Question

Obtain the relation between orbital velocity and acceleration due to gravity g, for a satellite orbiting very close to the surface of the earth

Answer 1

ANSWER'_

I think you cannot, really. There are many possible orbital velocities, but only one escape velocity [for every astronomical body]

Answer 2

Explanation:

In this case, it is required to find the relation between orbital velocity and acceleration due to gravity g for a satellite orbiting very close to the surface of the Earth.

To find,

The orbital velocity of the satellite.

Solution,

Centripetal force is acting on the satellite when it is revolving such that,

$F_c=\dfrac{mv^2}{r}$ .......(1)

v is orbital velocity

r is radius of Earth

This force is balanced by the gravitational force between Earth and satellite. So,

$F_g=\dfrac{GMm}{r^2}$ ......(2)

From equation (1) and (2) we get :

$v=\sqrt{\dfrac{GM}{r}}$ ......(3)

Since, acceleration due to gravity is given by :

$g=\dfrac{GM}{r^2}\\\\M=\dfrac{gr^2}{G}$

So, equation (3) becomes :

$v=\sqrt{\dfrac{G\dfrac{gr^2}{G}}{r}}\\\\v=\sqrt{\dfrac{gr^2}{r}}\\\\v=\sqrt{gr}$

Therefore, this is the relation between orbital velocity and acceleration due to gravity.`

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