QUESTION:
How are the locations of the different planets predicted?

ANSWER from TOny Roman on April 30, 1996: 
We can predict where the planets will be in the future by studying where
they were in the past.  As we observe a planet travel through its orbit,
we learn the size and shape of that orbit.  Planets' orbits don't change;
so once we know what the orbit looks like, we can predict where the planet
will be in the future since planets follow their orbits the same way every
time.
 
In the case of Pluto, we cannot predict its location as well as we
can for the other planets.  This is because Pluto takes about 250 years to
complete 1 orbit, but we have had only about 65 years to study it since it
was discovered.  Since we have not seen Pluto complete a full orbit, yet
we have to guess what it's orbit looks like based on the part that we have
seen.  While we can guess pretty well, it's not quite as good as knowing
the orbit exactly.
 
Tony Roman
STScI