Modern ephemerides (orbital predictions) are based on extremely precise numerical simulations that model the pull of the planets on each other. The forces involved are much smaller than that caused by the sun but are still large enough to cause detectable effects in the planets’ positions. An anti-earth, apart from being an impossibly unlikely coincidence, couldn’t exist without us seeing effects which we’re not seeing. The only out would be for the body to be very small and then it wouldn’t count as a planet.
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