Retrograde motion of a planet when viewed from Earth is caused by

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To begin analyzing retrograde motion, we should evaluate what could cause a planet to appear to move backward in the sky from Earth’s perspective.
Option 1: 'the movement of the planet along an epicycle.' This describes a geocentric model where planets travel on small circles (epicycles) atop larger orbital paths. While epicycles were used historically to explain retrograde motion in Ptolemaic astronomy, they are not a description of the actual cause in the heliocentric, modern view. So this explanation is outdated and not the true cause in current understanding.
Option 2: 'its elliptical orbital path.' The shape of a planet’s orbit (which is elliptical) explains the speed variation along the orbit, but retrograde motion as seen from Earth is not caused by the planet simply following an ellipse. The elliptical path by itself does not produce a retrograde loop when viewed from another planet; it’s the observer’s motion that creates the apparent reversal.
Option 3: 'the relative motions of Earth and planet.' This is the correct explanation. Retrograde motion arises because Earth and the other planet orbit the Sun at different distances and speeds. When Earth overtakes an outer planet, or when the inner planet laps Earth, the line of sight to the planet changes direction briefly, producing the apparent backward motion relative to the background stars. This is an observed effect of our moving frame of reference.
Option 4: 'the inclination of its orbit to the ecliptic plane.' The inclination describes how tilted a planet’s orbital plane is relative to the Earth’s orbital plane, but this tilt does not by itself cause retrograde motion. A high inclination changes the planet’s path on the sky but is not the mechanism behind the temporary reversal of motion.
In summary, the phenomenon can be understood as a perspective effect caused by the differing orbital motions of Earth and the planets, rather than a complication arising from epicycles, orbital shape alone, or orbital tilt.

2261 ASTRON 0088 SEC1070 Homework 5 - The Greeks

Retrograde motion of a planet when viewed from Earth is caused by

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