Calculating Pluto's velocity (angular momentum)

[J3551C4]

1. Pluto moves in a fairly elliptical orbit around the sun. Pluto's speed at its closest approach of 4.43×109km is 6.12 km/s.

Homework Equations

: L=mvr, F_g: (GMm/r^2), A_c: mv^2/r[/B]

The Attempt at a Solution

:

I found the answer here, but I'm more interested in why we would use angular momentum. I took L=mvr and used the given variables to set Pluto's momentum at its furthest point to its momentum at its closest. so I went from L=mvr to miviri=mfvfrf.
The masses cancel, so the equation simplifies to viri = vfrf. I only came to this conclusion after a classmate hinted at me to think about angular momentum, so I'm still confused as to why angular momentum is the key to solving this, rather than Newton's universal law of gravitation set to centripetal acceleration, which gives me the wrong answer.

I'm sorry if I was unclear on anything, thanks for your time. [/B]

 

[gneill]

Hello J3551C4 (Jessica?), Welcome to Physics Forums.

Was there more to the problem statement? I don't see an actual question. It would appear from your attempt that you're looking for the velocity at its furthest distance from the Sun, but you haven't mentioned what that distance is.

EDIT: Okay, I see that your question is actually in the solution attempt rather than the problem statement.

Judging by what I can see of the problem statement and thread title it looks like you're looking for Pluto's velocity at aphelion (its furthest distance from the Sun), so it is an unknown quantity.

You can't evaluate the centripetal acceleration at that location without knowing the velocity (or angular angular velocity), so your proposed method of equating centripetal acceleration to gravitational acceleration there isn't viable.

 

[J3551C4]

Hello gneiLL, yes it does stand for Jessica, and thank you.

I'm sorry for the wonky format, I will try to adhere more exactly to the template in the future. Thank you very much for your explanation, it makes sense and is a lot simpler than I was trying to make it. It seems I need to go back over some concepts. Thanks again.