Question

Need help on number 5. Got the answer but don’t know how to use the formulas. I need the formulas very simplified as possible

Answer 1

Given:

The mass of the satellite is,

`\begin{gathered} m=900000\text{ kg} \\ \end{gathered}`

The mass of the earth is,

`\begin{gathered} M=5.98*10^(24)\text{ kg} \\ \end{gathered}`

The radius of the earth is,

`\begin{gathered} R=6.38*10^6\text{ m} \\ \end{gathered}`

The altitude of the satellite is,

`\begin{gathered} h=4000\text{ km} \\ =4000*10^3\text{ km} \end{gathered}`

To find:

The time period of the satellite

Step-by-step explanation:

The orbital speed of the satellite is,

`\begin{gathered} v=\sqrt{(GM)/(R+h)} \\ Here,\text{ G=6.67}*10^(-11)\text{ N.m}^2.kg^(-2) \end{gathered}`

The orbital speed is,

`\begin{gathered} v=\sqrt{(6.67*10^(-11)*5.98*10^(24))/(6.38*10^6+4000*10^3)} \\ =6.199*10^3\text{ m/s} \end{gathered}`

The period is,

`\begin{gathered} T=(2\pi(R+h))/(v) \\ =(2\pi(6.38*10^6+4000*10^3))/(6.199*10^3) \\ \approx10521\text{ s} \end{gathered}`

The time period is 10521 s.