**This worksheet contains numerical problems on Orbital speed & Escape speed.**

1) a) Confirm that the escape speed from the Earth’s surface is 11.2 km s−1.

b) Explain why all masses have the same escape speed.

c) Determine the escape speed from a planet that had twice the radius of Earth, but the same density.

2) The escape speed of the Moon is 2.4 km s−1.

a) If the mass of the Moon is 7.3 × 1022 kg, use its escape speed to determine its radius.

b) Explain why the escape speed from the Moon is much lower than from the Earth.

3 a) Calculate the orbital speed needed for a satellite to orbit the Earth at a height of 200 km.

b) What is the time period of this orbit?

4) Mars has a radius of 3390 km and a mass of 6.4 × 1023 kg. It has a day that is 40 minutes longer than Earth’s.

Determine the radius of the orbit of a satellite around Mars which always remains above the same place on the planet’s surface.

5) The radius of the Earth is 6.4 × 106 m. Determine the minimum theoretical speed that a mass would need if, when projected vertically upwards it was to reach a height of 500 km. Assume there was no air resistance.