Orbiting Satellite Energy Conservation

In summary, the conversation discusses a problem with a circular orbit and the equation L=mvR. The attempt at a solution involves an uploaded answer and a question about the energy before and after a collision. The conversation then raises the issue of the work-energy theorem and potential energy.
  • #1
oasis13
1
0

Homework Statement


I have uploaded the question. See attachment "question001"

Homework Equations


L=mvR for circular orbit

The Attempt at a Solution


See attachment "answer001". The problem is that my final answer seems to be imaginary, and I have tried to look for mistakes in my algebra which would lead me to this and haven't found any. Am I wrong in assuming that the Energy before the explosion is the same as the energy after the collision? I assumed that because no work was done on the orbiting mass, the energy was conserved. And there is no torque acting so angular momentum should be conserved.

I would be really grateful if someone could point out where I am going wrong :smile:
 

Attachments

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  • answer001.jpg
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Last edited:
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  • #2
The work-energy theorem refers to the change of kinetic energy. The KE of the satellite remains the same if no work was done on it. But what about the potential energy?

ehild
 

FAQ: Orbiting Satellite Energy Conservation

What is the energy of an orbiting satellite?

The energy of an orbiting satellite is the sum of its kinetic energy, which is the energy it has due to its motion, and its potential energy, which is the energy it has due to its position in the Earth's gravitational field.

How is the energy of an orbiting satellite calculated?

The energy of an orbiting satellite can be calculated using the formula E = K + U, where E is the total energy, K is the kinetic energy, and U is the potential energy. The kinetic energy can be calculated using the formula K = (1/2)mv^2, where m is the mass of the satellite and v is its velocity. The potential energy can be calculated using the formula U = -GMm/r, where G is the universal gravitational constant, M is the mass of the Earth, m is the mass of the satellite, and r is the distance between the satellite and the center of the Earth.

How does the energy of an orbiting satellite affect its orbit?

The energy of an orbiting satellite determines the shape and size of its orbit. A satellite with higher energy will have a larger orbit, while a satellite with lower energy will have a smaller orbit. This is because the energy of the satellite affects its velocity, which in turn affects its altitude and speed in orbit.

Can the energy of an orbiting satellite change?

Yes, the energy of an orbiting satellite can change due to external forces such as atmospheric drag or gravitational interactions with other objects. The energy can also be changed intentionally by using thrusters on the satellite to adjust its velocity and altitude.

Why is the energy of an orbiting satellite important?

The energy of an orbiting satellite is important because it determines the stability and longevity of its orbit. If the energy is too low, the satellite may eventually fall back to Earth. If the energy is too high, the satellite may escape Earth's orbit and enter into a new orbit around the Sun. Maintaining the proper energy level is crucial for the satellite to fulfill its intended purpose and continue to function in orbit.

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