Gravitation and Circular Orbits

[kevi555]

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.

 

[foxjwill]

Try expanding the equation and see what you get. (HINT: think $$W=-\Delta U_g$$)

 

[kevi555]

"W" as in work? or what variable?

 

[foxjwill]

"W" as in work? or what variable?

Work.

 

[Shooting Star]

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.

 

[Shooting Star]

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.