Can we rule out the existence of a twin planet to Earth just on the other side of the Sun?

The point you refer to in your question is what we know as the Lagrange point 3 (L3), which is an equilibrium point in space, located on the opposite side of the Sun to Earth. It would be the antipodal point in our planet's orbit. On the spheroid that is the Earth, the antipodal points of many Spanish towns are in New Zealand or in the waters of the Pacific Ocean that surround it, although Australia has historically been referred to as "the antipodes."
L3 is an unstable equilibrium point, meaning that any object located there would move from its position if a constant force weren't applied to it to keep it there. For that reason, among others, we don't launch satellites to L3 , but we do launch them to other Lagrange points—L4 or L5— because once we place them in one of those two places, they stay there, which wouldn't happen at L3. At L3, the gravitational attraction between the Sun and Earth is balanced; but, as I was saying, it's a very unstable equilibrium because any other nearby celestial body would upset it.
That point is completely invisible from Earth, so direct communications from our planet would be blocked by the Sun. I suppose that's why you place the possibility you raise in your question there, because if there were a celestial object in that location, we wouldn't be able to see it. But just because we can't see it directly doesn't mean we wouldn't be able to detect whether or not there is a celestial body there.
As for whether we could detect it, I can answer that no, there is no planet or massive celestial object at that point. And we know this for several reasons.
First of all, an Earth or any other planet located there would exert a gravitational force, and that force would influence everything that moves , so we would have measured it. For example, all the probes we've sent to Venus, Mars, or any other location couldn't have landed if an Earth existed there because, for those probes' navigation calculations, it would have been necessary to include its gravitational mass; which would be quite substantial. And given that the probes arrived without any problems, this is the first argument. We can rule out objects larger than 100 kilometers in diameter. Below that diameter, the force of gravity would be negligible, but above that diameter, we should have noticed it.
That's the first reason we can rule out the presence of what is commonly known as a counter-Earth. There's another argument: we've also launched space probes to observe the sun, which would have seen something there. For example, NASA's STEREO probes , launched in 2006, would have detected this hypothetical Earth because L3 was visible to them.
And finally, the third argument is that, since it's an unstable equilibrium point, an object at that point would eventually move. For example, Venus approaches that position every few months; and so, it would displace any massive object from that antipodal point to another orbit where it would be visible from Earth. So the answer is clear: there is no other Earth at L3.
Overall, we have a fairly complete census of the solar system for bright asteroids, although it's not entirely exhaustive, especially because small, faint, and distant bodies are difficult to detect. By small bodies, I mean objects a hundred meters in diameter or smaller. With asteroids and such smaller objects, the census is becoming increasingly complete. However, their monitoring and recording has only been going on for a relatively short time—a couple of decades—so we know less about objects sixty or fifty kilometers in diameter because they are more difficult to detect.
We have well measured large bodies, the planets, although if there is a possibility that what we call planet 9 or planet X exists, it would be in the confines of the solar system. Its existence is inferred from the movement of a certain group of asteroids in the Kuiper Belt. To explain the movements of this group of asteroids, there is a hypothesis that there could be a planet beyond the orbit of Neptune; and that it would be a relatively small body, but larger than the Earth. The search continues, but the problem with a planet in an orbit so far from the Earth is that it has very long periods; and it is very difficult to detect an object that takes so many years to complete its orbit around the Sun.
Eva Villaver Sobrino is an astrophysicist, Research Professor and Deputy Director of the Instituto de Astrofísica de Canarias (IAC).
Coordination and writing: Victoria Toro .
Question sent by Alex .
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