The acceleration due to gravity on the surface of the earth is Use Exercise 43(b) to show that a satellite orbiting at the earths surface would have period T e 2 R e g 84 5 minutes Then estimate the distance R m from the moon to the center of the earth Assume that the period of the moon (sidereal m...

Hence By part b of Exercise 43 it follows that Gme 47 R T2 T Re Te 2 2 8 4nR 4 Re Gme 637810 9 ...

The acceleration due to gravity on the surface of the earth is Use Exercise 43(b) to show

Question:

The acceleration due to gravity on the surface of the earth is

g= = 9.8 m/s, where R = 6378 km Gme R

Use Exercise 43(b) to show that a satellite orbiting at the earth’s surface would have period T_e= 2π √R_e/g ≈ 84.5 minutes. Then estimate the distance R_m from the moon to the center of the earth. Assume that the period of the moon (sidereal month) is T_m ≈ 27.43 days.

Exercise 43(b)

b) According to Newton’s Laws of Motion and Gravity,

x"(t) = - Gme X R y"(t) = -Gme R

where G is the universal gravitational constant and me is the mass of the earth. Prove that R³/T²= Gme/4π². Thus, R³/T²has the same value for all orbits (a special case of Kepler’s Third Law).