The acceleration due to gravity at pole and equator can be related as

A satellite is revolving around the earth in a circular orbit with kinetic energy of $$1.69 \times 10^{10} \mathrm{~J}$$. The additional kinetic energy required for just escaping into the outer space is

A planet has double the mass of the earth and double the radius. The gravitational potential at the surface of the Earth is $$\mathrm{V}$$ and the magnitude of the gravitational field strength is $$\mathrm{g}$$. The gravitational potential and gravitational field strength on the surface of the planet are

Energy required for moving a body of mass $$\mathrm{m}$$ from a circular orbit of radius 3R to a higher orbit of radius 4R around the earth is.