Energy of a satellite of mass `m` orbiting at a distance `r` from the centre of planet of mass `M` and radius `R` is

A satellite A of mass m is at a distance of r from the centre of the earth. Another satellite B of mass 2m is at distance of 2r from the earth's centre. Their time periode are in the ratio of

What is the minimum 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 2R?

If M_(e) is the mass of earth and M_(m) is the mass of moon (M_(e)=81 M_(m)) . The potential energy of an object of mass m situated at a distance R from the centre of earth and r from the centre of moon, will be :-

A lauching vehicle carrying an artificial satellite of mass m is set for launch on the surface of the earth of mass M and radius R . If the satellite intended to move in a circular orbit of radius 7R , the minimum energy required to be spent by the launching vehicle on the satellite is

The potential energy of a satellite of mass m revolving at height R above the surface of the earth where R= radius of earth is

Find potential at a point 'P' at a distance 'x' on the axis away from centre of a uniform ring of mass M and radius R .

A point particle of mass m is released from a distance sqrt(3)R along the axis of a fixed ring of mass M and radius R as shown in figure. Find the speed of particle as it passes through the centre of the ring.

A solid spherical planet of mass 2m and radius 'R' has a very small tunnel along its diameter. A small cosmic particle of mass m is at a distance 2R from the centre of the planet as shown. Both are initially at rest, and due to gravitational attraction, both start moving toward each other. After some time, the cosmic particle passes through the centre of the planet. (Assume the planet and the cosmic particle are isolated from other planets)

An astronaut of mass m is working on a satellite orbiting the earth at a distance h from the earth's surface the radius of the earth is R while its mass is M the gravitational pull F_(G) on the astronaut is

The work done by gravitational force on a point mass m_0 in moving from the surface of a planet off mass M and radius R to a height R/2 is