Gravitation and Circular Orbits

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Homework Help Overview

The discussion revolves around gravitational equations related to launching a satellite into a circular orbit at a specific altitude above the Earth. The original poster seeks assistance in demonstrating a specific energy equation involving gravitational potential energy and kinetic energy, while neglecting Earth's rotation.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • Participants discuss substituting variables and expanding equations, with one suggesting to think about work in terms of gravitational potential energy. There is also a query about the meaning of "W" in the context of work.

Discussion Status

The discussion is ongoing, with participants exploring different aspects of the problem, including the relationship between potential and kinetic energy in orbit and the forces involved in circular motion. Some guidance has been offered regarding the concepts of work and energy, but no consensus has been reached.

Contextual Notes

Participants are working under the assumption that Earth's rotation can be neglected, and there is an emphasis on understanding the forces that maintain circular motion.

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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