Calculating Energy Requirements for Satellite Placement in Circular Earth Orbit

[rocketboy]

Hey everyone,

The following question is giving my friend and I a really hard time. My work is shown below.

'what is the total amount of energy needed to place a 2.0 x 10^3 kg satellite in circular Earth orbit, at an altitude of 5.0 x 10^2km above the surface of the earth?

Here are all the numbers needed to carry out the problem:

M = 5.8 x 10^24 kg (mass of earth)
m = 5.0 x 10 3 kg (mass of satellite)
r1 = 6.38 x 10^6 m (radius of earth)
r2 = 5.0 x 10^5 m + 6.38 x 10^6 m (altitude plus radius of earth)
G = 6.67 x 10^-11 N/kg. (Earth's gravitational field strength)

I figured that the energy needed would be equal to the energy of the satellite in orbit minus the energy of the satellite on Earth's surface...giving thus:

E(needed) = -1/2(GMm/r2) - (-GMm/r1)

where did I go wrong?

Thx!

 

[Fermat]

you have r2 as 500m instead of 500 km.
Or, is that a typo ?

 

[rocketboy]

uh...oops...lol, thanks man. yea that should be 500 km. i'll edit it out in the first post.

 

[rocketboy]

alright, but it still gives me the wrong answer...the correct one is 6.7 x 10^10 J.

 

[Fermat]

...
E(needed) = -1/2(GMm/r2) - (-GMm/r1)
...

Just noticed, where did the -1/2 come from ? is that another typo ?

 

[rocketboy]

the equation for total energy is -1/2(GMm/r2) is it not?

 

[Fermat]

alright, but it still gives me the wrong answer...the correct one is 6.7 x 10^10 J.

Hmm, I got 8.8 x 10^9 J.
I'll check my working.

 

[Fermat]

the equation for total energy is -1/2(GMm/r2) is it not?

To be honest, I've never seen that expression.
I used calculus and got,
E(needed) = GMm(1/r1 - 1/r2)

 

[rocketboy]

Interesting...using my method I got a similar answer to yours.

I'm starting to think the answer given to me is wrong. Thanks a lot for all your help man!