Question

45. The Solar Maximum Mission Satellite was placed in a circular orbit about 150 mi above Earth. Determine (a) the orbital speed of the satellite and (b) the time required for one complete revolution.

Answer 1

(a)

$$F_c=F_g,$$ $$\dfrac{m_{sat}v^2}{R}=\dfrac{Gm_{sat}M_E}{R^2},$$ $$v=\sqrt{\dfrac{GM_E}{R}}=\sqrt{\dfrac{GM_E}{R_E+h}},$$ $$v=\sqrt{\dfrac{6.67\times10^{-11}\ \dfrac{N\times m^2}{kg^2}\times5.98\times10^{24}\ kg}{6.37\times10^6\ m+2.41\times10^5\ m}}=7767\ \dfrac{m}{s}.$$

(b)

$$\dfrac{T^2}{R^3}=\dfrac{4\pi^2}{GM_E},$$ $$T=\sqrt{\dfrac{4\pi^2R^3}{GM_E}},$$ $$T=\sqrt{\dfrac{4\pi^2\times(6.37\times10^6\ m+2.41\times10^5\ m)^3}{6.67\times10^{-11}\ \dfrac{N\times m^2}{kg^2}\times5.98\times10^{24}\ kg}}=5348\ s=1.48\ h.$$