Gravitation

A planet has surface gravity 6 m/s² and radius 4×10⁶ m. Find its mass. (G = 6.674×10⁻¹¹ N·m²/kg²)

At what height above Earth's surface does g reduce to 25% of its surface value?

Find the orbital speed of a satellite at height h = R above Earth's surface (so orbital radius = 2R). (R = 6400 km, g = 10 m/s²)

Find the escape velocity from a planet with g = 5 m/s² and R = 6.4×10⁶ m.

Find the minimum energy needed to completely remove a 500 kg satellite from Earth's surface to infinity. (R = 6400 km, g = 10 m/s²)

Find g at a depth equal to 3/4 of Earth's radius. (Surface g = 10 m/s²)

A 60 kg person's weight at a height equal to Earth's radius above the surface (so g reduces to g/4). Find their weight there. (g = 10 m/s²)

A planet orbits the Sun with period 1 year at distance r. Another planet orbits at distance 4r. Find its period, using Kepler's third law.

Find the gravitational field intensity at a point 8×10⁶ m from the centre of a planet of mass 6×10²⁴ kg.

Find the orbital speed of a satellite at height h = 2R above Earth's surface (orbital radius = 3R). (R = 6400 km, g = 10 m/s²)

Find the binding energy of a 200 kg satellite orbiting at Earth's surface level (radius R). (R = 6400 km, g = 10 m/s²)

A planet has the same average density as Earth but twice Earth's radius. Find the surface gravity on this planet, in terms of Earth's g.