The altitude and velocity of a satellite in a geosynchronous orbit of mars:

Sub- Topic: Relative Clause

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\frac{\sqrt{GM}}{r}

\frac{\sqrt{GM}}{2 r}

None of these

answer is A.

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Detailed Solution

Concept- We must describe in this question how to determine a satellite's altitude and speed while it is in a geosynchronous orbit around Mars. So let's start by defining a geosynchronous orbit. The process for determining a satellite's altitude and velocity in a geosynchronous orbit around Mars will then be clear to us.
Geosynchronous orbit: A high earth orbit that enables satellites to coincide with the earth's rotation is known as a geosynchronous orbit. This orbit is 35,786 kilometers above the equator of the planet.
The steps below must be taken in order to determine any planet's geosynchronous orbit:
To begin with, we need to understand the centripetal force acting on the object while it is rotating. Using the formula below,

The gravitational pull between two objects will then be discovered. Using the formula below,

Where,

is the mass of mars and

is the mass of satellite

is the distance between them

is the gravitational constant
The centripetal force and gravitational force must now be equal for the satellite to remain stable in its orbit.

Simplifying the equation above yields the relation shown below.

We obtain the following relationship by simplifying the preceding equation.

If the time period of rotation is

and the orbit length is

. So, we can write following equation;

It implies following equation;

By simplifying this we get following equation;

By using the above relation we can find the distance. We obtain the following relationship by simplifying the aforementioned equation.
We will use the following formula to determine the velocity;

By using the above formula we can find the velocity of the satellite in the geosynchronous orbit of mars.
So, from the above explanation we can clearly understand the method to calculate the altitude and velocity of a satellite in a geosynchronous orbit of mars.
Hence, option 1 is correct.

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