Period of a satellite orbiting Earth

[fawk3s]

Homework Statement

A satellite is orbiting Earth 4200 km from Earth's surface. Considering the trajectory to be a circle, calculate the period of the orbiting satellite.

Homework Equations

a=v²/r
F=GmM/r²
c=2r*PI
v=l/t

The Attempt at a Solution

Well, the textbook gives the mass of the Earth to be M=5,98*10²⁴ kg and the radius of Earth R_E=6,38*10⁶ m

So the radius of the orbit is R=R_E+4200 km=10,58*10⁶ m

Now off to find the gravitational acceleration for the satellite at the given distance (which is also the centripetal acceleration in this case)

F=GmM/R²
a=F/m

so

a=GM/R²
a=3,56 m/s²

a=v²/R => v=sqrt(a*R)
v=6,14*10³ m/s

c=2R*PI
c=66,44*10⁶

And now for the period

v=c/T => T=c/v
T=10820 s

The textbook says it ought to be 8300 s. Where did I go wrong? Have double checked the numbers, so don't think its a calculation error.

Thanks in advance,
fawk3s

 

[vela]

I get the same answer you do. The book's answer is wrong.

 

[Lobezno]

This post may be redundant, as I'm not sure exactly what you did on the second half, but...

If you use the Newtonian variation of Kepler's third law, the number pops out straight away!

 

[fawk3s]

Thanks guys.