The force due to gravity on an object with mass m at a height h above the surface of the earth is

where R is the radius of the earth and t is the acceleration due to gravity for an object on the surface of the earth.

(a) Express F as a series in powers of h/R.

(b) Observe that if we approximate F by the first term in the series, we get the expression F ≈ mg that is usually used when h is much smaller than R. Use the Alternating Series Estimation Theorem to estimate the range of values of h for which the approximation F ≈ mg is accurate to within one percent.

Transcribed Image Text:

mgR? 12 F = (R + h)?