Derivation of an expression for centripetal acceleration

[Sophieg]

Homework Statement

I have derived the expression for the velocity of the satellite v= root of GM/r however I'm struggling to derive an expression for the centripetal acceleration of a satellite orbiting Earth.

Homework Equations

The Attempt at a Solution

I'm not entirely sure which equations to relate or equate. To find the velocity I equated the force between two masses and the centripetal force and rearranged.

 

[Sophieg]

update: I think I've worked it out.. I equated the equation for centripetal force F=mv^2/r (of the planet) to the force between the two masses (planet and the satellite) to get:
- Gm1m2/r^2 = mv^2/r ... canceled a mass from either side and obtained Gm/r^2=v^2/r and since v^2/r = centripetal acceleration then the answer is GM/r^2?
Is this correct?
Thanks in advance!

 

[Andrew Mason]

Hi sophleg. Welcome to PF!

Your answer is correct but I am a bit puzzled by how you determined that $v = \sqrt {GM/r}$ before working out the centripetal acceleration.

AM

 

[Sophieg]

Hello Andrew,

Thank you!

I equated the force between two masses F=Gm1m2/r^2 = centripetal force F=mv^2/r and rearranged for v!