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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

=

mV_{c}^{2}

r^{2}

r

\ V_{c}^{2 }=

GM

R + h

\ V_{c} =

Alternate Expressions for Critical Velocity

mg^{'} =

\ GM = g^{'} r^{2}

= =

But GM = gR^{2}

Now, Density =

mass

volume

\ Mass = Density ´ volume

\ M = r ´

4

pr^{3}

3

Where r - mean density of earth

= 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, V_{c} =

2 p r

T

\ T =

V_{c}

But, V_{c} =

\ =

\ T^{2} =

4 p2

. r^{3}

\ T^{2} = Kr^{3}

\ T^{2 }a r^{3}

Þ Kepler's 3^{rd} 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

Geostationary satellites are used for communication and are also called communication satellites or geosynchronous satellites.