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fawk3s
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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 RE=6,38*106 m
So the radius of the orbit is R=RE+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