4Orbits

IA Dynamics and Relativity

4 Orbits

The goal of this chapter is to study the orbit of a particle in a central force,

m

¨

r = −∇V (r).

While the universe is in three dimensions, the orbit is confined to a plane. This is

since the angular momentum

L

=

mr×

˙

r

is a constant vector, as we’ve previously

shown. Furthermore

L · r

= 0. Therefore, the motion takes place in a plane

passing through the origin, and perpendicular to L.