Answer to Question #104008 in Physics for Emily Pons

Question #104008
A satellite revolves around the earth at a height h = 4Re, where Re = 6400 km is the earth’s radius.
(a) Find the speed of the satellite in terms of the earth’s radius and the gravitational acceleration on the
surface of the earth (g0 = 9.8 m/s2).
(b) Calculate the speed of the satellite at the height h = 4Re, by using the formula in part (a).
(c) Calculate the period of the satellite around the earth.
1
Expert's answer
2020-02-28T10:22:20-0500

a)


mv2r=GMmr2v2=GMr\frac{mv^2}{r}=\frac{GMm}{r^2}\to v^2=\frac{GM}{r}

v=GMr=GMRe+4Re=g0Re5v=\sqrt{\frac{GM}{r}}=\sqrt{\frac{GM}{R_e+4R_e}}=\sqrt{\frac{g_0R_e}{5}}

b)


v=(9.8)(6400103)5=3500msv=\sqrt{\frac{(9.8)(6400\cdot 10^3)}{5}}=3500\frac{m}{s}

c)


T=2π(5Re)vT=\frac{2\pi (5R_e)}{v}

T=10π(6400103)3500=57446 s=16 hT=\frac{10\pi (6400\cdot 10^3)}{3500}=57446\ s=16\ h


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