What are the directions of rotation of a polar satellite and the Earth?

If $\rho$ is the density of the planet,the time period of a nearby satellite is given by

If the mass of a satellite is doubled and the time period remains constant,the ratio of the orbital radii in the two cases will be:

The mass density of a spherical galaxy varies as $\frac{K}{r}$ over a large distance $r$ from its centre. In that region,a small star is in a circular orbit of radius $R$. Then the period of revolution,$T$ depends on $R$ as

If the horizontal velocity given to a satellite is greater than critical velocity but less than the escape velocity at the height,then the satellite will

Consider a star of mass $m_2 \ kg$ revolving in a circular orbit around another star of mass $m_1 \ kg$ with $m_1 \gg m_2$. The heavier star slowly acquires mass from the lighter star at a constant rate of $\gamma \ kg/s$. In this transfer process,there is no other loss of mass. If the separation between the centers of the stars is $r$,then its relative rate of change $\frac{1}{r} \frac{dr}{dt} \ (\text{in } s^{-1})$ is given by: