### Solution Found!

# a) By examining the effective potential energy (8.32) find

**Chapter 8, Problem 8.12**

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**QUESTION:**

a) By examining the effective potential energy (8.32) find the radius at which a planet (or comet) with angular momentum can orbit the sun in a circular orbit with fixed radius. [Look at dUeff I dr 1 (b) Show that this circular orbit is stable, in the sense that a small radial nudge will cause only small radial oscillations. [Look at d2 Ueff I dr2 1 Show that the period of these oscillations is equal to the planet's orbital period.

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### Questions & Answers

**QUESTION:**

a) By examining the effective potential energy (8.32) find the radius at which a planet (or comet) with angular momentum can orbit the sun in a circular orbit with fixed radius. [Look at dUeff I dr 1 (b) Show that this circular orbit is stable, in the sense that a small radial nudge will cause only small radial oscillations. [Look at d2 Ueff I dr2 1 Show that the period of these oscillations is equal to the planet's orbital period.

**ANSWER:**

Step 1 of 4

(a)

Differentiating both side with respect to

Again, differentiating both side with respect to