Edit: Spleling

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In geocentricity, neither Venus nor Mars are closer to Earth than Mercury is

This is actually (kind of) true, mercury is the closest planet to every planet on average

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I more meant the layers of their concentric orbits as distanced from their center (the Sun or the Earth). Considering how quickly Mercury orbits the Sun while being the closest planet to it, it makes sense it’d be at perigee more frequently and with less variable distance than other planets that have a wider orbit.

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