Question

Mars rotates on its axis once every 24.8 hours. What is the altitude of a geosynchronous satellite orbiting Mars.

I have the speed of geosynchronous orbiting Mars. But I cant find the altitude of a geosynchronous satellite orbiting Mars.

Answer 1

To find the altitude of a geosynchronous satellite orbiting Mars, you can use the formula Altitude = (GMm/4π²)^(1/3) - R, where G is the gravitational constant, M is the mass of Mars, m is the mass of the satellite, and R is the radius of Mars.

A geosynchronous satellite is one that orbits at the same rate as Mars rotates on its axis.

Since Mars rotates on its axis once every 24.8 hours, the geosynchronous satellite would also complete one orbit in 24.8 hours.

To find the altitude of the geosynchronous satellite orbiting Mars, we can use the formula:

Altitude = (GMm/4π²)^(1/3) - R

Where G is the gravitational constant, M is the mass of Mars, m is the mass of the satellite, and R is the radius of Mars.

By plugging in the known values, we can calculate the altitude of the geosynchronous satellite orbiting Mars.

Answer 2

You have the answer right there in your hand, but
you're not sure of what you have yet.

If you have the speed, then ...

-- you know how far the satellite travels in 24.8 hours
and
-- you can figure out the radius of the circle that has
that distance for its circumference.

-- That radius is the distance of the satellite from the center of
the planet, when it's revolving once in 24.8 hours at that speed.
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By the way ... I wouldn't exactly call that a 'geo-synchronous' satellite,
because 'geo...' means something related to the Earth.
It would have to be a 'marso-synchronous' satellite, or whatever the
Greek word for Mars is.