A satellite of mass ms travels in a circular orbit of radius a around a planet of mass mp?ms.

Part A

Derive expressions for the orbital speed of a satellite.

Express your answer in terms of some or all of the variables mp, ms, a, and gravitational constant G.

vs =

Orbital speed of the satellite is   .

Explanation:

Given:

Gravitational constant =

Mass of the satellite =

Mass of the planet =

Radius of the orbit =

We have to derive the expressions for the orbital speed.

Let the orbital speed be 'vs'.

According to the question:

Force between the planet and the satellite.

From universal law of gravitation.

⇒ ...equation (i)

And

Their is centripetal force acting towards the planet.

And we know centripetal acceleration = .

From Newtons second law.

⇒

⇒

Here the velocity is vs and r = a and mass of the satellite is ms.

⇒    ...equation (ii)

Equating both the equations.

equation (i) = equation (ii)

⇒

⇒

⇒

So,

The orbital speed of the satellite is Sq-rt(Gm_p/a).

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