Why does gravity seem to get energy out of nowhere?

Question

Most of the forces have an end point. A positively charged object, when it touches a negatively charged object, becomes neutral and stops attracting other negatively charged objects. We need energy to ionise it again. A permanent magnet constantly loses its magnetism as its atoms and their magnetic alignment slowly get misaligned. We need energy in forms like electricity to constantly keep something magnetic. Radioactive fusion and fission break down or form new atoms out of the old ones, but the new atoms are very stable compared to the old ones, even neuclear energy seems to reach an end point. But why is it that gravity does not have an end point? As an object gathers mass, it has more gravitational force. I agree, to separate the object from the mass, we must require energy, but still the object don't stop attracting new objects. What causes this anomaly?

To summarise, electric, magnetic and nuclear forces all need energy to be created and maintained. Why does gravity not require this energy of maintainance?

Answer 1

You have described a few forms of potential energy storage that "leak" energy over time. As a radioactive sample decays, potential energy in the atoms gets converted to other forms of energy. A charged battery may lose charge over time, as chemical energy in the battery is slowly dissipated into the environment. A capacitor can hold potential energy, which is discharged when the plates touch. A water tower with a small hole at the bottom will quite literally leak, losing the potential energy stored in the water. All of these are forms of potential energy storage that seem to spontaneously "lose" energy over time, but in reality we can in fact track how that energy seeps out of the storage device and is converted to other forms - the energy is never truly "lost", it just goes somewhere else.

Gravitational potential energy is no different. Unsupported objects spontaneously fall to the ground, dissipating the potential energy they once held. As mountains erode and become lower in elevation, they hold less potential energy. In order to maintain the gravitational potential energy in a system, you'd have to lift every pebble that rolled down a mountain back to where it started, performing work in order to keep the potential energy "topped up", exactly the same way you might need to recharge a battery that's slowly discharged over a long period of time. No form of energy fundamentally needs to be "maintained", it's just that most forms of energy storage are not perfect, and dissipate that energy in other forms.

The fact that as an object accrues mass it exerts a greater gravitational force does not say anything about the energy of the system. A large meteor far from the earth has a great deal of gravitational potential energy that would be dissipated if it collided with the earth. After it does, the earth now has greater mass and exerts a larger gravitational force on other distant objects, but the gravitational potential of the earth-meteor system is entirely dissipated.

Answer 2

The virial theorem applies to gravitational forces, with the result that, in a bound system, the average kinetic energy $K$ has half the magnitude of the average potential energy $U$:

$$ \left<K\right> = -\frac12\left<U\right> $$

This is in a picture where we think of a system as “bound” if its total energy $K+U<0$ is negative, because the particles don’t have enough kinetic energy to escape to infinity.

If we have enough bound gravitationally-interacting particles that we can think of them as “a gas,” then the temperature of that gas goes like the kinetic energy, $T\propto\left<K\right>$. This gives the surprising result that the heat capacity of a gravitationally-bound system is negative:

$$ C = \frac{\partial T}{\partial U} < 0 $$

This is different from our usual experiences with heat capacity. If I add energy to a block of iron, it’ll generally get hotter. But if I add energy to a gravitational system, it’ll generally get bigger, and all the orbits will get slower.

For example, consider what happens to a star when it runs out of hydrogen in its core and fusion slows down. It’s the energy from fusion that holds the star up, so the outer layers start to compress the core … making it hotter. If this compression goes on long enough, the core will get hot enough to start burning the helium “ash” left over from the hydrogen fusion. Helium burning is much more energetic than hydrogen burning, so the star as a whole heats up … which makes the outer layers of the star expand and cool off. When this happens to our Sun, it’ll become a “red giant star”: its surface will be cooler than now, but its total brightness will increase. In some “variable” stars, feedback between these processes can cause the star to oscillate.

The “end point” for a gravitationally-bound system is when all of the mass has collapsed to a black hole. However, quantum mechanics predicts that black holes emit Hawking radiation with a temperature like $T \propto 1/M$, and black holes still have negative heat capacity. A black hole in a hot environment will be a net absorber of radiation, and will get bigger and colder. A black hole in a cold environment will be a net emitter of radiation, and will get smaller and hotter.

That’s why you can seemingly extract energy from a gravitational system for ever: the more energy you remove, the hotter it gets. Negative heat capacities are weird.

Answer 3

Why does gravity seem to get energy out of nowhere?

You are mixing concepts of energy and force. The gravitational force "does not get energy", but it does work on an object if the object moves. The work is a scalar quantity defined as force over displacement

$$W = \int \vec{F} \cdot d\vec{r}$$

If there is no displacement, no work is being done!

A positively charged object, when it touches a negatively charged object, becomes neutral and stops attracting other negatively charged objects.

This is true because electromagnetic force can be both attractive and repulsive, while the gravitational force is only attractive. Note that there are four known fundamental forces - gravitational, electromagnetic, strong, and weak. These cannot be explained by some more fundamental force*, it is just how nature works. Maybe one day scientists will manage to find the common denominator for all four forces - check the Grand Unified Theory for more details.

What causes this anomaly?

There is no anomaly. Gravitational force is only attractive because mass, unlike charge, is only positive.

To summarise, electric, magnetic and neuclear forces all need energy to be maintained. Why does gravity not require this energy of maintainance?

No fundamental force needs energy to be "maintained". Note that energy is an abstract concept that is just that - an abstraction. The equation for work was recognized to give useful results, and that is how concept of energy was introduced to physics.

Answer this question - how much work is being done while you sit motionless on your chair? Gravitational force pulls you down, towards the Earth center, but it does no work in this example.

What I noticed is that students are usually relating work (energy) to the effort they need to do to carry something, walk, climb, swim etc. Although there are some similarities, you should not relate the work as defined in physics to the effort you invest to do some "work". For example, when you hold some heavy object without moving it, although you feel effort and like doing some work, as far as physics is concerned you are not doing any work.

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^{*As a matter of fact, the electroweak interaction is the unified description of electromagnetic and weak fundamental forces. Check here for more details: "Electroweak interaction"}