Time Periods of Orbiting Satelites

A geostationary sattelite orbits around the earth in a circular orbit of radius 36000 KM, then, What will be the time period of a sattelite orbiting of a few hundred kilometres above the earth's surface (R=6400 KM ) ?
- Shrinivas Shendye (age 16)
Indore, MP, INDIA

Hello Shrinivas,

This is a straightforward problem involving Kepler's third law:  "The ratio of the period of orbit squared T² to the mean radius of orbit cubed R³ is a constant".   The constant involved is 4π²/(G M_e) where G is Newton's gravitational constant and M_e is the mass of the earth.  You can do the arithmetic.

Kepler derived his laws from painstaking observations by Tycho Brahe and his assistants.   Newton was able to derive them by applying his laws of motion to the problem of orbiting satelites and assuming an inverse square for the gravitational force.

 

LeeH

 

(published on 12/29/2013)