# Is it possible to convert gravitational energy directly into electrical energy?

It is possible to produce strong gravitational accelerations on the free electrons of a conductor in order to obtain electrical current. This allows the conversion of gravitational energy directly into electrical energy.

Considering that there is formal analogy between gravitational theory and electromagnetic theory, then it seems like that such a proposition is possible, at least theoretically.

And if it is indeed possible to convert gravitational energy into electrical energy, will it imply potential destruction of natural gravitational field?

• Snarky answer to the title question: that's what a hydroelectric dam does. May 2 at 14:37
• @MichaelSeifert The keyword is "directly". In a dam the energy takes a few detours, from gravitational potential (reservoir) to kinetic (falling water), to mechanical rotary (in the turbine), and then finally to electrical energy (in the generator). OP is talking about having gravity pull on electrons directly to make them move.
– J...
May 2 at 16:04
• @MichaelSeifert The dam uses the gravitational energy of the aptly named baryons, not so much of the leptons. The particles are named that way for a reason ;-). May 3 at 12:46
• It's not the most practical in terms of power generation, but if you do that experiment where you drop a permanent magnet down a copper (or other non-ferrous metal) pipe, you can get a small but measurable charge on the pipe. Slightly more direct than hydro power. Not sure how you'd go about turning that into useful power, but it is an electrical charge just from dropping something. May 3 at 13:24

## 3 Answers

Suppose you have a charged parallel plate capacitor, with fixed equal and opposite charges on the plates. Both plates are parallel to the ground (i.e. perpendicular to the gravitational field). The upper plate is fixed, and the lower plate can be released to fall a certain distance under the influence of gravity. You release the lower plate, and the plate spacing gets bigger as it falls. Neglecting fringe fields, the electric field between the capacitor plates stays the same, but now occupies a greater volume, so more energy is stored in the electric field. You have converted gravitational potential energy directly into electrical energy. You have not destroyed the gravitational field in the process.

• How does greater volume between electrical capacitor plates makes more energy? May 1 at 7:09
• The energy density is constant (as it is a function of the electric field), but exists in a greater volume as the lower plate falls, so the energy (which is energy density times volume) is greater. An alternative description of the process is that the weight of the lower plate does work against the attractive electrical force on the lower plate, increasing the electrical energy.
– Puk
May 1 at 7:16
• Or, from a circuits perspective: the greater plate spacing reduces the capacitance $C\propto d^{-1}$ but the charge imbalance $Q$ on the plates is constant, so the voltage $V=\frac QC\propto d$ across the capacitor rises (the charges are less able to cancel each other out from far away). Then the energy $E=\frac12 QV\propto d$ also rises.
– HTNW
May 1 at 8:44
• @WestCoastProjects A capacitor is a very simple energy storage device, and using gravity to move one of the plates and increase the capacitor energy seems like a natural way to illustrate the possibility of the kind of energy conversion in the question.
– Puk
May 1 at 22:18
• maybe but turning the capacitor on its side and just dropping the lower end was an interesting twist. i've often been impressed by the creativity of physicists and inquire not only about the result but how they came up with the idea May 1 at 22:23

Electromagnetic interaction is about $$10^{35}$$ times stronger than gravitational interaction, which is why e.g. a television cathode ray tube (yes, I'm old) would work all the same on the Moon as on Earth, even though the Moon's gravitation on the surface is only a fraction of the Earth's. The electrons are so fast that they have left the apparatus before they even notice they are in a gravity well: At 3000V in a CRT they are apparently accelerated to 1/10 c, or 30,000,000 m/s, giving them 33 nanoseconds or so within a 1 m CRT. During that time they fall $$s = 1/2 a t^2 = 1/2 * 9.81m/s^2 * (33*10^{-9}s)^2 \approx 5.3*10^{-15}m$$.

Electrons are also very light, hundreds of times lighter than the neutrons and protons, and therefore are heavily accelerated by electric fields but don't gain much energy from gravitational fields. Even the capacitor experiment suggested by Puk doesn't use the gravitational force on the electrons (much) — those would go wherever the electrostatic field wants them to. Instead, he converted the gravitational energy of the much heavier protons and neutrons. It is also noteworthy that the vast majority of atoms in a normal metal plate capacitor is electrically neutral. The charge is measured in Coulomb, which is $$6.24*10^{18}$$ electrons, as opposed to about $$10^{25}$$ atoms in a kg of copper. At a charge of 1 Coulomb in a one kg capacitor there are about a million neutral copper atoms before you are finding a lacking or excess electron. If all of the atoms were ionized the electrostatic force would be much stronger than the gravitation.

• Don't be so sure about that cathode ray tube on the moon. I remember back in the 80's we (in the UK) were getting complaints from a customer in Australia about the colour quality of the computer monitors that we were shipping them. Somebody suggested that it might be the earth's magnetic field. We tested this by turning one of our monitors upside down, and immediately the colours blended and faded into each other. So a cathode ray tube doesn't work the same way on the moon, which has no magnetic field! May 3 at 14:02
• @TonyK Good point, a CRT may be calibrated for a specific geolocation. I'd argue this rather supports my point of gravitation vs electromagnetism ;-). May 3 at 14:14

If you have two objects that are charged with the same polarity, but the electrical force between them is slightly less than the gravitational pull, then they will accelerate towards each other, but this acceleration will be partially counteracted by the repulsion between them. The gravitational field goes work on the objects, the objects do work on the electrical field, and so part of the gravitational potential energy is converted to electrical potential energy.