To determine which observation(s) support the heliocentric model but not the geocentric model, let's analyze each observation:
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Observation 1: Mars reverses its direction of motion in the night's sky.
This phenomenon, known as retrograde motion, can be explained by the heliocentric model, where Earth and Mars are both orbiting the Sun at different distances and speeds. When Earth overtakes Mars in its orbit, Mars appears to move backward relative to the background stars. In the geocentric model, which posits that all celestial bodies orbit Earth, this observation is more complex and does not fit neatly into the model, as it requires additional complex explanations (like epicycles) to account for the retrograde motion. -
Observation 2: The stars move across the sky with Earth's rotation.
This observation does not specifically support either model; both models agree that stars appear to move across the night sky due to Earth's rotation. In the heliocentric model, this is a result of Earth's rotation on its axis, while in the geocentric model, it is explained as a result of the heavens rotating around a stationary Earth.
Based on this analysis, the only observation that supports the heliocentric model but not the geocentric model is:
Only observation 1.