Answer to Question #104644 in Mechanics | Relativity for Emily

Question

Calculate the height of a satellite from the surface of the earth if its period is 12 h. Compare this height with the radius of the earth.

Answer 1

$m\frac{v^2}{r}=m\frac{GM}{r^2}$

$v=\frac{2\pi r}{T}$

So,

$r^3=(R+h)^3=\frac{GM}{4\pi^2}T^2$

$(6.38\cdot 10^{6}+h)^3=\frac{(6.67\cdot 10^{-11})(5.97\cdot 10^{24})}{4\pi^2}(12\cdot 3600)^2$

$h=20.22\cdot 10^{6}\ m$

$\frac{h}{R}=\frac{20.22\cdot 10^{6}}{6.38\cdot 10^{6}}=3.17$