MHT-CET : Physics Entrance Exam

MHT - CET : Physics - Gravitation Page 2

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10.

Expression for the Critical Speed of a Satellite in a Circular Orbit around the Earth

Mass of satellite - m
Mass of earth
- M
- R
Height of satellite
- h
Distance between centre of the earth and satellite =
r = R + h

Gravitational force = Centripetal force

 \ GMm = mVc2 r2 r

 \ Vc2 = GM = GM r R + h

 \ Vc =

Alternate Expressions for Critical Velocity

 mg' = GMm r2

\ GM = g' r2

 \ Vc = = =

 But GM = gR2

 \ Vc = =

Now, Density =

 mass volume

\ Mass = Density ´ volume

 \ M = r ´ 4 pr3 3

Where
r - mean density of earth

 \ Vc = = 2R

11.

Expression for Time Period

Period is the time taken by the satellite to complete one full revolution around the earth.
Distance travelled in one revolution = 2
p r

 Since Critical Velocity, Vc = 2 p r T

 \ T = 2 p r Vc

 But, Vc = \  = 2 p r T

 \ T2 = 4 p2 . r3 GM

\ T2 = Kr3

\ T2 a r3

Þ Kepler's 3rd law

 T = =    Þ  Period of a satellite

 12. Geostationary Satellite A satellite which appears to be stationary when viewed from the earth is called a geostationary satellite. Conditions to be satisfied for a satellite to be geostationary Time period of 24 hours. It should orbit in the equatorial plane. It should have the same sense of rotation as the earth. Geostationary satellites are used for communication and are also called communication satellites or geosynchronous satellites.

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