What the other answers fail to mention is that the mass of your orbiting object actually cancels out. It does not matter. See these two equations:
(1) F1 = F2 = Gm1m2 / r^2$F_1 = F_2 = G m_1 m_2 / r^2$
(2) F1 = m1 * a1$F_1 = m_1 a_1$
Where FF is force, GG is the universal gravitational constant, mm is mass, and rr is distance between centers of mass of the orbiting and orbited bodies in question. The 1 and 2 represent the object in question, for example m1$m_1$ is the mass of object 1 and F1$F_1$ is the force exerted on object 1.
Thus,
a1 = G*m2 / r^2$a_1 = G m_2 / r^2$
i.e., the mass of the orbiting object does not influence its acceleration in any way.
edit: added an index of 1 to aa.