How Do You Calculate the Final Speed of a Comet in Orbit?

[Qnslaught]

Homework Statement

(a) A certain comet of mass m at its closest approach to the Sun is observed to be at a distance r1 from the center of the Sun, moving with speed v1. At a later time the comet is observed to be at a distance r2 from the center of the Sun, and the angle between rvec2 and the velocity vector is measured to be θ. What is v2?

Homework Equations

The Attempt at a Solution

I thought it would be mv1cos(90-theta). But it's counting that wrong, and I only have one more attempt at this problem, and I'm not sure how to approach it.

 

[kuruman]

Angular momentum is conserved, so find expressions for the angular momentum at the two points and set them equal.