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Setup:

We are in a alternate timeline where there is a Counter-Earth that always stays perfectly on the exact opposite side of the Sun from our Earth. It has about the same size and mass as our planet, but is lifeless. It doesn't have a moon.

Everything that happened on our planet historically goes down the same way, i.e. the effective point of departure from our timeline is the discovery of Counter-Earth.

Question:

Roughly in what year would scholars first start suspecting Counter-Earth exists? When would its existence be proven? What tools would be used to do so?

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    $\begingroup$ Not quite a duplicate, but a number of questions have covered counter-Earths and the discovery thereof: worldbuilding.stackexchange.com/questions/8651/… worldbuilding.stackexchange.com/questions/40225/… worldbuilding.stackexchange.com/questions/21479/… worldbuilding.stackexchange.com/questions/102685/… $\endgroup$ – Mark Mar 11 '18 at 8:16
  • $\begingroup$ It's probably worth reading about the Stability of the Solar System and that page summarizes some studies made into just how small a starting difference can result in huge differences over geological time scales. $\endgroup$ – StephenG Mar 11 '18 at 8:23
  • $\begingroup$ Probably when we actually get people in space or when we start sending probes nearer the sun. $\endgroup$ – skout Mar 11 '18 at 14:09
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    $\begingroup$ I am not sure you are asking the right question. Really, doesn't it amount to 'When was it discovered by our world that there was NOT another planet at the far Lagrange point L3? Such a planet has been hypothesized throughout Human history, at least since the concept of our solar system developed. We did not prove it's existence, but we did prove its non-existence. At this point, what if we had proven the opposite? $\endgroup$ – Justin Thyme Mar 11 '18 at 14:13
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    $\begingroup$ @JBH, I may have expressed myself imprecisely. As things stand the planet is impossible. The OP must change something (or introduce something). I have suggested magic and alien ACS. The how the planet is there will perforce influence how it's discovered, and therefore when (that is why I've upvoted James K's answer and yours, but not RonJohn's). I do know that "my job is to answer the OP's question"... I was merely stating why I felt I was unable to do my job. $\endgroup$ – LSerni Mar 11 '18 at 16:51
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As soon as we started closely observing the sky.

https://en.wikipedia.org/wiki/Counter-Earth#Scientific_analysis

The gravitational forces of the other planets on a Counter-Earth would make its orbit unstable. Venus has 82% of the mass of Earth and would come within 0.3 AU of the location of a Counter-Earth every 20 months, providing considerable gravitational pull that over the years would move its orbit into sight of observers on Earth.

EDIT: adding @a4android's excellent comment clarifying my answer

What RonJohn is saying is that a Counter-Earth won't remain perfectly on the opposite side of the Sun. This will have happened, possibly, billion of years ago. The Counter-Earth would keep being seen as a star almost as bright as Venus & close to the Sun quite often. The ancients would know it was a planet.

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  • $\begingroup$ What RonJohn is saying is that a Counter-Earth won't remain perfectly on the opposite side of the Sun. This will have happened, possibly, billion of years ago. The Counter-Earth would keep being seen as a star almost as bright as Venus & close to the Sun quite often. The ancients would know it was a planet. $\endgroup$ – a4android Mar 11 '18 at 11:28
  • $\begingroup$ There is nothing in the OP question that indicates the solar system has to mimic our own, except for the location of this alternate earth. There is nothing in the question that demands that Venus exists. In fact, Venus could BE this other planet, perhaps, with just a bit of handwaving in the formation of our solar system. $\endgroup$ – Justin Thyme Mar 11 '18 at 14:23
  • $\begingroup$ For the effects of Venus instability (or actually any gravitational instability whatever the cause), see e.g. farside.ph.utexas.edu/teaching/336k/Newtonhtml/node126.html . The point we're interested in is L-3. $\endgroup$ – LSerni Mar 11 '18 at 14:59
  • $\begingroup$ This is the right answer, but it doesn't really answer the OP's question. In what year did we start "closely observing the sky?" Personally, methinks it would have been at the time of Kepler and Galileo, mid-life would have been the year 1600, but it could have been as early as Copernicus, 1500. $\endgroup$ – JBH Mar 11 '18 at 15:36
  • $\begingroup$ If "everything that happened on our planet historically goes down the same way", then there must be a Venus: after all, every astrological / astronomical culture on Earth has recorded observations of this planet! $\endgroup$ – elemtilas Mar 11 '18 at 15:37
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Given your requirements that the counter-earth orbit entirely opposite the Earth and ignoring the factual difficulties involved with this orbital alignment, when would we have discovered (aka, "proved") that the counter-earth must exist?

Answer: sometime between the years 1500 and 1600, the years of Copernicus, Galileo, and Kepler.

That's when we developed the mathematics of orbital mechanics well enough that we could determine what was causing the orbital perturbations in the other planets.

Before this time, people would have created everything from messy stories to very complex astrolabes in the effort to rationalize the planetary movements they were seeing. They would have been whomping complex and would demonstrate time and time again that something wasn't properly understood.

Once orbital mathematics moved from infancy to reasonable maturity, one of those great astronomers would have published a treatise exclaiming, "there must be a planetary body directly opposite from ours!" And that's when history would diverge.

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  • $\begingroup$ These orbital mechanic calculations would have lead us to believe there was another planet at L3, but they are not proof. Consider that our current orbital mechanics indicate a planet in a very elliptical orbit beyond Pluto's orbit, but it is only a THEORY until it is actually OBSERVED.Planet 10? Another Earth-Size World May Lurk in the Outer Solar System $\endgroup$ – Justin Thyme Mar 11 '18 at 17:09
  • $\begingroup$ But I do agree that it's existence would have been first hypothesized in the period you indicated. Now, it begs the follow-up question be asked, "What difference would that knowledge have made, and when would it start to make a difference?" Would it matter, until we could actually GET to it? It would, perhaps, be a better (easier?) objective than Mars, as it is in the same orbit. That would put the date around the beginning of the first Sci-Fi space novels - say 1860 or so - before the narrative changed. $\endgroup$ – Justin Thyme Mar 11 '18 at 17:21
  • $\begingroup$ @JustinThyme, your follow-up question is entirely correct. While the point of divergence may have been the 1500-1600s, the amount of divergence wouldn't be substantial (perhaps not even significant) until we had the ability to care. In that regard, JamesK's answer may be the better as the world's space programs would and could launch satelites to prove the planet, which would be a measurable divergence. It would have advanced long-distance satelite recon considerably because it was close enough to be achievable and would hold the potential of life. $\endgroup$ – JBH Mar 11 '18 at 18:44
  • $\begingroup$ It would also be really, really neat for a stereoscopic view of the universe. But it would need repeater satellites. $\endgroup$ – Justin Thyme Mar 11 '18 at 19:55
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In a system of universal gravity obeying an inverse square law, such a planet will not exist, as is discussed in other questions. As such we must suppose that gravity behaves differently in this universe. In particular I will assume that there are no gravitational consequences of this planet. It causes no perturbations of Venus, and is in a stable "orbit" of the sun.

It could not be detected by Earth bound observers. I would be hidden by the sun for anyone on Earth. It could not be detected by its reflected light off Venus (too dim)

It would only be found by space probe, probably one of the Mariner series, or the Russian Venus probes in the 1960s. As they take an image of the stars, for navigation purposes the extra bright object would be very clear and very surprising.

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As others have noted, the gravitational pull of other planets, notably Venus, would prevent this planet from always remaining exactly on the opposite side of the sun. I haven't done the calculations, so I'm not sure if it would deviate ENOUGH to actually be visible from our Earth.

But regardless, I suppose, for the sake of the question let's assume not. Counter-Earth is always behind the Sun or so close to the Sun that it is invisible.

Once people discovered gravity and starting figuring out orbital mechanics, they would figure out that there must be another planet of this mass and in this orbit. Neptune was discovered this was in 1846, and it's effects are much smaller and more difficult to observe than Counter-Earth's would be. So absolute latest is early 1800s. I would have said earliest is when Newton formulated theory of gravity, 1687. (I'm not sure on what basis others have said 1500s. Maybe they're making different assumptions or maybe they know something about the history of astronomy that I don't.) But I'd say that -- going by the assumption that it is never visible from Earth and we can only deduce its existence from gravitational effects -- it would have been discovered sometime in the 1700s.

As to what difference it makes to history ... hard to say. How would Earth history be different if Mars or Venus did not exist? This depends a lot on how "fragile" you think history is. Think of all those time travel stories. If someone went back in time and changed one little thing, would the effects quickly peter out, lost in the rounding errors, and history proceeds as before? Or would that one small change create larger and larger ripples until history was totally different?

In this case, if someone said, "Hey, I've proven that there is this Counter-Earth on the other side of the Sun", would people basically say, "Wow, how interesting", and go on with their lives as before? Or would it lead one person to spend a night standing on a hill staring at the sky, and while he's standing there he catches cold and dies, and he was the person who would have made some crucial scientific discovery, and so, etc. Or, would someone wonder how life on Counter-Earth might be the same or different from life on Earth, and this leads him to philosophize about why history happens the way it does, and he proposes some ground-breaking new theory that changes how we look at the world, etc.

You say this world is lifeless, so there would be no issue of people communicating with the (non-existent) inhabitants. So aside from the philosophical implications, and possible "butterfly effect" sort of incidental implications, there would be no direct effect until space travel was developed to the point where people could travel there.

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