# Perturbed circular orbit under central force motion?

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1. Mar 11, 2015

### physicsxlove

I am self studying Kleppner and Kolenkow's an Introduction to mechanics. But i have one doubt about how they got in to the equation no 3 of the example problem 9.3 in Central Force Motion.

2. Mar 11, 2015

### mathman

I suggest you quote it or give a link.

3. Mar 15, 2015

### physicsxlove

Here i have attached the photo graph of that page.

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4. Mar 15, 2015

### diegzumillo

Seems pretty straight forward. Differentiate $U_{eff}$ twice, evaluate it at $r=r_0$ and replace $l$ by the one we obtained earlier. This should equal k, which is related to beta.

5. Mar 15, 2015

### physicsxlove

Omg. I am so dumb. I just calculated the second derivative and then used to sit brooding over what to do next without plugging the value of l from equation 1. I am feeling embarrassed.

Anyway,,, thank you. I got it. Better late than never.

6. Mar 16, 2015

### diegzumillo

No problem :) This is just the peeking-over-the-shoulder effect.