Gravitational Potential

ryandaniels2015

Hi, Just a question on gravitational potential,

There is a satellite of mass 750kg, and it stays on the surface of the earth, it is then moved into a geosynchronous orbit, and both gravitational potential energies are told to be calculated,

When you use the equation V=-GM/r Why do you use M as the mass of the earth even when calculating the satellite in a geosynchronous orbit away from the surface of the earth, why don't you use the mass of the satellite?

Thanks!

Reply 1

The-Spartan

6

Ok so you have:

Now you have the circular motion equation defined as

F=\frac{mv^2}{r}

And you have the gravitational equation

F=\frac{GMm}{r^2}

You can equate these two equations:

\dfrac{GMm}{r^2}=\dfrac{mv^2}{r}

Doing some cancellations of

m

and

r

\dfrac{GM}{r}=v^2

Which is the equation for velocity of a satellite in orbit. Note how this only involves the mass of the planet (Earth)

Reply 2

crashMATHS

16

Original post by ryandaniels2015

Hi, Just a question on gravitational potential,

There is a satellite of mass 750kg, and it stays on the surface of the earth, it is then moved into a geosynchronous orbit, and both gravitational potential energies are told to be calculated,

When you use the equation V=-GM/r Why do you use M as the mass of the earth even when calculating the satellite in a geosynchronous orbit away from the surface of the earth, why don't you use the mass of the satellite?

Thanks!

The gravitational field is being caused by the Earth, so you use the mass of the Earth when looking at the gravitational potential.