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## Homework Statement

Planet 1 orbits Star 1 and Planet 2 orbits Star 2 in circular orbits of the same radius. However, the orbital period of Planet 1 is longer than the orbital period of Planet 2. What could explain this?

A) Star 1 has less mass than Star2.

B) Star 1 has more mass than Star 2

C) Planet 1 has less mass than Planet 2

D )Planet 1 has more mass than Planet 2.

E) The masses of the planet are much less than the masses of the stars.

## Homework Equations

F=(G m

_{1}x m

_{2}) / (r

^{2})

a

_{c}= mv

^{2}/ r

(2π x r ) / T = V

## The Attempt at a Solution

I think it is C.

I used F=(G m

_{1}x m

_{2}) / (r

^{2}) and set it equal to mv

^{2}/ r

I didn't see anything related to Period so I remembered that circumference divided by period equals V.

I solved for V in the first equation and got : v = √[(Gm)/r]. Mass is the only variable that could cause the speed and therefore the Period to change. So I thought that increasing the mass of Planet would increase the speed and make the Period longer.

I probably messed up .....