Given:
The mass of the satellite is,
[tex]\begin{gathered} m=900000\text{ kg} \\ \end{gathered}[/tex]The mass of the earth is,
[tex]\begin{gathered} M=5.98\times10^{24}\text{ kg} \\ \end{gathered}[/tex]The radius of the earth is,
[tex]\begin{gathered} R=6.38\times10^6\text{ m} \\ \end{gathered}[/tex]The altitude of the satellite is,
[tex]\begin{gathered} h=4000\text{ km} \\ =4000\times10^3\text{ km} \end{gathered}[/tex]To find:
The time period of the satellite
Explanation:
The orbital speed of the satellite is,
[tex]\begin{gathered} v=\sqrt{\frac{GM}{R+h}} \\ Here,\text{ G=6.67}\times10^{-11}\text{ N.m}^2.kg^{-2} \end{gathered}[/tex]The orbital speed is,
[tex]\begin{gathered} v=\sqrt{\frac{6.67\times10^{-11}\times5.98\times10^{24}}{6.38\times10^6+4000\times10^3}} \\ =6.199\times10^3\text{ m/s} \end{gathered}[/tex]The period is,
[tex]\begin{gathered} T=\frac{2\pi(R+h)}{v} \\ =\frac{2\pi(6.38\times10^6+4000\times10^3)}{6.199\times10^3} \\ \approx10521\text{ s} \end{gathered}[/tex]The time period is 10521 s.