Gravitational potential energy of satellites

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Homework Help Overview

The problem involves calculating the gravitational potential energy and kinetic energy of two satellites in circular orbits around the Earth, as well as determining the work required to change the orbit of one satellite to match the other. The subject area is gravitational potential energy and orbital mechanics.

Discussion Character

  • Exploratory, Assumption checking, Mathematical reasoning

Approaches and Questions Raised

  • The original poster attempts various calculations involving the gravitational potential energy and kinetic energy of the satellites, but expresses difficulty in arriving at correct values. Some participants suggest clarifying the radius used in calculations, indicating a potential misunderstanding of the orbital radius.

Discussion Status

The discussion is ongoing, with participants providing hints and prompting the original poster to show their work. There is an indication that arithmetic errors may be present in the calculations, but no consensus has been reached on the correct approach or values.

Contextual Notes

The original poster has been working on the problem for several days and is seeking assistance. There may be constraints related to homework rules that limit the type of help that can be provided.

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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