1. The problem statement, all variables and given/known data
The three planets (v1, v2 and v3) in the diagram all have similar mass and are in a line equally spaced so that v1 and v3 are orbiting around v2 synchronously. If the mass of each of the planets are M and the radius of the orbit is R, what is the orbital period?
2. Relevant equations
T=[itex]\frac{2*pi*r}{v}[/itex]
v=[itex]\sqrt{GM/r}[/itex]
Fg=GMm/r^2
3. The attempt at a solution
I am pretty sure you just need to set two equations equal to each other and solve for the variable T, but I am unsure which two equations this is. It would be appreciated if somebody could explain all this to me. Thank you.
The three planets (v1, v2 and v3) in the diagram all have similar mass and are in a line equally spaced so that v1 and v3 are orbiting around v2 synchronously. If the mass of each of the planets are M and the radius of the orbit is R, what is the orbital period?
2. Relevant equations
T=[itex]\frac{2*pi*r}{v}[/itex]
v=[itex]\sqrt{GM/r}[/itex]
Fg=GMm/r^2
3. The attempt at a solution
I am pretty sure you just need to set two equations equal to each other and solve for the variable T, but I am unsure which two equations this is. It would be appreciated if somebody could explain all this to me. Thank you.
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