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The Moon and Earth are approximately spherical conductive balls and the Earth has a self-capacitance of around 710uF. Is there ever a significant potential difference in the Earth-Moon system? Is there even a way to tell if there is? Presumably the Apollo astronauts didn't expect to be electrocuted on landing.

I was thinking that a huge charge would not build up because they are both bathed in a flow of charged particles from the Sun which I would have thought would equalize the voltage. Is this true?

Also what voltage difference would have to build up for a massive bolt of lightening to jump through space between them?

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    $\begingroup$ For lightning to jump, it must overcome the resistance to electric current presented by air and ionize it in the process. As quoted from wikipedia on electric sparks, "A spark is formed when the electric field strength exceeds the dielectric field strength of air. This causes an increase in the number of free electrons and ions in the air, temporarily causing the air to become an electrical conductor through dielectric breakdown." I suppose if you could find the dielectric strength of outer space it would be calculable. $\endgroup$ – David Ball Mar 24 '14 at 21:09
  • $\begingroup$ Thats a good point. However I do think that a current can flow if electrons are released from the surface. This can happen if the field strength is great enough to locally ionize the surface material, after which electrons will be accelerated by the field, even without atoms in the space to be ionized. In a vacuum tube the electrons will flow even without a space charge if enough voltage is provided. $\endgroup$ – Robotbugs Mar 29 '14 at 6:32
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    $\begingroup$ I neither have the data nor the math to answer your question. However, while there are, to our knowledge, no interesting electrical phenomena going on between the Earth and the Moon... Do check how Jupiter's impressive electrical field affects its sattelite Io. You will be impressed. There is actual an exchange of matter between them following Jupiter's magnetic field. Jupiter sweeps mass from Io at a rate of a ton per second. $\endgroup$ – Renan Dec 1 '14 at 4:19
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    $\begingroup$ Lightning works in our atmosphere because you are ionizing a neutral fluid/gas and the "ionization path" is defined during discharge. In the space between the Earth and the moon, there already exists an ionized gas called a plasma. Any currents flowing in this space tend excite instabilities that then act to limit or destroy the current. Instabilities are observed as the electromagnetic waves they radiate. So yes, there is "electrical activity" between the Earth and moon, but it will not be a static discharge like lightning. $\endgroup$ – honeste_vivere Jan 19 '15 at 17:41
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There could easily be a potential difference between the Earth and the Moon but the charge is spread in a relatively homogeneus way on the Earth's surface and on the Moon's too.It means that a very little charge could be delivered to the Moon by the astronauts and their spaceship because their surface area is vanishingly small compared to the earth's surface. So when an astronaut steps down from the spaceship's ladder to the they can not get electrocuted. But le's calculate an example! Let's assume that the potential difference is $10V$ the Earth's surface area is around $5.101\cdot 10^{14}m^{2}$ and an average adult's surface area is around $2m^{2}$ . So an astronaut could carry $$Q_{ASTRONAUT}=\frac{C_{Earth}A_{Astronaut}}{VA_{Earth}}\approx2.784\cdot10^{-19}\Rightarrow Around\ 2\ electrons! $$ And 2 electrons can't kill a human being. And no phenomena can produce a potential difference between the Earth and the Moon which is big enough for a discharge because there is nothing to ionise in the vacuum of space. I hope my answer was useful :)

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