Question

The potential energy of a satellite, having mass m and rotating at a height of 6.4 x $10^6$ m from the earth surface, is

• A. -mgR$_e$
• B. -0.67mgR$_e$
• C. -0.5 mgR$_e$
• D. -0.33 mgR$_e$

Answer 1

Answer: (C)

-0.5 mgR$_e$

Answer 2

For a satellite at height h = 6.4×10⁶ m above the Earth’s surface and with Earth’s radius Rₑ = 6.4×10⁶ m, the distance from the centre is

r = Rₑ + h = 2Rₑ.

The gravitational potential energy is given by

U = – GMm/r.

Using GM = gRₑ², we have

U = – (gRₑ² m)/(2Rₑ) = –0.5 m g Rₑ.