# Retrograde motion and Kuiper Belt Objects

As seen from Earth, planets such as Mars and Jupiter exhibit retrograde motion when they are near opposition (from Earth). I am wondering how this effect extends to very distant objects, such as those in the Kuiper Belt.

Since objects in the Kuiper Belt orbit the Sun at a velocity much slower than Earth (or Mars or Jupiter for that matter) because of Kepler's third law I'd imagine that retrograde motion for these objects is more extreme in the sense that these objects are seen to be in retrograde motion for a longer time and over a larger portion of the sky (in an angular sense) than would be seen for any of the planets.

In an extreme case, is it possible that a very distant Kuper Belt Object (KBO) would never be observed in prograde motion? I imagine that if you were to observe a KBO that was in the direction of Earth's motion then there would be no contribution from the Earth's velocity on the observation and you would be able to see the object in prograde motion, no matter how slow it was travelling. However, such an object would likely be obscured by sunlight, since objects that lie in the direction of Earth's motion lie above the day/night interface on the Earth. My question here is that, given real-life observational constraints (like sunlight) how far from the Sun would an object have to be to never be seen in prograde motion? You can be mathematical.