Expert: Tom Whiting - 2/4/2005

Question
Hello Tom,
I was watching the 2nd DVD of Cosmos yesterday and Sagan was discussing Kepler's laws of planetary motion.  For he 2nd law, where all the orbits of planets are ellipses with the sun at one focus ("foci")...  I was wondering, what is the other foci then??  Based on the graphics on the dvd, the foci must be inside the orbit of Mercury.  But obviouisly there is no other astronomical body (and I would imagine it would have to be huge)inside that orbit.   If the sun is indeed the only gravitatinal force working here, then wouldn't with time all the elliptical orbits eventually become circular?  

Thanks!
Tim

Answer
Hi Tim,
I believe..... that is still  Kepler's first law, the second being ...
equal area's are swept out in equal time intervals,
and the 3rd is.... Period squared is proportional to the distance cubed.
So it's the first law, all planets orbit the sun in ellipses.
With planetary ellipses, or any ellipse for that matter, that other focus is called an "empty focus"....there is nothing there;
it's just a point in space.

No, with just the sun's gravity, the orbit does not become
circular with time, but what it does do, it precesses the elliptical orbit so the perihelion point continuously shifts around the sun.  But very slowly...even the Earth's orbit
around the sun precesses a small amount.
Elliptical orbits are stable.  A circle is merely a special case of an ellipse, where both foci are at the exact center.

Technically, today, we know that Kepler's first law is not quite exact...in a two body system, one body is not really revolving  purely around the other, but both are orbiting a common barycenter axis...take the moon around the Earth...technically the Earth-moon system orbits a common barycenter axis,  but the Earth is so much more massive, that the axis of revolution is located well below the Earth's surface....the same is true of any planet orbiting the sun.  That barycenter axis is well within the actual body of the sun, because the sun is so much more massive, containing 99.86% of the mass of the Solar System.
Hope all this helps,
Clear Skies,
Tom Whiting