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A geo-stationary stellite orbits around ...

A geo-stationary stellite orbits around the earth in a circular orbit of radius 36,000km. Then, the time period of a spy stellite orbitting a few hundred km above the earth's surface `(R_(earth) = 6400km)` will approximately be

A

`1/2 h`

B

`1 h`

C

`2 h`

D

`4h`

Text Solution

Verified by Experts

The correct Answer is:
`C`

Accroding to Kepler's law `T^(2) propR^(3)`
`:. ((T_(2))/(T_(1)))^(2)=((R_(2))/(R_(1)))^(3)`
Let the time period at earth's surface `=T_(1)`
For geo-stationary satellite,`T_(2)=24` hour,
`R_(2)=36,000 km`
For spy satellite, `T_(1)=? R_(1)~~6400 km`
`:. (24/(T_(1)))^(2)=(36000/6400)^(3)` or `T_(1)=24/13.34=1.8 h`
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