Question

Satellite orbits at a distance from earths center of about 6.6 earth radii and takes 24h to go around once. What distance (in meters) does the satellite travel in one day? What is the orbital velocity (in m/s)?

Answer 1

We know that the radii of the orbit is 6.6 the earth one. To get the distance travel in one day we calculate the circunference of that orbit:

`\begin{gathered} C=(6.6)(6371)(2\pi) \\ C=264,199.14 \end{gathered}`

Therefore the distance travel by the satellite is 264199.14 km per day.

Now, to get the orbital velocity we need to use the equation:

`v=\sqrt[]{(MG)/(r)}`

where M is the mass of the object at the center (in this case the earth), G is the gravitational constant and r is the radius of the orbit, then we have:

`\begin{gathered} v=\sqrt[]{((5.9722*10^(24))(6.67*10^(-11)))/((6.6)(6.371*10^6))} \\ v=3077.89 \end{gathered}`

Therefore the orbital velocity is 3077.83 m/s.