Question

A orbiting satellite stays over a certain spot on the equator of (rotating) Mars. What is the altitude of the orbit (called a "synchronous orbit")?

Answer 1

Answer:

$h=17011.9143\ km$

Explanation:

The  synchronous orbit is that path around a planet where a satellite revolves around it such that its angular speed of revolution is equal to the angular speed of rotation of the satellite in the corresponding plane of rotation normal to the axis of spin of the planet.

As a result the satellite appears stationary from any point on the planet.

This height for any planet is calculated by the formula:

$h=\sqrt[3]{\frac{(G.M.T^2)}{4\pi^2} }-R$

where:

R = radius of hte planet

M = mass of the planet mars

T = rotational period of the planet

G = universal gravitational constant

Now using the above formula for the known facts:

$h=\sqrt[3]{\frac{(6.67\times 10^{-11}\times 6.4\times 10^{23}\times (24\times 60\times 60+37\times 60)^2)}{4\pi^2} }-3389950$

$h=17011.9143\ km$