Problem geostationary satellite

[fluidistic]

Homework Statement

At what height (from the ground of the Earth) must be placed a geostationary satellite?

Homework Equations

The Attempt at a Solution

I'm not sure I understand well the question. I guess they are asking for a satellite in such a position that he would not deviate from the point over the ground it is situated. Well, I believe that the height doesn't matter at all and what matters is the velocity you put the satellite in orbit that matters. But the answer of the question is 3.58 \cdot 10^5 \text{km}. I have no idea of how to get the solution. Do you have an idea?

 

[Redbelly98]

They mean that the orbital period is 1 day, so that the satellite is always directly over the same place on Earth.

Also, assume a circular orbit. What equations do you know that apply to:
1. gravity
2. circular motion

 

[fluidistic]

They mean that the orbital period is 1 day, so that the satellite is always directly over the same place on Earth.

Also, assume a circular orbit. What equations do you know that apply to:
1. gravity
2. circular motion

Hmm... I guess they want me to use F_c=m_ca_c=m_c\frac{v^2}{r}. Also F_c=\frac{Gm_cM_E}{r^2} which led me to conclude that r=\frac{GM_E}{v^2}. But the velocity is unknown so I'm stuck. At last I could calculate it but only in function of the altitude (using the formula v=\omega r) which is precisely what I'm looking for...

 

[alphysicist]

Hmm... I guess they want me to use F_c=m_ca_c=m_c\frac{v^2}{r}. Also F_c=\frac{Gm_cM_E}{r^2} which led me to conclude that r=\frac{GM_E}{v^2}. But the velocity is unknown so I'm stuck. At last I could calculate it but only in function of the altitude (using the formula v=\omega r) which is precisely what I'm looking for...

What is \omega for this satellite?

 

[Redbelly98]

r=\frac{GM_E}{v^2}. But the velocity is unknown so I'm stuck. At last I could calculate it but only in function
of the altitude (using the formula v=\omega r) which is precisely what I'm looking for...

You're on the right track. What happens if you substitute v=\omega r into the previous equation here?

 

[fluidistic]

Oh... Thanks to both! I didn't think about replacing v by \omega r!