Elliptical orbits and focal points

**Agent M27** · Nov1-09, 01:01 PM

I was recently studying elliptical orbits and the precession of the perihelion of Mercury. I remembered from my pre-calc class that all ellipses have two focal points. In this case the obvious would be the Sun as on focal point for all the planets, but where would the second be? I have a feeling it is something simillar to the Lagrangian points in that there is no concentration of anything, just a point in coordinate space relative to the repective bodies, i.e. L1 for Earth-Sun. Of course there would be a different focal point for each orbit. How might this point be affected if at all, by the presence of another body such as a moon. I don't know if this is a valid question or not due to the space being 3 dimensional and the material to which I am refering was dealing with 2 dimensional ellipses, but I had no idea how to word that in google or the search. Thanks in advance everyone.

Joe

**Ich** · Nov3-09, 05:31 AM

there is no concentration of anything, just a point in coordinate space relative to the repective bodies

Yes, there is nothing special at the second focal point. Precession will change its position with time.

**D H** · Nov3-09, 07:37 AM

Originally Posted by Agent M27

n this case the obvious would be the Sun as on focal point for all the planets, but where would the second be? I have a feeling it is something simillar to the Lagrangian points in that there is no concentration of anything, just a point in coordinate space relative to the repective bodies, i.e. L1 for Earth-Sun.

The other focal point has zero physical meaning. In contrast, the Lagrange points have a very real and very practical physical meaning. Several of the space agencies around the world take advantage of the Lagrange points. For example, the Solar and Heliospheric Observatory (SOHO) is in a halo orbit and the Advanced Composition Explorer (ACE) is in a Lissajous orbit the about the Sun-Earth L1 point. Several vehicles similarly take advantage of the Sun-Earth L2 point.

How might this point be affected if at all, by the presence of another body such as a moon. I don't know if this is a valid question or not due to the space being 3 dimensional and the material to which I am refering was dealing with 2 dimensional ellipses, but I had no idea how to word that in google or the search.

As soon as you move from the ideal world of the two body problem in Newtonian mechanics to the real world with the Sun, ~~nine~~ eight planets, a bunch of dwarf planets, and an even larger number of small bodies, orbits are no longer ellipses. They aren't even planar. The Lagrange points are still real.