Gravity violating the conservation of energy in a closed system?

In summary, in my thought experiment, the gravitational potential energy decreases as the kinetic energy increases, accounting for the missing energy.
  • #1
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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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  • #2
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.
 
  • #3
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.
 
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  • #4
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:
 
  • #5
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
 

Related to Gravity violating the conservation of energy in a closed system?

1. How can gravity violate the conservation of energy in a closed system?

Gravity does not actually violate the conservation of energy in a closed system. The law of conservation of energy states that energy cannot be created or destroyed, only transferred or converted from one form to another. In a closed system, the total amount of energy remains constant. Therefore, gravity does not violate this law as it only causes a transfer of energy between objects.

2. What is an example of gravity violating the conservation of energy in a closed system?

One example that may seem like gravity is violating the conservation of energy in a closed system is the orbit of planets around a star. However, in this scenario, the gravitational potential energy of the planets is converted into kinetic energy as they move closer to the star, and vice versa as they move farther away. This maintains the total energy in the closed system.

3. How does the concept of potential energy relate to gravity in a closed system?

Potential energy is the energy an object has due to its position or configuration in a force field, such as gravity. In a closed system, the potential energy of an object may change due to the influence of gravity, but the total amount of energy in the system remains the same.

4. Can gravity ever create energy in a closed system?

No, gravity does not create energy in a closed system. As mentioned before, the total amount of energy in a closed system remains constant. Therefore, gravity can only cause a transfer or conversion of energy, not create it.

5. Are there any exceptions to gravity following the law of conservation of energy in a closed system?

No, there are no exceptions to the law of conservation of energy. While gravity may seem to defy this law in certain situations, it is always in accordance with the principle of energy conservation. Other factors, such as friction or external forces, may play a role in the apparent violation of this law, but gravity itself always follows the law of conservation of energy in a closed system.

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