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In a short sci-fi story i am writing, Earth has a shadow twin. A planet with the same chemical/geological characteristics as Earth and wildlife very similar (but different species because evolution and mutations are random).

The humanity in Earth-prime XXI century knows of the shadow twin existance, but I am having difficulty in pin-pointing when it became common knowledge.

So, the technical stuff:

Same planetary masses. The Shadow-Earth, Earth and the Sun orbit each other using the Figure-Eight orbit. This is not tagged , so lets do a minor hand-wave on the orbital issues, and assume the figure eight three body orbit really works.

Also, if you know of any works of fiction dealing with this setup, please state in your answer or leave a comment. thanks.

Keeping the suspension of disbelief as low as possible, in a sci-fi setting on our Earth, when is the historical earlier I could place the "discovery" of the existance of Earth-Shadow? Renaissance? Ancient Egypt/Greece? Space Race? Victorian period?

Mark
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Mindwin Remember Monica
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    We would need to know more about your alternate universe. In order for an orbit at L3 to be stable, you would either have to have (a) somewhat different laws of physics to keep the object at L3 or (b) make sure there are no other massive bodies in the solar system to kick the planet out of L3. What is keeping shadow Earth at L3? – browly Apr 18 '16 at 19:36
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    Generally speaking we first knew that some planets our solar system existed not because we observed them, but because their presence was throwing off other measurements and predictions. In other words the existence of Shadow Earth would probably be predicted before we could go there/see it. – AndreiROM Apr 18 '16 at 19:42
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    For some of the issues to be had with parking a planet at the Earth/Sun L3, see this question: http://worldbuilding.stackexchange.com/questions/21479/making-a-counter-earth/21491 But, I'll see if I can put an answer together assuming it was stable anyway. Also, how do you define 'Common Knowledge.' Because early scientists knew a lot about our solar system long before the common person did. – guildsbounty Apr 18 '16 at 19:43
  • @browly changed the orbital pattern. thanks a lot. L3 is not stable indeed. – Mindwin Remember Monica Apr 18 '16 at 19:54
  • As AndreiROM stated, we would most likely notice a planet we can't see because of its gravitational effects on other planets, but your question requires that we alter how gravity works. This makes it hard to answer. – browly Apr 18 '16 at 20:09
  • That 3-body orbit doesn't work for the Earth, Shadow-Earth, and the Sun. The three bodies are orbiting around a common center of mass, all three bodies have to have the same mass. "We consider three bodies of unit mass...". – Schwern Apr 19 '16 at 17:48

2 Answers2

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Since none of these orbits work it's hard to say when an impossible planet would be discovered. I'll instead go through when we could disprove the existence of a Shadow Earth. At any of these points you can alter how your universe functions to turn it from evidence against to evidence for.

In a figure eight orbit, or any other orbit that doesn't put it on the other side of the Sun, the Shadow Earth would be visible to the naked eye in the night sky, like any other classical planet, as a "wandering star". However, this orbit does not work in an Earth/Shadow-Earth/Sun system. For that system to work the three bodies must have the same mass; they're orbiting their common center of mass. It is also unstable in the n-body problem which is our Solar System.

Counter-Earths have been proposed for thousands of years, usually hidden on the other side of the Sun. Since the L3 point (the point opposite the Earth on the other side of the Sun) is not stable, especially with Venus and Mars tugging at it, this cannot exist. We know this through indirect and direct observations.

Earth's elliptical orbit also makes this configuration impossible. Since the Earth's orbit is not circular, the L3 point opposite the Sun moves around. This would make the Shadow-Earth even less stable, and it would allow it to peek out from behind the Sun twice a year. We've known orbits are elliptical since the early 1600s.

Such an object would also have its own gravitational effects on Venus and Mars and other objects in the inner solar system. These would be detectable as soon as astronomical observations were sensitive enough. For example, it was noticed that the precession of Mercury could not be explained by Newtonian gravity in 1859 which became one of the tests of general relativity. Mercury is rather hard to observe, being very small and very close to the Sun, so the changes to the orbits of Venus and Mars would be noticeable sooner.

Direct observation to refute this idea came in the 1960s when we started putting satellites in heliocentric orbits (ie. orbiting the Sun).

Schwern
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Since you're now working with a Figure-8 orbit, it's easy. In the orbit, there will come a point where Earth-Prime, Earth-Shadow, and the sun are in a line with each other. Here is the paper from the link you referenced; see how the bodies not only align, but align in changing orders? That's the key. People will notice that every [so often] there's another planet that goes through the night sky. It would probably take the development of calculus (or maybe even computers) to actually figure out the orbit, but people would know that the planet exists from ancient times, just as they knew of most of the other planets.

As far as references in fiction, it's not the Figure-8 orbit specifically, but the idea of a Counter-Earth was a relatively common one in the early-mid 20th Century.

John Robinson
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