A question asks the following: Using Newton’s Law of Gravity, show that the mass of a planet can be written:
$$M = \frac{4\pi^2a^3}{ GP^3}$$
where $a$ is the semi-major axis and $P$ is the orbital period.
However, having gone through a calculation where I made the centripetal force equal to the force of gravity between the two, I found that the mass of the orbiting planet actually cancelled out, so I suspect that the question may be wrong and that this equation actually gives the mass of the body being orbited. If this is true, is there anyway to calculate the mass of the orbiting body given only its orbital information (radius, period, mass of the body it orbits etc.), and not information about a satellite that orbits it?
Hope that makes sense