Consider a binary star system consisting of two stars of masses $M_1$ and $M_2$ separated by a distance of $30 \text{ AU}$ with a period of revolution equal to $30 \text{ years}$. If one of the two stars is $5$ times farther from the centre of mass than the other, find the masses of the two stars in terms of solar masses.

Two satellites of masses $m$ and $4m$ are revolving in the same orbit around the Earth. Which one of the following statements is correct?

An artificial satellite is placed into a circular orbit around the Earth at such a height that it always remains above a definite place on the surface of the Earth. Its height from the surface of the Earth is ........... $km$.

Two satellites,$A$ and $B,$ have masses $m$ and $2m$ respectively. $A$ is in a circular orbit of radius $R,$ and $B$ is in a circular orbit of radius $2R$ around the earth. The ratio of their kinetic energies,$K.E._A / K.E._B ,$ is

$A$ planet is revolving around the Sun as shown in the figure. The radius vectors joining the Sun and the planet at points $A$ and $B$ are $90 \times 10^6 \text{ km}$ and $60 \times 10^6 \text{ km}$,respectively. The ratio of velocities of the planet at the points $A$ and $B$ when its velocities make angles $30^{\circ}$ and $60^{\circ}$ with the major axis of the orbit is:

The period of a satellite,in a circular orbit near an equatorial plane,will not depend on