Speed of a comet orbiting the sun?

Question

A comet with an elliptical orbit with one focus at the sun. The maximum distance to the Sun (aphelion distance) is rA = 5 x 10^9 km. The minimum distance (perihelion distance) is rP = 5 x 10^7 km. Find the speed of the comet at the perihelion position.

Answer 1

1. As the first answer noted, conservation of angular momentum gives you one relationship between the velocity at aphelion and that at perihelion.

2. Also, conservation of energy give you another:

total energy = potential energy plus kinetic energy

potential energy is a function of the distance to the Sun and the mass of the Sun.

So with these two equations you can figure out the minimum and maximum velocities.

check out: http://en.wikipedia.org/wiki/Astrodynamics

Answer 2

Angular momentum is conserved.

mvr at A = mvr at P

So its vel at P is 100 times vel at A