Page 110 - text book form physics kssm 2020

As GM is constant, linear speed of the satellite only depends on the radius of its orbit. If a
satellite is at a height, h above the surface of the Earth,

Radius of its orbit, r = R + h
that is R = radius of the Earth
GM
Th erefore, linear speed of the satellite, v =
R + h

Man-made satellites can be launched to keep orbiting at specifi c heights around the Earth at

GM
radius of orbit, r if the satellite is given linear speed, v = . Figure 3.35 shows a Global
r
Positioning System (GPS) satellite at an altitude of 20 200 km from the Earth.

Global Positioning System
(GPS) satellite

h = 20 200 km

R R r

How does GPS work?
Earth

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Radius of orbit = (Radius of Earth) + (Height of orbit)
r = R + h
Figure 3.35 GPS satellite orbits the Earth

In a stable orbit, linear speed of satellite is
GM
Height, h = 20 200 × 1000 m v = . Th is linear speed is high enough for
= 2.02 × 10 m r
7
the satellite to move in a circular orbit around
6
Radius of orbit, r = (6.37 × 10 ) + (2.02 × 10 ) the Earth. Centripetal acceleration is the same as
7
7
= 2.657 × 10 m
gravitational acceleration.
Linear speed If the linear speed of the satellite becomes
of satellite, v =
GM
r less than the required linear speed, the satellite
will fall to a lower orbit and continue to revolve
(6.67 × 10 ) × (5.97 × 10 )
–11
24
=
2.657 × 10 7 towards the Earth until it enters the atmosphere.
3
= 3.87 × 10 m s –1 Th e movement of the satellite at a high linear
speed against air resistance will generate heat
and eventually causes the satellite to burn.
104 3.3.1
104
3.3.1