Gravitational potential energy of satellites

AI Thread Summary
The discussion revolves around calculating the gravitational potential and kinetic energies of two satellites, A and B, with a mass of 980 kg each, orbiting at different altitudes. The potential energy equations are derived using the formula U = -GmM/r, where r is the radius of the orbit, including Earth's radius. The user struggles with arithmetic and the correct application of the formulas, leading to incorrect energy values. Additionally, the work required to change satellite A's orbit to that of satellite B is also calculated using the formula W = GmM(1/R1 - 1/R2). Accurate calculations and careful attention to detail are emphasized for correct results.
pbumper1
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Homework Statement


Two Earth satellites, A and B, each of mass each of 980kg, are launched into circular orbits around the Earth's center. Satellite A orbits at an altitude of 4500kg, and satellite B orbits at an altitude of 13600km.
What are the potential energies of the two satellites?
What are the kinetic energies of the two satellites?
How much work would it require to change the orbit of satellite A to match that of satellite B?

Homework Equations


GmM2/r^2


The Attempt at a Solution


I have tried this problem several ways adding the radius of the earth, not adding the radius. I have been working on this problem for the past 3 days and can't seem to get any of it. Please help!
 
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Show what you've done so far.

Hint: The "r" you need is the radius of the orbit, which is the radius of the Earth plus the altitude.
 
R=6378.1+4500=R1 R=6378.1+13600=R2
R1=10878.1 R2=19978.1
U1=-6.6*10^-11x980x5.974*10^24/R1 =-3.59*10^13
U2=-" "/R2 =-1.96*10^13 got them both wrong
v^2=6.6*10^-11x980/R1
plug v^2 to 1/2mv^2 i got 2.94*10^9 and 1.6*10^9 got them both wrong

W=GmM(1/R1-1/R2)=1.60*10^13 got that wrong too
 
pbumper1 said:
R=6378.1+4500=R1 R=6378.1+13600=R2
R1=10878.1 R2=19978.1
OK.
U1=-6.6*10^-11x980x5.974*10^24/R1 =-3.59*10^13
Check your arithmetic.
 
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