Why conservation of angular momentum is not applicable here

[Mohammed Shoaib]

Comets travel around the sun in elliptical orbits with large eccentricities. If a comet has speed 2.0×104 m/s when at a distance of 2.6×1011 m from the center of the sun, what is its speed when at a distance of 5.2×1010 m .
Express your answer using two significant figures

I applied conservation of angular momentum. But my answer goes wrong. Why?
my working

 

[rcgldr]

Since the orbit is elliptical, the comet's velocity has a component in the direction of the sun (radial line) as well as a component perpendicular to a radial line to the sun. I'm not sure how you would determine angular momentum in this situation. You could use potential versus kinetic energy, but you'd have to know the mass of the sun (the comets mass, being much smaller than the sun's mass, could be ignored), and the problem statement doesn't include the mass of the sun.

 

[Simon Bridge]

The equation for angular momentum you used includes an assumption about the relationship between the velocity vector and the radial vector.
The relation you should use is $\vec L = \vec r \times \vec p$
[edit: beat me to it...]

 

[A.T.]

I'm not sure how you would determine angular momentum in this situation.

By using the general definition, as Simon said:
https://en.wikipedia.org/wiki/Angular_momentum#Vector_.E2.80.94_angular_momentum_in_three_dimensions

 

[Mohammed Shoaib]

Thanks for help.