The mass of a planet that has a moon whose time period and orbital radius are $T$ and $R$ respectively can be written as

On a hypothetical planet,a satellite can only revolve in quantized energy levels,i.e.,the magnitude of the energy of a satellite is an integer multiple of a fixed energy. If two successive orbits have radii $R$ and $\frac{3R}{2}$,what could be the maximum radius of the satellite (in $R$)?

The distance of a geostationary satellite from the centre of the earth (Radius $R = 6400 \ km$) is nearest to (in $R$)

An artificial satellite is moving around the Earth in a circular orbit with a speed equal to one-fourth the escape speed of a body from the surface of the Earth. The height of the satellite above the Earth's surface is ............ ($R$ is the radius of the Earth). (in $R$)

The relay satellite transmits the $T.V.$ programme continuously from one part of the world to another because its

Two point masses of mass $m_1 = fM$ and $m_2 = (1 - f)M$ $(f < 1)$ are in outer space (far from the gravitational influence of other objects) at a distance $R$ from each other. They move in circular orbits about their centre of mass with angular velocities $\omega_1$ for $m_1$ and $\omega_2$ for $m_2$. In that case: