Question

The gravitational force of the Sun on the Earth is approximately how many times greater than the gravitational force of the Moon on the Earth?

150

100

50

175

Answer 1

Gravitational force between two objects of mass m1 and m2 with placed at a separation of r is

F = Gm1m2/r^2 where G is Universal Gravitational constant = 6.67 x 10^-11 Nm^2/kg^2

mass of Sun = m1 = 1.989 × 10^30 kg

mass of Earth = m2 = 5.972 × 10^24 kg

mass of Moon = m3 = 7.348 × 10²² kilograms

Separation between Sun and Earth = r12 = 149.6 x 10^6 km = 1.496 x 10^11 m

Separation between Moon and Earth = r23 = 384,400 km = 3.844 x 10^8 m

Gravitational force between Sun and Earth = F12 = Gm1m2/r12^2

= (6.67x 10^-11)(1.989 × 10^30)(5.972 × 10^24)/(1.496 x 10^11)^2

= 3.54 x 10^22 N

Gravitational force between Moon and Earth = F23 = Gm3m2/r23^2

= (6.67x 10^-11)(7.348 × 10²²)(5.972 × 10^24)/(3.844 x 10^8 )^2

= 1.98 x 10^20 N

F12/F23 = 3.54 x 10^22 N/ 1.98 x 10^20 N = 178.7 = 175 (approximately)