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# Satelite orbiting the earth

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1. Satelite orbiting the earth
In a question, I'm shown that the orbital time period of a satelite is given by a formula:

T = 4pi^2 (R + h)^3 / GM, where R = radius of planet, h = height above surface of planet

and I'm asked to use it to prove that the period of orbit around the earth cannot be less than 85mins.

Basically the way to answer this question is to sub in h = 0, and assume that the orbit is literally just above the the earth's ground.

However I was just thinking, why would this be sufficient proof, doesn't the actual speed of the satellite need to be taken into account?

surely time period of orbit would vary with a given distance from the centre of earth, depending on how fast the satellites are orbiting, for example isn't it theorectically possible to take less than 85mins to orbit the earth if the satelitte is powered by some sort of mega rocket engine?
Last edited by internet tough guy; 08-06-2012 at 23:46.
2. Re: Satelite orbiting the earth
Can't you use the formula and put 85mins in it to get a value of how low it would be orbiting and why it's not plausible?
3. Re: Satelite orbiting the earth
(Original post by justravi)
Can't you use the formula and put 85mins in it to get a value of how low it would be orbiting and why it's not plausible?
i think the lowest value (o) would have to be inserted to prove you cant get lower i thin ..
beacause when the hight is zero, time taken is the least..
mabye..
4. Re: Satelite orbiting the earth
Just tried both ways, I think you're missing a squared in your time period tough guy.

Using 85 minutes as the time period would mean the height is 12,380m according to my calculations (probably wrong in that case lol)

And using height as 0 I get the time period to be 84.75.. minutes.
5. Re: Satelite orbiting the earth
(Original post by internet tough guy)
In a question, I'm shown that the orbital time period of a satelite is given by a formula:

T = 4pi^2 (R + h)^3 / GM, where R = radius of planet, h = height above surface of planet

and I'm asked to use it to prove that the period of orbit around the earth cannot be less than 85mins.

Basically the way to answer this question is to sub in h = 0, and assume that the orbit is literally just above the the earth's ground.

However I was just thinking, why would this be sufficient proof, doesn't the actual speed of the satellite need to be taken into account?

surely time period of orbit would vary with a given distance from the centre of earth, depending on how fast the satellites are orbiting, for example isn't it theorectically possible to take less than 85mins to orbit the earth if the satelitte is powered by some sort of mega rocket engine?
No, all satellites in a set orbit must travel at the same speed given by the equation v=sqrt(GM/r) which can be found by equating the centripetal force to the force due to gravity, this is the condition for a satellite to be in orbit. This shows that v depends only on the radius of the orbit and the mass of the planet it is orbiting.
If a satellite in orbit was powered by some external force, It would either escape into space or move into an orbit closer to earth

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Last updated: June 9, 2012
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