Gravitational potential energy of satellites

I get -3.591*10^13.Just make sure you're using the correct values for the masses of the satellites (980kg) and the Earth (5.974*10^24kg), and that your radius is in meters. Also, don't forget to square the radius in the equation.U2=-" "/R2 =-1.96*10^13Again, check your arithmetic. I get -1.963*10^13J. And make sure you're using the correct value for the radius in meters.v^2=6.6*10^-11x980/R1This is the wrong equation. You should be using the relation between velocity and radius for a circular
  • #1
pbumper1
6
0

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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  • #2
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.
 
  • #3
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
 
  • #4
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.
 

1. What is gravitational potential energy?

Gravitational potential energy is the energy an object has due to its position in a gravitational field. It is a form of potential energy that can be converted into other forms of energy, such as kinetic energy.

2. How is gravitational potential energy of satellites calculated?

The formula for calculating the gravitational potential energy of a satellite is E = -(GmM)/r, where E is the potential energy, G is the gravitational constant, m is the mass of the satellite, M is the mass of the object it is orbiting, and r is the distance between the two objects.

3. How does the gravitational potential energy of a satellite affect its orbit?

The gravitational potential energy of a satellite determines its orbit by determining its speed and distance from the object it is orbiting. A higher potential energy will result in a larger orbit, while a lower potential energy will result in a smaller orbit.

4. Can the gravitational potential energy of a satellite change?

Yes, the gravitational potential energy of a satellite can change if its distance from the object it is orbiting changes. This can occur due to external forces, such as the gravitational pull of other objects, or by using a propulsion system to change the satellite's orbit.

5. How is the gravitational potential energy of a satellite used in space exploration?

The gravitational potential energy of a satellite is used in space exploration to determine the trajectory and speed of spacecrafts, as well as to plan and execute maneuvers, such as orbit transfers and rendezvous with other objects in space. It is also used in the design and operation of satellites for communication, Earth observation, and other purposes.

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