Gravitational potential energy of satellites

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SUMMARY

The discussion centers on calculating the gravitational potential energy and kinetic energy of two Earth satellites, A and B, each with a mass of 980 kg. Satellite A orbits at an altitude of 4500 km, while satellite B orbits at 13600 km. The correct formula for gravitational potential energy is U = -GmM/r, where G is the gravitational constant, m is the satellite mass, M is the Earth's mass, and r is the distance from the Earth's center. The user struggled with the calculations, particularly in determining the correct radius for each satellite's orbit, which includes the Earth's radius of 6378.1 km.

PREREQUISITES
  • Understanding of gravitational potential energy calculations
  • Familiarity with the gravitational constant (G = 6.674 × 10^-11 N(m/kg)^2)
  • Knowledge of circular orbital mechanics
  • Basic algebra for manipulating equations
NEXT STEPS
  • Review gravitational potential energy calculations using U = -GmM/r
  • Learn about kinetic energy in orbital mechanics, specifically using KE = 1/2 mv^2
  • Study the concept of work done in changing orbits, particularly W = GmM(1/R1 - 1/R2)
  • Explore the effects of altitude on satellite energy calculations
USEFUL FOR

Students studying physics, particularly those focusing on gravitational forces and orbital mechanics, as well as educators looking for examples of satellite energy calculations.

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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