Rudinhoob said:
So any node I wire to the Earth has 0 potential?
Does this apply to the Moon? Mars? other planets? What about spacecraft s?
It's a bit tricky. This is one of those situations best described as "the spherical cow approximation".
Potential is defined uniquely up to an additive constant. You are free to pick the value that best suits your calculations for that constant, as long as you stick to it for every other potential in your circuit or system. For example, you could choose the potential of one wire of a high voltage line as your 0 potential and express the voltage difference of nearby lines with respect to that. But you would not want to touch that line while sitting on the mast just because you arbitrarily called its potential 'zero'.
When dealing with potentials there are some arbitrary choices that - notwithstanding their arbitrarity - make more sense than others. For example, with constant fields and linear potentials, any location at a finite distance will best suit your needs. The gravitational potential near the surface of the Earth (g h) is usually referred to a zero height of your choice, be it the lab floor or sea level.
When dealing with fields and potentials that decrease with distance to a finite asymptotic value, it is easier to consider a zero reference at infinity (the reason is that you can set the additive constant to zero and forget about it). For example, the electric potential of a point charge[*] decrease as 1/r, and 1/r goes to zero as r->infinity. By setting the conventional zero potential at infinity you will end up with a zero value for the additive constant, so that you won't have to drag it along in all your calculations.
Now, back to our spherical cow, the one we all live on.
The Earth, in a very wild approximation, can be seen as a very big spherical conductor. A very big spherical conductor has a very big capacitance (i.e. can gobble a lot of charge almost without changing its potential) and - by definition - has a very big radius. If this radius were infinite, we could actually give the Earth the potential of zero volts.
Now, where is the catch?
Ok, the radius is not infinite but from a practical point of view, we can give zero potential to points so distant from us that any change in their distance won't appreciably affect the potential we can measure. In a way it's just like calling the antipodes 'infinity' and giving zero potential to the potential we are all accustomed to: the potential of the Earth we walk on.
But it's the conduction part of our spherical cow that can be really tricky. Conductivity is not uniform and depends on many conditions, like terrain, soil composition, humidity, weather conditions...
You cannot trust that if you put an electrode into the ground near your house, then it would be at the same potential as an electrode in the ground at the local electric facility. Heck, you cannot even be sure that electrodes in the ground around your house and those around your garden shack would be at the same potential!
But locally, if you plant enough electrodes deep enough, close enough and in an average enough type of soil in average enough conditions, you could at least have a nice 'earth' connection with all electrodes at about the same potential and capable of gobbling up all the charge you throw at it without batting an eye.
As for your question about the potential on other planets, if the other planets surface can be considered conductive (and that remains to be seen, in absence of an atmosphere and water in the ground), the same spherical cow trick can be pulled on their surface too. You will call 'zero' the potential on the surface of that particular planet.
Is the 'moon zero' the same as the 'earth zero'? Good question, I wish I knew the answer. Because that's where the spherical cow approximation breaks up: the distances involved between the Earth and the Moon are greater than those of our supposedly infinite spherical cow. Moreover, the environmental condition are different - there is plasma in between I believe, solar winds, magnetic fields and who knows what (recently
Nasa has found a new set of radiation belts). I (and I mean I) don't know what would be the potential difference between the Earth and the Moon.
As for the spacecraft , I guess that you will find measurable limits in the amount of charge you can place on it without having its potential changed. But not in the range of the charge any electrical circuit on board could displace.
Corrections and/or integrations are most welcomed.
Note: [*] Or, more importantly, any distribution of nonzero total charge at a reasonable distance - call this the 'monopole approximation'.
