Satellite Energy and Orbit problem

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Homework Help Overview

The problem involves a spy satellite in a circular orbit around the Earth, which experiences an increase in velocity due to a thruster firing in the outward radial direction. Participants are exploring how this change affects the satellite's total energy and its new orbit.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning, Problem interpretation

Approaches and Questions Raised

  • Participants discuss the initial kinetic and potential energy of the satellite, questioning how the additional velocity impacts these values. There is an exploration of the relationship between energy and forces in the context of orbital mechanics.

Discussion Status

Some participants have provided calculations for initial kinetic and potential energy, while others have raised questions about the implications of the additional velocity. There is a recognition of the negative total energy prior to the thruster firing, and a suggestion that the new orbit may be an open orbit, indicating a productive line of inquiry.

Contextual Notes

Participants are navigating the complexities of orbital mechanics, including the definitions of kinetic and potential energy in the context of gravitational fields. There is an ongoing discussion about the implications of escape velocity and its relationship to the satellite's tangential velocity.

Dextrine
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Homework Statement


A spy satellite of mass m is in a circular orbit with radius R and velocity v around
the earth. One of the satellites thrusters suddenly fires giving it an additional
velocity v in the outward radial direction (same v). What is the new total energy
of the satellite? What is the new orbit of the satellite?

Homework Equations


mv^2/r
GMm/r^2
-K=.5U
2K+U=0

The Attempt at a Solution


I honestly don't really have an idea how to even set up the problem. From what I understand mv^2=GMm/r^2 for circular orbit which should I could then use to find the energy, but I don't know how the velocity increasing radially will affect this. Any helpful nudge in the right direction would be greatly appreciated.
 
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Dextrine said:
mv^2=GMm/r^2
I think you mistyped the left hand side. As a result you have energy on the left and a force on the right.

What is the initial KE?
What is the initial PE?
How much energy was added?
 
haruspex said:
I think you mistyped the left hand side. As a result you have energy on the left and a force on the right.

What is the initial KE?
What is the initial PE?
How much energy was added?
So initially I got my K=1/2GMm/r and my U=-GMm/r

Since we are adding another V, which is Sqrt[GM/r], i get that my new total energy = -.5GMm/r+.5GMm/r=0

however, this doesn't seem right
 
Dextrine said:
So initially I got my K=1/2GMm/r and my U=-GMm/r

Since we are adding another V, which is Sqrt[GM/r], i get that my new total energy = -.5GMm/r+.5GMm/r=0

however, this doesn't seem right
It's right :). Remember, the total energy beforehand was negative.
So what do you get for the new orbit?
 
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haruspex said:
It's right :). Remember, the total energy beforehand was negative.
So what do you get for the new orbit?
AH, infinite radius? so we get an open orbit? Thanks a ton. Didn't think it would be so simple
 
Dextrine said:
AH, infinite radius? so we get an open orbit? Thanks a ton. Didn't think it would be so simple
That's it. So what general rule do you deduce for vertical escape velocity from a given orbit?
 
Hmm, it must be equal to or greater than tangential velocity?
 
Dextrine said:
Hmm, it must be equal to or greater than tangential velocity?
Equal. ("Escape velocity" means the minimum necessary to escape the gravitational field.)
 
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