Question

a satellite revolve around the earth at a height 900 km above the surface of the earth in a circular orbit. calculate its orbital velocity.

Answer 1

Dear Student,

$$\begin{gathered} \mathrm{Let}\mathrm{mass}\mathrm{of}\mathrm{earth},\mathrm{M}=6\times {10}^{24}\mathrm{kg} \\ \mathrm{Radius}\mathrm{of}\mathrm{earth},{\mathrm{R}}_{\mathrm{e}}=64\times {10}^5\mathrm{m} \\ \mathrm{height},\mathrm{h}=900\mathrm{km}=9\times {10}^5\mathrm{m} \\ \mathrm{Radius}\mathrm{of}\mathrm{orbit},\mathrm{R}={\mathrm{R}}_{\mathrm{e}}+\mathrm{h} \\ \mathrm{R}=64\times {10}^5+9\times {10}^5 \\ \mathrm{R}=73\times {10}^5\mathrm{m} \\ \mathrm{G}=6.67\times {10}^{-11}{\mathrm{Nm}}^2/{\mathrm{kg}}^2 \\ \mathrm{Orbital}\mathrm{velocity},\mathrm{V}=\sqrt{\frac{\mathrm{GM}}{\mathrm{R}}} \\ \mathrm{V}=\sqrt{\frac{6.67\times {10}^{-11}\times 6\times {10}^{24}}{73\times {10}^5}} \\ \mathrm{V}=\sqrt{5.48\times {10}^8} \\ \mathrm{V}=2.34\times {10}^4\mathrm{m}/\mathrm{s} \end{gathered}$$