John Johnson edited The Earth.tex  over 10 years ago

Commit id: 983dc0680d669dadcc90578dedf38d539ce26b46

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\begin{enumerate}  \item {\it What is the radius of the Earth?}  My most recent frequent-flyer statement says that there are 3000 miles from Boston (BOS) to Los Angeles (LAX). Since planes travel along great circles, this distance $D_{\rm us}$ $D_u$  represents a segment of the Earth's circumference. There are four time zones (three intervals) from Boston to Los Angeles, out of 24, so $D_{\rm us}$ $D_u$  represents 1/8 of the Earth's circumference. \begin{align}  2\pi R_\oplus &= 8 D_{\rm us} D_u  \nonumber \\ R_\oplus &= \frac{8 D_{\rm US}}{2 D_u}{2  \pi} \nonumber \\ &= \frac{8 (3000 {\rm miles}}{2\times3} \nonumber \\  &= 4000~{\rm miles} \nonumber \\  &= 6400~{\rm km}