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Let's say that another earth popped into existence in our solar system on the exact same orbit around the sun as our earth. Say it is exactly opposite to the earth in the orbit. How would this new planet effect our earth?
Also how would this scale to many earths evenly spread along our orbit?

A Lambent Eye
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AbsurdHero
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    You might try Googling for "Planet X" as this has been a favorite subject of folks who are either naive astronomers or conspiracy nuts. But your idea of putting a bunch of planets in the orbit (not at all like electrons) is more interesting. Their gravitational fields will interact, so it would have to be a system built purposely -- by comparison the asteroid belt will collapse into separate objects over sufficient time. – Carl Witthoft Sep 26 '19 at 14:48
  • Welcome to the Worldbuilding Stack Exchange! Currently your question is not phrased very clearly and is in danger of being closed. Please distinguish between the orbit of the planets around the sun (the path the planets take), the orientation of the earth's axis (how tilted the earth is in comparison to it's orbit) and the rotation of the earth (how fast and in which direction the earth is spinning around it's own axis, i.e. a day). Also take note that electrons are not equally spaced around the nucleus and that the earth's orbit is not a perfect circle, but en ellipse. – A Lambent Eye Sep 26 '19 at 14:52
  • @MorrisTheCat I disagree, since the possible duplicate focuses on the astronomical discovery of this other planet, whereas this question focuses on the astrophysical implications of this planetary arrangement. – A Lambent Eye Sep 26 '19 at 15:12
  • @ALambentEye the questions are different, but the content in the answers to the thread I linked speak pretty directly to the OP's question. – Morris The Cat Sep 26 '19 at 15:38
  • I think that kingledion's answer would be more to the point here. – Alexander Sep 26 '19 at 16:41

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Adding one Earth-like planet on the opposite side of the Sun from Earth would have very little immediate effect, since the mass is negligible compared to that of the Sun (about three parts in a million). It would have some very minor, but measurable effects on the Earth's orbit, maybe making the year a second or so shorter. Over time, however, the two Earths would cease to be in exactly the same orbit due to influence from other planets, and one would have a slightly faster orbit and eventually catch up to the other. They would probably not crash, but swap orbits like the Saturnian moons Epimetheus and Janus. The close passage would however create strong tidal effects and likely rip our moon loose from its orbit.

Adding more planets would make the above happen faster, and the orbit-swapping would be more complex, with the possibility of eventually having three or more planets passing each other closely, with complicated and possibly orbit-disrupting effects.

It is, however, possibly possible to have another Earth appear near 30 degrees forward or backward in the Earth's orbit, where the two planets would be in each other's Lagrangian points L4 and L5, which are (fairly) stable. You would have to compensate for some initial gravitational effects, though.

In response to a comment that such a system might be unstable, since the mass of the second Earth isn't negligible, I offer Gascheau's Stability Condition:

For a system of three bodies of mass m0, m1, and m2 circularly orbiting a common center of mass to be stable, their masses must fulfil the following requirement:

(m1 + m2 + m0)^2/(m1 · m2 + m1 · m0 + m2 · m0) > 27

Making m0 the mass of the Sun and knowing that the masses of the two Earths, m1 = m2, are negligible compared to the sun, this reduces to m0^2/2m0 · m1 > 27 or simply m0 > 54 · m1. Given that the Sun is far more than 54 times heavier than the two Earths, the system easily fulfils the requirement.

You can read about Gascheau's Stability Condition and how it is derived in the online paper "An Examination of the Mass Limit for Stability at the Triangular Lagrange Points for a Three-Body System and a Special Case of the Four-Body Problem".

Klaus Æ. Mogensen
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  • For L4 and L5 Lagrangian points to be stable, the objects within them need to have a substantially less mass than the larger object (in this case Earth). – overlord Sep 26 '19 at 15:00
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    "swap orbits" is a good way to put it - it sound tidy. Folks on either planet who like an atmosphere or a good biosphere will, of course, find the swap process to be quite catastrophic and un-tidy, but the question didn't ask about them. – user535733 Sep 26 '19 at 15:33
  • @overlord: That is incorrect. In this case, the larger body is the Sun, not the Earth. Two small bodies can be in each others' Lagrangrian points around a much larger body. Gascheaou's stability condition for a three bodies circularly orbiting a common center of mass is that (m0 + m1 + m2)^2/(m1 · m2 + m1 · m0 + m2 · m0) > 27. Given that the mass of the sun (m0) is much higher than the two planets (m1 = m2), this reduces to m0^2/2m0 · m1 > 27. So as long as the sun is 54 times as heavy as the planets (and it is far more than that), the system is stable. – Klaus Æ. Mogensen Sep 27 '19 at 08:03
  • Link to a paper explaining the above: https://scholarworks.sjsu.edu/cgi/viewcontent.cgi?article=8093&context=etd_theses – Klaus Æ. Mogensen Sep 27 '19 at 08:04
  • @user535733: Epimetheus and Janus never get closer than 15.000 km to each other, though their orbits differ by only 50 km. Given the far larger sizes of two Earths, the pass-by distance will likely also be far larger, enough to create strong tidal effects, but not enough to rip out the atmosphere. That would require getting within the Roche limit. Our moon's orbit, however, would be in trouble. – Klaus Æ. Mogensen Sep 27 '19 at 08:08