Question

It’s 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 sit of this satellite? (Take the potential energy at infinity to be zero). Mas of the earth = 6.0 × 10²⁴ kg, radius = 6400 km.

Answer 1

Mass of the Earth = 6.0× 10²⁴ kg

Radius of Earth = 6.4 × 10⁶m.

Height of the satellite from surface of Earth is 36000 km 

= 3.6 × 10⁷m

Distance of the satellite from centre of Earth is 

d = (3.6 × 10⁷m + 6.4 × 10⁶ m)

= 4.24 × 10⁷ m

Gravitational potential due to Earth on the satellite is v = -GM/d

\(\frac {6.67 \times 10^{-11} \times 6 \times 10^{24}}{4.24 \times 10^7}\)

= – 9.438 × 10⁷ J/kg

= – 9.4 × 10⁷J/kg.