The planets DO NOT orbit the sun, nor do the moons orbit the planets.
The 2 bodies actually orbit the point in space which is the
instantaneous center of mass of the two bodies.
It is prudent to note that the instantaneous center of mass of the two
bodies is constantly changing to do interactions between the 2 bodies
and other solar and extra-solar masses. For instance, while the earth
and the moon interact, the Earth and the sun AND the moon and the sun
The interesting problem is to describe the movements of 3 bodies
(instead of just 2 ) in terms of calculus. It is claimed to be
currently impossible, but is an interesting problem none the less. The
best anyone has been able to achieve is a time-stop system where you
calculate the effect of all bodies on every other body, go forward x
time units and do this again. Not a very precise method when you
extend over a significantly large number of iterations.
Thanks, Red, for that little tidbit.