Mass of moon is $\frac{1}{81}$  times the mass of a planet and radius is $\frac{1}{9}$  times the radius of the planet. The ratio of escape speed from planet to escape speed from moon is ________.

At a point away from planet of radius 6400 km, the gravitational potential and field are –6.4 × 10⁷ SI units and 6.4 SI units respectively. Find height of that point above surface of planet.

If the gravitational acceleration at the surface of earth is g, then increase in potential energy in lifting an object of mass m from earth surface to a height equal to half of radius of earth from surface will be:

Gravitational force between two point masses is found to be F when both are in vacuum. If both the masses are immersed in water, new gravitational force will be:

Determine the energy required to launch a satellite of mass m from the surface of a planet of mass M and radius R in a circular orbit at an altitude of 3R.

Suppose the gravitational force varies inversely as the $n^{th}$  power of distance. Then, time period of a planet in circular orbit of radius R around the sum will be proportional to