# How do you calculate the distance above the surface of the earth to geosynchronous orbit?

##### 1 Answer

The height of a geostationary orbit is calculated as the distance required to have an orbital period of 24 hours.

#### Explanation:

The **force of gravity** acting on a satellite is given by the formula

#F=(GMm)/r^2# .

Where

The **centripetal force** required to keep the satellite in orbit is given by the formula

#F=m * r * omega^2# .

Where

#omega = (2pi)/(24*60*60)#

is the angular velocity of the satellite in radians per second. The value of

When a satellite is in orbit the gravitational force must equal the centripetal force which gives the formula

#(GMm)/r^2=mromega^2#

The

#r^3=(GM)/(omega^2)# .

The distance is from the centre of the Earth so we need to subtract the radius of the Earth

So the height of geostationary orbit h is given by the formula:

#h=((GM)/(omega^2))^(1/3) - R#

If the stated values of G, M,