The figure shows two planets of mass m orbiting a star of mass M. The planets are in the same orbit, with radi?

The figure shows two planets of mass m orbiting a star of mass M. The planets are in the same orbit, with radius r, but are always at opposite ends of a diameter.



Find an exact expression for the orbital period T.The figure shows two planets of mass m orbiting a star of mass M. The planets are in the same orbit, with radi?The force acting on one of the masses m by the other two is

[GMm /R^2] + [Gmm / 4R^2]



This acts as the centripetal force and hence = mR蠅^2



[GMm /R^2] + [Gmm / 4R^2] = mR蠅^2



R ^3 * 蠅^2 = G [4 M + m] / 4



蠅 = 2蟺 / T and hence



T = 4 蟺 R ^ (3/2) / 鈭歿 G [4 M + m]}



===============鈼勨晳鈻?===============The figure shows two planets of mass m orbiting a star of mass M. The planets are in the same orbit, with radi?However, for stellar systems, the presence of a third star orbiting a stellar binary can ... The same is true for planetary systems. The interval between successive transits of the ... We assume that the two planets are coplanar, have orbits that are ... induced by a second planet with mass M2 = 10鈥? M {odot} .