A satellite of mass m is orbiting the earth (of radius R) at a height h from its surface. The total energy of the satellite in terms of g₀, the value of acceleration due to gravity at the earth's surface, is

The ratio of escape velocity at earth (v_e) to the escape velocity at a planet (v_p) whose radius and mean density are twice as that of earth is

At what height from the surface of earth the gravitation potential and the value of g are $$-$$5.4 $$ \times $$ 10⁷ J kg^$$-$$1 and 6.0 m s^$$-$$2 respectively? Take the radius of earth as 6400 km.

A remote-sensing satellite of earth revolves in a circular orbit at a height of 0.25 $$ \times $$ 10⁶ m above the surface of earth. If earth's radius is 6.38 $$ \times $$ 10⁶ m and g = 9.8 ms^$$-$$2, then the orbital speed of the satellite is