How Does Comet Speed Change at Aphelion Compared to Perihelion?

[lakersgrl786]

Homework Statement

A particular comet has an elliptical orbit. When closest to the Sun (perihelion) it is at a distance of 8.823 1010 m and moves with a speed of 54.6 km/s. The greatest distance between this comet and the Sun (aphelion) is 6.106 1012 m.
(a) Is the speed of the comet greater than or less than 54.6 km/s when it is at aphelion?
-this is less than
(b) Calculate its speed at aphelion.

Homework Equations

I tried using conservation of energy where Ki + Ui = Kf + Uf where K = to 1/2mv^2 based on the velocities of the comet at both locations. I set U = (-GMm/r) where G = the gravitational constant, M = the mass of the sun, m = the mass of the comet, and r = the distance from the sun (the given values in the problem). You can cancel out m as the mass of the comet is present in all terms and is not given in the problem. However, each time I solved this problem with the values given, I'm not getting the correct answer. Is there another approach?
I tried the conservation of angular momentum as well, but that did not work.

 

[dynamicsolo]

There is a similar problem on another thread. I'd suggest, though, that you show here the actual calculation you did -- it's awfully hard to troubleshoot your solution if we can't see it...