Work required to lift object from earth's surface to circular orbit

[aeromat]

Homework Statement

How much work must be done by a rocket engine to lift a 1000kg payload from rest on the Earth's surface to a circular orbit of radius 2Re (2 times the radius of the earth)?

Homework Equations

Eg = -GmM/r
Ek = GmM/2r

The Attempt at a Solution

I know ΔE = W
I know that the energies are the following:
Initial E {0 + Eg} <-- assuming its at rest
Final E {0 + Eg} <-- when it has reached this distance.

However, I don't know how I am going to solve this out, or whether or not what I did was correct...

 

[ideasrule]

Initial E {0 + Eg} <-- assuming its at rest

This is correct.

Final E {0 + Eg} <-- when it has reached this distance.

This is not. Kinetic energy can't be zero, or else the satellite would plummet to the ground instead of orbiting.

Once you figure out the final and initial energies, work done is just the difference between the two, as you've noted in your first equation.

 

[HallsofIvy]

Yes. Note that "Work required to lift object from Earth's surface to circular orbit" and "How much work must be done by a rocket engine to lift a 1000kg payload from rest on the Earth's surface to a circular orbit of radius 2Re (2 times the radius of the earth)?" are completely different questions!

 

[gneill]

It might be pertinent to note that "at rest on the Earth's surface" does not mean it truly motionless. The Earth rotates on its axis, so even while the rocket is "at rest" on the surface it can take advantage of an initial velocity (kinetic energy).