Astrophysics - calculating orbital period

[superdave]

Homework Statement

Show that a satellite in low-Earth orbit is approximately P = C(1 + 3h/2R_E) where h is the height of the satellite, C is a constant, and R_E is the radius of the earth)

Homework Equations

Unsure

The Attempt at a Solution

I have no idea how to approach this.

 

[tiny-tim]

hi superdave!

(try using the X₂ icon just above the Reply box )

use centripetal acceleration and Newton's gravtiational law …

what do you get? ​

 

[superdave]

a= GM/r² =v²/r

v²=GM/r

Aaand, I'm stuck again.

 

[tiny-tim]

hi superdave!

(just got up :zzz: …)

hint: you need P, so write the centripetal acceleration as ω²r instead of v²/r

(and then compare r with r+h)