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.
F=(G m1 x m2 ) / (r2)
ac = mv2 / r
(2π x r ) / T = V
The Attempt at a Solution
I think it is C.
I used F=(G m1 x m2 ) / (r2) and set it equal to mv2 / 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 .....