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## Homework Statement

I'm given a force law is [tex] F = \frac{-k}{r^3} [/tex] and that initially, the particle is in a circular orbit the particle is given an impulse parallel and in the opposite direction to its velocity find the distance from the center for the particle as a function of time.

## Homework Equations

I started with the first integral of motion. We know the energy is conserved because this is central force motion (also know angular momentum is conserved).

## The Attempt at a Solution

After taking the time derivative of the first integral of motion I get: [tex] r^3*\frac{dr^2}{dt^2} = \frac{L^2-mk}{m} [/tex]

I'd then have to solve that and I'd technically have my answer I think? I guess I'd have to analyze its form and figure out what it's doing when it's going slower than a certain threshold to find it's motion after the impulse is given? Is there possibly a simpler way to approach this problem? Thanks.

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