would change the system so, that it results yet more deviation. Only $\rm{L}_4$ and $\rm{L}_5$ are stable, and even this has some requirements (the third body can be at most $\approx$ 3.5% of the second).

Corresponding this, the space on the other side of our Sun was examined by some space probes already, and there is nothing.

answered Sep 12 '19 at 16:31

peterh

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Sorry this was a duplicate question, thank you for answering though. – throwaway Sep 12 '19 at 18:02
@throwaway No, it is not a really dupe - only one of the questions cited by uhoh are on this site, this: https://astronomy.stackexchange.com/q/16239/1891. It could be an original candidate. There are no cross-site dupes in the StackExchange model. If you are not sure that it would be a dupe, a possibility is that you initiate its closure as dupe. But, only posting a dupe is not a big problem (if the post is voted up). Don't remove the post, just close as dupe. I rollbacked your edition. – peterh Sep 12 '19 at 20:51
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Perhaps worth noting we also examined L4 and L5 and DID find something in L4, 2010 TK7. – Maury Markowitz Sep 18 '19 at 10:36

Would two Earth-like planets on opposite sides of a Sol-like star at about 1 AU be a stable configuration?

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