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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
Radius of earth
- 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

Kepler's 3rd law

 

T =

=     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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