Chapter S3, Problem 59EAP

Gravitational Time Dilation on Earth. For a relatively weak gravitational field, such as that of a planet or an ordinary star, the following formula tells us the fractional amount of gravitational time dilation at a distance r from the center of an object of mass  $\begin{array}{l}{M}_{\text{object}}\text{:}\\ \frac{1}{c^2}\times \frac{G{M}_{\text{object}}}{r}\end{array}$ $\left[\text{G = 6}{\text{.67×10}}^{\text{-11}}{\text{m}}^{\text{3}}\text{/}\left({\text{kg × s}}^{\text{2}}\right){\text{; c = 3×10}}^{\text{8}}\text{m/s}\right]$ For example, while 1 hour passes in deep space far from the object, the amount of time that passes at a distance r is 1 hour multiplied by the factor above. (This formula does not apply to strong gravitational fields, like those near black holes.) Calculate the amount of time that passes on Earth’s surface while 1 hour passes in deep space.