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A SATELLITE ORBITS THE EARTH AT A HEIGHT EQUAL TO THE RADIUS OF THE EARTH FIND ITS 1)ORBITAL SPEED AND2)PERIOD OF REVOLUTION

A SATELLITE ORBITS THE EARTH AT A HEIGHT EQUAL TO THE RADIUS OF THE EARTH FIND ITS 1)ORBITAL SPEED AND2)PERIOD OF REVOLUTION

Grade:11

1 Answers

sam
22 Points
6 years ago
Let V be the orbital speed of the satellite.
Then,
The centripetal acceleration required by it to move in an orbit of radius 2R( measured from the centre of the Earth) would be provided by the gravitaional force of atraction between Earth and the satellite.
Hence,
 
mV2/2R = GMm/4R2
V2 = GM/2R
Hence 
V= (GM/2R)^1/2       ...(i)
Now for period of revolution,
We know 
Time = Distance/ Speed
Therefore,
T = (2*Pi*2R) / V     ...(ii)
Substitute the value of V in (ii) to get the time period
 

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