Retrograde motion describes the backward motion of the stars relative to earth

False.

Retrograde motion is something that the outer planets do relative to the background stars, when they are on the same side of the sun as the earth (at which time they are seen most of the night).

Usually, the orbital motion of the planets causes them to move eastward relative to the stars. When the Earth passes by them at a faster rate of speed, however, they appear to go west relative to the stars for a month or two.

The inner planets, Venus and Mercury, appear to go back and forth relative to the sun, as seen from Earth. One does not usually talk about retrograde motion for those planets.

That's correct! Retrograde motion refers to the apparent backward or reverse motion of celestial objects, such as planets or stars, with respect to the Earth. It is an optical illusion caused by the differing orbital speeds and distances of these objects as they revolve around the Sun.

To understand retrograde motion, let's focus on planets as an example. When observing planets from Earth, we typically see them moving eastward (from west to east) across the night sky, as they orbit the Sun in the same direction. However, at certain times, planets seem to slow down, stop, and then move backward (westward) for a period of time. This backward motion is retrograde motion.

The explanation for retrograde motion comes from our own orbital motion around the Sun and the varying speeds of the planets. As the Earth moves faster in its orbit, it overtakes the slower-moving outer planets, temporarily causing them to appear to move backward against the background of stars. Once the Earth moves past the planet, it appears to resume its normal eastward motion.

So, retrograde motion is an apparent motion observed due to the complex interactions of Earth's orbit and the orbits of other celestial objects.