When a body is near the surface of the earth, we usually assume that the force due to

Chapter 0, Problem 51

(choose chapter or problem)

When a body is near the surface of the earth, we usually assume that the force due to gravity on it is a constant mg, where m is the mass of the body and g is the acceleration due to gravity at sea level. For a body at a distance h above the surface of the earth, a more accurate expression for the force F is F = mgR2 (R + h)2 where R is the radius of the earth. We will consider the situation in which the body is close to the surface of the earth so that h is much smaller than R. (a) Show that F mg. (b) Express F as mg multiplied by a series in h/R. (c) The first-order correction to the approximation F mg is obtained by taking the linear term in the series but no higher terms. How far above the surface of the earth can you go before the first-order correction changes the estimate F mg by more than 10%? (Assume R = 6400 km.)