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Question: The force due to gravity on an


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



The force due to gravity on an object with mass m at -1

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 ~ mt 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. (Use R = 6400 km.)





Transcribed Image Text:

mgR? F = (R + h)?

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