GRAVITATION

1. The International Space Station has a mass of approximately 4.19 x 10⁵ kg and orbits at a height of 400km. Calculate the force the ISS exerts on the Earth.
2. Calculate the radius of a planet of mass 2.8 x 10²⁶ kg if the acceleration due to gravity on the surface is twice that of the planet Earth.
3. Jupiter has a mass of 1.898 x 10²⁷ kg and orbits at a mean distance of 778 x 10⁹ m from the Sun. Find the distance from Jupiter to the ‘null point’ in the gravitational field of the Sun/Jupiter system.
4. A satellite orbits the Earth with a period of 30 hours.

Calculate its orbital velocity and height above the Earth’s surface.

5. At what distance from a mass of 1.0 x 10⁴ kg would the gravitational potential be,

(a) -0.10 Jkg^-1 (b) -2.0 x 10^-9 Jkg^-1.

6. A spacecraft of mass 4.5 x 10³ kg is in orbit 12,000km above the surface of Mars. Calculate how much work must be done by the engines to move it out to an orbital radius of 20,000km.
7. Calculate the escape velocity of Venus.
8. For the Moon in orbit around the Earth, Find

(a) its kinetic energy

(b) its total energy.