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## Homework Statement

The picture has the problem question.

OK.

When the moon is at point B, the distance from the moon to the center of the planet is most nearly:

A) (1/25) * rA

B) (1/5) * rA

C) (1/ sqrt(5) ) * rA

D) rA

E) sqrt(5) * rA.

## Homework Equations

newton's law of gravitation. kepler's third law

## The Attempt at a Solution

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Ok. I am told that the correct answer is

**B**but I do not know why.

I got A instead. Here's what I did.

I solved from my rA for the planet at point A.

I apologize for my bad math formatting, but I am in a rush and can not use latex. Hope you understand.

Gravitational force causes centripetal acceleration:

G * mPlanet * mMoon mMoon * (v0)^2

--------------------------- = -----------------------

(rA)^2 rA.

I cancel mMoon and one of my rA terms and I solve for v0^2. I got v0^2 to be equal to

G * mPlanet/r.

I then did the same thing for my planet in position B.

G * mPlanet * mMoon mMoon * (5v0)^2 mMoon * 25 * v0^2

--------------------------- = ----------------------- = ----------------------

(rB)^2 rB. rB

I plugged in my calculated result for v0^2 for position A into the expression and solved for rB.

My G and my mPlanet terms cancel. I got rB = rA/25.

Where did I mess up?

Thanks in advance.