Hello, was Heliocentrism adopted because it’s more “logical” or because it solves a problem?
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The most obvious way to tell that planets don’t orbit the earth in any nice way is that they don’t move at a constant speed or direction on the background of stars from day to day. They sometimes move in retrograde from a geocentric point of view.
However, if you look at their positions relative to the sun, you’ll start to see nice patterns that can be explained with much simpler geometry.
Firstly you’ll notice that mercury and venus just oscillate back and forth, never having much angular separation from the sun. This should tell you that these two at least are obviously orbiting the sun. You can use some trigonometry to get their distance from the sun in AU, and you may be able to guess a simple relationship between orbital period and orbit radius using the period of these oscillations and the length of an Earth year – since mercury, venus, and earth all fit this relationship, you might guess that in fact, earth orbits the sun, not the other way around.
You may also fairly easily notice that the brightening of mars, combined with it’s retrograde motion, can be very easily explained by having it orbit the sun beyond earth, but close enough that these effects are significant. You’ll find that it too fits the same relationship between orbital period and distance to the sun.
You can then check Jupiter and Saturn, and find that they orbit a fair bit further out, but still fit the relationship.
The only exceptions you’ll notice are the stars, which seem to behave like a background, not obviously orbiting anything, the moon, which besides from clearly looking very different to the planets, does appears to actually orbit the Earth, and if you look closely (through a telescope), you’ll see the gallilean moons of jupiter, which very clearly orbit jupiter. You’ll also notice that the moons of jupiter fit the same relationship of distance to period relative to each other, but there are seemingly different constants involved when you look at things orbiting the sun, the earth, jupiter, etc.
To really wrap everything up into one single equation, which simultaneously explains the orbits of everything in the solar system AND why apples fall off trees onto the ground, you need a genius like Newton.
Newton basically found that there’s a single universal law for gravity which explains all of Kepler’s laws, gravity on Earth, and provides new relationships between them.
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