Problem

# Short-answer questions a. State Newton's universal law of gravitation. b. Show that the gravitational potential energy of a body of mass

m

, at the surface of the Earth, of radius

R

, and mass

M

, is given by the expression

E_P = -G \frac{Mm}{R} .

c. Hence, show that the gravitational potential at the Earth's surface is

62.5 \text{ MJ kg}^{-1}

. (

M_{\text{Earth}} = 6 \times 10^{24}

R = 6.4 \times 10^6 \text{ m}

G = 6.67 \times 10^{-11} \text{ N m}^2 \text{ kg}^{-2}

)