__Question 8.22__:
As you have learnt in
the text, a geostationary satellite orbits the earth at a height of
nearly 36,000 km from the surface of the earth. What is the potential
due to earth’s gravity at the site of this satellite? (Take the
potential energy at infinity to be zero). Mass of the earth = 6.0
× 10

^{24}kg, radius = 6400 km.

__Solution__:*M*= 6.0 × 10

^{24}kg

Radius of the Earth,

*R*= 6400 km = 6.4 × 10

^{6}m

Height of a geostationary satellite from the surface of the Earth,

*h*= 36000 km = 3.6 × 10

^{7}m

Gravitational potential energy due to Earth’s gravity at height

*h,*

= -GM / (R + h)

= - 6.67 X 10

^{-11}X 6 X 10

^{24}/ (3.6 X 10

^{7}+ 0.64 X 10

^{7})

= -9.4 X 10

^{6}J/kg

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