Radious of the geosynchronous ORBIT

[8parks11]

a)

What is the radius of the orbit of a communications relay satellite that always reamins above one point on the Earth's surface? Such an orbit is called a geosynchronous orbit.


- I could find this on google but what is an another way to solve this?


b) Can such a satellite be placed in geosynchronous orbit over ANY point on Earth's surface? WHY?

 

[QuantumCrash]

You can find it out by calculating it really. Are you sure that is the only important point? Radius is simply the height from the centre of the Earth and you can have almost any radius you want. What is important is angular velocity.
(Hint: How long does it take fo the Earth to make 1 full rotation?)

b) Yes and no really. The point is not as important as the actual orbit itself.

 

[andrevdh]

We assume that the satellite is in a circular orbit. This means that it is experiencing a centripetal force $$F_C$$ supplied by the gravitational attractive force $$F_G$$ of the earth

$$F_C = F_G$$

the centripetal force is given by

$$F_C = m\frac{v^2}{r}$$

with the mass and orbital speed of the satellite. r is its distance from the centre of the earth. The gravitational attractive force is given by

$$F_G = G \frac{Mm}{r^2}$$