What is the ratio of the gravitational pull of the sun on the moon to that of the earth on the moon? (Assume the distance of the moon from the sun can be approximated by the distance of the earth from the sun.) Use the data in Appendix F. Is it more accurate to say that the moon orbits the earth, or that the moon orbits the sun?

Solution 1E Gm 1 2 The expression for gravitational force between two objects is given by F = r 2 …..(1), where m 1 and m 2 are the masses of the objects, G is the gravitational constant and ris the separation between the particles. From the Appendix F, Mass of the sun m = s.99 × 10 30kg Mass of the moon m m = 7.35 × 10 22kg 24 Mass of the earth m =e5.97 × 10 kg 11 Distance between the sun and the moon r = 1.10 × 10 m (earth’s orbit radius) 8 Distance between the earth and the moon r = 3284 × 10 m ( moon’s orbit radius) 11 2 2 Gravitational constant G = 6.67 × 10 N.m /kg Gravitational pull of the sun on the moon, Gm s m F 1 = 2 r1 6.67×1011N.m /kg ×1.99×1030kg×7.35×1022kg F 1 = (1.50×101) m 2 19 F 1 = 43.4 × 10 N 20 F 1 = 4.34 × 10 N …..(1) Gravitational pull of the earth on the moon, Gm e m F 2 = 2 r2 6.67×101N.m /kg ×5.97×10 24kg×7.35×1022kg F 2 = 8 2 2 (3.84×10 ) m F = 19.84 × 10 19 N 2 F = 1.98 × 10 20N …..(2) 2 Dividing equation (1) by equation (2), F1 4.34×100N F 2= 1.98×100N F 1 = 2.19 F 2 Therefore, the required ratio is 2.19. The moon orbits the earth.