Gravitation and Circular Orbits

AI Thread Summary
The discussion focuses on calculating the energy required to launch a satellite into a circular orbit at a specific altitude, neglecting Earth's rotation. The equation provided relates gravitational potential energy and kinetic energy, emphasizing the need to consider both when determining the total energy required. Participants suggest substituting variables and expanding equations to simplify the problem, with hints to use the work-energy principle. The conversation also touches on the forces involved in circular motion and the relationship between potential and kinetic energy in this context. Understanding these concepts is crucial for solving the problem accurately.
kevi555
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Just a question about gravitation equations:

Neglecting Earth's rotation, show that the energy needed to launch a satellite of mass m into circular orbit at altitude h is equal to:

(\frac {GMm}{R})(\frac{R+2h}{2(R+h)})

Where R = the radius of the Earth and M = the mass of the Earth.

I've tried subbing in r=h+R and it hasn't given me much help.

Any help would be truly appreciated! Thanks all.
 
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Try expanding the equation and see what you get. (HINT: think W=-\Delta U_g)
 
"W" as in work? or what variable?
 
kevi555 said:
"W" as in work? or what variable?

Work.
 
kevi555 said:
Just a question about gravitation equations:

Neglecting Earth's rotation, show that the energy needed to launch a satellite of mass m into circular orbit at altitude h is equal to:

(\frac {GMm}{R})(\frac{R+2h}{2(R+h)})

Where R = the radius of the Earth and M = the mass of the Earth.

I've tried subbing in r=h+R and it hasn't given me much help.

Any help would be truly appreciated! Thanks all.

What is the force that makes a body go round in a circle? What is supplying that force here? You have to equate the two.
 
Some addition which I didn't bother to mention:

Energy reqd = (PE + KE) in orbit - PE on surface of earth. You have to use the previous concept anyway.
 

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