Satellite motion – determining planets’ masses

1. Determine the ratio of the masses of the planets Earth and Mars by using only information about their orbital periods and orbital radii about the sun. Assume the planets can be treated as points with mass and assume circular orbits.

2. Relevant equations
Gravitational force: [tex] F_g = G m_1 m_2 / R^2 [/tex]
where [itex]G[/itex] is the gravitational constant and [itex]R[/itex] is the distance between the two masses.

Tangential velocity in uniform circular motion: [tex] v = 2∏R/T [/tex]
where T is the period.

Centripetal acceleration in uniform circular motion: [tex] a_c = v^2/R = 4(∏^2)R/T^2 [/tex]

3. The attempt at a solution
I know centripetal force is provided by the force of gravity, so:
[itex] F_g = G m_1 m_2 / R^2 [/itex] [itex] = m_1a_c [/itex]

I can express centripetal acceleration in terms of radius and period and shown above, but since [itex] m_1 [/itex] appears on both sides of the equation! I conclude that the mass of an orbiting object has nothing to do with its orbital period or it’s orbital radius.
This professor is notorious for accidentally giving problems that can’t actually be done, and I suspect that this is one. Am I missing something?

In case that wasn’t clear, my problem is that the mass of an orbiting body can’t be expressed in terms of its orbital radius and period. Thus I can’t determine the ratio of the masses of two orbiting bodies using only this information.

http://ift.tt/1bLrm6m

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