Why Is the Binding Energy of a Satellite Equal to Its Total Energy?

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SUMMARY

The binding energy of an orbiting satellite is equal to its total energy expressed as a positive value. In this case, if the total energy of the satellite is -1.4 x 1012 J, the binding energy is calculated to be 1.4 x 1012 J. This relationship is defined by the equations for gravitational potential energy and binding energy, specifically Eg = (-GMm)/r and Binding energy = (GMm)/2r. The binding energy represents the energy required to remove the satellite from its orbit, confirming that it is indeed the positive counterpart of total energy.

PREREQUISITES
  • Understanding of gravitational potential energy
  • Familiarity with the concepts of binding energy
  • Knowledge of the equations Eg = (-GMm)/r and Binding energy = (GMm)/2r
  • Basic principles of orbital mechanics
NEXT STEPS
  • Study gravitational potential energy in detail
  • Learn about the derivation of binding energy equations
  • Explore the implications of negative total energy in orbital mechanics
  • Investigate the role of mass and radius in satellite orbits
USEFUL FOR

Students studying astrophysics, physics educators, and anyone interested in understanding the principles of orbital mechanics and energy relationships in satellite dynamics.

rpullo
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Homework Statement



If an orbiting satellite has a total energy of -1.4 x 1012 J, then the binding energy is...

b. 1.4 x 1012 J

Homework Equations



Eg = (-GMm)/r
Binding energy = (GMm)/2r

The Attempt at a Solution



I was just wondering why the answer is 1.4 x 1012 J. Thanks
 
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Isn't it because binding energy is the same thing as total energy, only positive?
 

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