Question

In your own words, explain a crucial piece of evidence that an ancient Greek astronomer could have used to support the geocentric model of the solar system.

Answer 1

An Greek astronomer could have noticed the clouds moving.  They also could use the stars.  They didn't have much technology to do much.

Answer 2

The sun pass around the Earth, the moon move around the Earth, every star go about the Earth.
The things we see in the atmosphere goes around the Earth, therefore clearly, the Earth midst everything.