Orbital mechanics, corrected

Red sent in this little gem of an email, explaining that, in fact, planets don't orbit the sun, exactly. From his email:

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

interact.



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.