Take the mean distance of the moon and the sun from the earth to be 0.4 × 10 6 km and 150 × 10 6 km , respectively. Their masses are 8 × 10 22 kg and 2 × 10 30 kg , respectively. The radius of the earth is 6400 km . Let Δ F 1 be the difference in the forces exerted by the moon at the nearest and farthest point on the earth, and Δ F 2 be the difference in the forces exerted by the sun at

Step-by-step solution

F 1 = G M e m r 1 3 , F 2 = G M e M s r 2 2   Δ F 1 = (-) 2 G M e m r 1 3   Δ r 1  ,   Δ F 2 =(-) 2 G M e M s r 2 2   Δ r 2 Δ F 1 Δ F 2 =   m Δ r 1 r 1 3   r 2 3 M s Δ r 2 = m M s r 2 3 r 1 3 Δ r 1 Δ r 2 Using Δ r 1 = Δ r 2 = 2 R e a r t h m = 8 × 10 22   kg M s =   2 × 10 30   kg r 1 = 0.4 × 10 6   km r 2 = 150 × 10 6   km We get Δ F 1 Δ F 2 = 2 .