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This question discusses the charges that exist on the Lunar surface. Would it be possible or practicable to use the differential between the surface and subsurface or different locations on the surface to power a station there?

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While you may have a static charge difference between night and day sides, 100V is not going to be that useful.

You can't connect them and use the moon as a battery, because it is a static charge- it will not flow.

Your better option would be solar power, as there is no atmosphere to absorb the Sun's rays.

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I'll throw some math at this problem. Given that the negative charge is much greater than the positive charge, I'll treat the moon as basically an isolated sphere capacitor. This really only applies to the side facing away from the sun, so I'll make the egregious assumption of dividing it by half, but that is very approximate.

$$ C \approx 2 \pi \epsilon_0 R = 1 \times 10^{-4} F = 100 \mu F $$

The moon has about $100 V$ stored within this capacitance.

I own capacitors that can store more energy than that. You can go pick up one for yourself for $2.50. Your microwave probably has a better capacitor than the moon is.

It still might be possible to get useful electricity this way, but it doesn't look good. We know that the charge difference is continuously replenished by the sun's effect on the moon's regolith. As you draw down the voltage, it's possible that will cause a huge current to flow from the sun side to the dark side. That could be usable, but it's hard to imagine. At the scale of $100 V$ you need a large current to produce a decent amount of energy.

None of the electrical specs of the moon are impressive. The voltage isn't impressive, the capacitance is pathetic, and we don't know much about the natural recharging rate.

I seriously doubt the idea has any merit. If anything, I think the reverse is more likely — that humans would control the charge of the moon's surface to help manage issues with solar wind, moon dust, and other things.

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It is possible to use the electrostatic charge on the lunar surface to generate the electricity, but it's only theoretical. One such study was done by the NASA Langley Research Center and the National Institute of Aerospace, and presented in their paper on Electrostatic Power Generation from Negatively Charged, Simulated Lunar Regolith (PDF):

The electrostatic power generator was devised to alleviate the hazardous effects of negatively charged lunar soil by neutralizing the charged particles through capacitive coupling and thereby simultaneously harnessing power through electric charging . The amount of power generated or collected is dependent on the areal coverage of the device and hovering speed over the lunar soil surface. A thin-film array of capacitors can be continuously charged and sequentially discharged using a time-differentiated trigger discharge process to produce a pulse train of discharge for DC mode output. By controlling the pulse interval, the DC mode power can be modulated for powering devices and equipment. In conjunction with a power storage system, the electrostatic power generator can be a power source for a lunar rover or other systems. The negatively charged lunar soil would also be neutralized mitigating some of the adverse effects resulting from lunar dust.

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    $\begingroup$ That solution does let you pickup charge, but I'm pretty certain you need to be moving to do it. Which led to a net power loss :-) $\endgroup$ – Rory Alsop Sep 2 '13 at 19:09
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My reaction to a Mwh ability uses grounding rods and a circle conductive net thrown around the lander, the ring it's attached to the bus, examining tries at dynamic charging gave the idea that lander feet smash into regosols to below the plasma layer.

This implies the feet can be conductors vs rods pounded into the stuff, the net of sufficient area as mentioned above to create my est. of -25vdc at some depth below the plasma layer's values, it took 50 hits for 68cm/27in into regosol by an astronaut.

An est. using 7.5, -25vdc days gives 32.5v; -25vdc, -100vdc about 75v so splits to a supply of charging voltage for 28v systems, wattage is load driven, capacity of rods & net the limiter.

Found nothing yet on charge by depth, my take on the plasma layer is it's thin and near the levitation zone so rather delicate.

The lander design is about 3kw, 105-amps @28vdc, the draw can be inverted to ac if needed. Trying to graph the day-night charge pulse aging cycle, math wise all ballpark, setting integral limits.

Doing large-scale rods & nets seems cheap & easy so worth a decent try.

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    $\begingroup$ But such a system won't do you any good because (as Alan's answer shows) there's not enough energy stored to drive anything significant. $\endgroup$ – Hobbes Nov 20 '18 at 17:57

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