The motivation for isaac newton to discover his laws of motion was to explain the properties of planetary orbits that were observed by tycho brahe and analyzed by johannes kepler. a good starting point for understanding this (as well as the speed of the space shuttle and the height of geostationary satellites) is the simplest orbit - a circular one. this problem concerns the properties of circular orbits for a satellite orbiting a planet of mass m. use g for the universal gravitational constant. find the orbital period t.

Explanation:

We know that , for an object to remain in  circular motion , a force towards centre is required which is called centripetal force. In the circular motion of

satellites around planet , this force is provided by the gravitational attraction between satellite and planet.

If M be the mass of planet and m be the mass of satellite,  G be gravitational constant and R be the distance between planet and satellite or R be the radius of orbit

Gravitational force = G Mm / R²

If v be the velocity with which satellite is orbiting

centripetal force

= m v² /R

Centripetal force = gravitational attraction

m v² /R  =  G Mm / R²

v =

Time period = time the satellite takes to make one rotation

= distance / orbital velocity

= 2πR/ v

=

T =

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