6.2 Newton’s Law of Gravitation

A satellite orbits the Earth with mass M above the equator with a period, T equal to 48 hours. The mass of the Earth is 5.972 × 10²⁴ kg. 

The mean radius of Earth is 6.37 × 10⁶ m.

The Hubble Space Telescope is in orbit around the Earth at a height of 490 km above the Earth’s surface.

Europa, a moon of Jupiter, has an orbital period of 85 hours and an orbital radius of  670 900 km.

Ganymede is the largest of Jupiter’s Moons. It has an orbital period of 7.15 days and an orbital speed of 10.880 km s^–1.

The diagram shows a satellite orbiting the Earth. The satellite is part of the network of global–positioning satellites (GPS) that transmit radio signals used to locate the position of receivers that are located on the Earth. 

When the satellite is directly overhead the microwave signal reaches the receiver 62 ms after leaving the satellite. 

The radius of Earth is 6.4 × 10⁶ m.

                      Mass of Earth = 6.0 × 10²⁴ kg

A satellite is in a circular orbit around a planet of mass M.

         r =

Because of friction with the upper atmosphere, the satellite slowly moves into another circular orbit with a smaller radius before.

Titus and Enceladus are two of Saturn’s moons. Data about these moons are given in the table.

Moon	Orbit radius / m	Angular speed / rad s-1
Titan	1.22 109
Enceladus	2.38  108	5.31 10-5