How can planet retrograde motion be explained by the Earth-center hypothesis By the Sun-center hypothesis?

Answer 1

In the Geocentric Hypothesis (Earth-centered), retrograde motion can only be explained by describing the motion of planets as complex, curlicue paths. In the Heliocentric Hypothesis (Sun-centered), retrograde motion is described as changes in relative motion as the Earth overtakes a slower-moving planet in an outer orbit, or is overtaken by a faster-moving planet in an inner orbit. In the Heliocentric Hypothesis, all planets move in more-or-less circular orbits at more-or-less constant speeds, but planets closer to the Sun move faster. Thus, the Earth can overtake and pass each of the outer planets, making them appear to move "backward" (retrograde) for a time.

Answer 2

The Earth-center hypothesis explains planet retrograde motion as a result of the planets moving at different speeds along their orbits, causing them to appear to move backward against the backdrop of fixed stars. The Sun-center hypothesis explains retrograde motion as an optical illusion caused by the difference in orbital speeds of Earth and other planets, creating the perception of planets moving backward when Earth overtakes them in their orbits. Both hypotheses rely on the relative positions and speeds of the planets in their orbits to account for retrograde motion.