Question

The famous Science Fiction author, Arthur C. Clarke, came up with the idea of a geosynchronous communication satellite in 1945, 20 years before the first one, the Intelsat I, was launched. This is a great example of Science Fiction becoming fact. If a satellite is geosynchronous then its period is one day. [So, it stays directly above one point on Earth's surface.] Let's say that we have a geosynchronous communication satellite in orbit around Earth. Calculate the altitude of the satellite (in miles).

Answer 1

The time period of a satellite is given by

g =GM/R² so

where R is the radius of earth and h is the height of satellite above earth's surface

squaring both sides we have

T = 24 h = 86400 s

R = 6400 Km = 6.4 X 10 ⁶ m

g = 9.81 m/s²

h = 3.5930 X 10⁷ m

h = 35930 Km

1 km = 0.621371 miles

h = 35930 (0.621371)

h = 22326 miles