How Do You Calculate the Height and Latitude of a Geostationary Satellite?

[TofuManiac]

1. Homework Statement
This is an question from (NZ) NCEA Scholarship Physics practise paper.
Calculate the height of geostationary satellite and hence calculate the lattidue of a satellite dish that must be placed vertical to point at it.
2. Homework Equations
Earth's rotational velocity = 465.1 m/s
therefore v of satellite = 465.1 m/s
using Fc = Fg
(mvsqr)/r = (GMm)/r
vsqr = GM/r
r = GM/vsqr

3. The Attempt at a Solution
Working so far from me:
geostationary satellite = satellite that orbits at of Earth's rotational velocity.
Earth's rotational velocity = 465.1 m/s
therefore v of satellite = 465.1 m/s
using Fc = Fg
(mvsqr)/r = (GMm)/r
vsqr = GM/r
r = GM/vsqr
= 1.8439x10pwrof9
therefore height of geostationary satellite from surface = r - radius of earth
= 1.8439x10pwrof9 - 6.39x10pwrof6
= 1.8375x10pwrof9 m
= 1.84 x 10pwrof9 m (3s.f.)
(I'm not very sure about the answer, it's quite rediculous)

And I'm having a problem with the second part of the question.
Please help :3

 

[gabbagabbahey]

geostationary satellite = satellite that orbits at of Earth's rotational velocity.
Earth's rotational velocity = 465.1 m/s
therefore v of satellite = 465.1 m/s

Careful, a geostationary satellite orbits at the same angular frequency (or period) as Earth's rotation, not the same velocity.

using Fc = Fg
(mvsqr)/r = (GMm)/r

You mean mv²/r=GMm/r² right?
[/QUOTE]

 

[tiny-tim]

Welcome to PF!

… hence calculate the lattidue of a satellite dish that must be placed vertical to point at it.

Hi TofuManiac! Welcome to PF!

For the second part, start by saying in words what the diagram would look like.

Remember that if the dish is vertical, then the direction of the satellite must be horizontal

 

[TofuManiac]

Thanks man, I totally forgot the most important fact about the geostationary satellite XD

Working:
so period of orbit = 24hr = 86400s
using derived formula - T = sqroot((4 pi^2 r^3)/(GM))
r comes down to 42250474.3m
therefore height of satellite from ground = 42250474.3 - 6.37x10^6 = 3.60x10^7m (3s.f.)

To Tiny-tim = thanks for the help too XD
Cheers :3