Calculating Orbital Height for a Satellite Orbiting the Earth

[shad0w0f3vil]

Hi there,

I received this question with regards to planetary (or in this case satellite) motion:

Determine at what height above the Earth an arteficial satellite must orbit if it is to remain in the same place relative to the Earth (Hint: Model the situation using Kepler's Laws of Motion).

I believe that both the second and third laws are not applicable for this question, meaing the first law should be used. I am just unsure of how to 'start' it off.

Any help with this would be greatly appreciated.

 

[Dick]

The third law is the only one that matters. What is it? Why can't you use it?

 

[shad0w0f3vil]

I thought I didnt have enough information. For example I do not know the period

 

[Dick]

I thought I didnt have enough information. For example I do not know the period

If it remains in the same place relative to the earth, it must go around the Earth in the same time it takes the Earth to rotate. I.e. it's period must be 24 hours.

 

[shad0w0f3vil]

ok so how do i work out my distance from the Earth then? or do i work with respect to the sun?

Just that when I try it i end up with the average distance being equal to 0km, which obviously is not correct

 

[shad0w0f3vil]

hold that thought, I managed to get a different answer from 0. I got, 6,380,000km.

any ideas on this value?

 

[Dick]

hold that thought, I managed to get a different answer from 0. I got, 6,380,000km.

any ideas on this value?

Yes. They are both way wrong. Could you show us the equation you are using and the numbers you are plugging into it?

 

[confuted]

Hint: $$T^2=\frac{4\pi r^3}{GM}$$

M is the mass of earth...