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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.

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No, this is not possible. Kuiper belt objects are in orbit around the Sun and their average distance (semi-major axis) will be beyond the orbit of Neptune. This means that their orbital period will be much longer than Earth's (following Kepler's third law). In the most extreme case (further away) the motion of the object will be virtually non observable and the object will appear not to move with respect to the background stars apart from the apparent motion due to parallax.

These objects will still show apparent retrograde and prograde motion because of the movement of the Earth around the Sun. This prograde and retrograde motion can also be observed in nearby stars where it is used to measure the parallax and thereby the distance to the star. See the figure below for the apparent motion of a star as measured by Hipparcos.

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.

The direction of the Earth's motion is constantly changing (changes 360° in a year) so the time at which a KBO will be in the direction of the motion of the Earth will be very short.

This figure shows prograde and retrograde motion of a star as measured by Hipparcos.

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  • $\begingroup$ A main component of my question is, given constraints like not being able to observe during the daytime, would we be able to see this prograde motion? If the prograde motion only ever occurs when the sun is up or close to up then we will never be able to observe it. $\endgroup$ – NeutronStar Jan 28 '15 at 18:18
  • $\begingroup$ Good point, the prograde motion of an object infinitely far away will take 6 months. And it will occur when the Earth is on the half of its orbit that is opposite to the KBO. That is when the KBO will be most difficult to observe. The worst circumstances will be when the KBO is exactly on the ecliptic. But even then it will still be observable when it just starts the prograde motion or when it is about to end the prograde motion. At least from somewhere on the Earth, for instance, one of the poles. At that point the angle KBO-Earth-Sun will be about 90 degrees. $\endgroup$ – Dieudonné Jan 28 '15 at 18:38
  • $\begingroup$ To add to my comment: astronomical twilight is defined when the Sun is 18 degree below the horizon. If the Sun is lower than that, observations should be possible from a site that is dark enough. When the KBO a starts or ends its prograde motion the angle is 90 degrees. That should be enough. $\endgroup$ – Dieudonné Jan 28 '15 at 18:43

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