Physics: Principles with Applications (7th Edition)

Published by Pearson
ISBN 10: 0-32162-592-7
ISBN 13: 978-0-32162-592-2

Chapter 1 - Introduction, Measurement, Estimating - Problems - Page 19: 34

Answer

$6.5\times10^6 m$.

Work Step by Step

From Figure 1-16, we see that the distance d is a tangent line, and hence is perpendicular to the radius R. A right triangle is formed, with legs of R and d, and a hypotenuse of R + h. Use the Pythagorean Theorem. $$d^2+R^2=(R+h)^2=R^2+2Rh+h^2$$ $$ d^2=2Rh+h^2$$ Because h is much less than R, we may neglect the term $h^2$ because it is so much smaller than the term 2Rh. $$ d^2\approx 2Rh$$ $$ R=\frac{d^2}{2h}=\frac{(4400m)^2}{2(1.5m)} 6.5\times10^6 m $$ This is surprisingly close to the accepted value.
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