Gravity violating the conservation of energy in a closed system?

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Discussion Overview

The discussion revolves around a thought experiment concerning gravity and its implications on the conservation of energy within a closed system. Participants explore the relationship between rest mass, kinetic energy, and gravitational potential energy as two masses are brought together by gravitational attraction.

Discussion Character

  • Exploratory
  • Technical explanation
  • Conceptual clarification

Main Points Raised

  • One participant proposes a scenario where two masses at rest in empty space begin to accelerate towards each other due to gravity, leading to questions about energy conservation and the implications for mass.
  • Another participant suggests that the potential energy imparted to the masses when the second mass is introduced accounts for the energy discrepancy noted in the thought experiment.
  • A question is raised regarding the rest mass of a gravitationally bound system, suggesting it may be less than the sum of its components due to escape energy considerations.
  • A later reply reiterates the importance of potential energy in the context of the conservation of energy, emphasizing that total energy remains constant in a closed system as kinetic and gravitational potential energies interchange.

Areas of Agreement / Disagreement

Participants generally agree on the role of potential energy in addressing the initial concerns about energy conservation. However, the discussion includes varying interpretations regarding the implications for mass and energy in gravitational systems, indicating that multiple views remain.

Contextual Notes

Some assumptions about the definitions of energy types and the nature of the closed system may not be fully articulated, and the discussion does not resolve the complexities surrounding the rest mass of gravitationally bound systems.

Who May Find This Useful

This discussion may be of interest to those exploring concepts in gravitational physics, energy conservation, and the implications of mass in dynamic systems.

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I have devised a simple thought experiment which leads me to an absurd conclusion and I feel I’m missing something obvious but I can't see where I’m wrong and I hope you could help point out my error.

I start with an empty space initially containing two masses that are at rest relative to each other, the total energy of this system would be the rest mass (E=mc2) right?

But as time starts gravity will start accelerating these masses towards each other giving me the energy of the rest mass + a non 0 kinetic energy. This would in my mind imply either a decrease in the mass of the objects or an increase of the total energy of the closed system, neither of which seem logical?

Now I realize I’m probably missing something obvious here but I can't for my life figure out what…
 
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When you put the first mass in the system, all is fine and dandy. However, by placing the second mass in the system, you obviously impart a potential energy to each mass. This potential energy is what accounts for the missing energy in your thought experiment.
 
What is the rest mass of a gravitationally bound system?

Presumably it is less than that of its components, by the amount of the escape energy. Might not be trivial to prove the difference in the system's inertia.
 
Last edited:
Pengwuino said:
When you put the first mass in the system, all is fine and dandy. However, by placing the second mass in the system, you obviously impart a potential energy to each mass. This potential energy is what accounts for the missing energy in your thought experiment.

Ah, of course. As I thought it’s obvious now that somebody pointed it out. I blame not noticing it myself on having substituted sleep with caffeine for to long now during exam season…

Anyway thanks so much for the help. :smile:
 
Be careful with those caffeine substitutions - they work for math but not so much for thought experiments in physics.

To add to the above:
Law of conservation of energy (simplified)
For this system -> Etotal = EK + EG
Where EK is the kinetic energy of the system and EG is the gravitational potential energy.

Etotal is constant in a closed system like the one you described, so you can see that as your masses are drawn together by the force of gravity, EG decreases as EK increases. :P
 

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