Check my work please: Jupiter as power station?

critchdizzle

I'm developing a realistic sci-fi story in which power for the outer planets is produced from Jupiter's magnetic field. Now from Faraday's law I have

V= N * A * (2*∏*RPM/60) B

where N is the number of coils, A is the area of each coil, RPM is, well, RPM, and B is the field strength. I've calculated that the orbital period at a Joviostationary (yes it's a made-up word, but it works) orbit would be 600 minutes, giving me an "RPM" of .001667. Using 100 "coils" of 1 square kilometer each, and assuming 1.4 mT field at the poles, I get a paltry 24V. Is this correct, and how would I get the amperage in order to calculate power?

Drakkith

Find the resistance of the coils and use ohms law to find the current? I'm not too familiar with electrical work, but I think that's what you would do.

nasu

So what provides the motion of the coils relative to the field?
Are they on the "Joviostationary" orbit? Then they don't move relative to the planet (the "stationary" part).

Matterwave

I would imagine that putting this generator on your space-ship would alter the orbit of the space-ship.

critchdizzle

That brings up an interesting point. Does the field rotate with the planet? If so, then we would have to have a different (lower or higher) orbit, which would slightly complicate matters but not prohibitively so. I was under the assumption that movement around the planet, even in a stationary orbit, would count as movement within the field.

Matterwave

My intuition tells me (no calculations, so this is purely intuition) that schemes of this kind would essentially just convert the kinetic+potential energy of the satellite to energy in the generator, and just force the satellite to enter Jupiter's atmosphere. Remember that magnetic fields do no work. My intuition is that your scheme of generating power would not generate more energy than the energy it took to get that satellite into orbit in the first place.

mfb

That.

You can use the giant gravity well of Jupiter as power source with the coils, but you have to sacrifice material from the moons or somewhere else for that. If you build those coils on a moon, they will last longer.

critchdizzle

The moon idea is a good one, IMO. I'll look into that. But besides using the wrong orbit, are my assumptions mostly correct? i.e. the orbital velocity can be used as RPM? Also, how can I find the power generated by a rig like this?

nasu

I am afraid that the orbit is not the only problem. In order to generate power, your coil has to somehow spin, relative to the local direction of the field. The emf and the power will depend on how fast is this spinning.
I am not sure how do you suppose to have the coils oriented but if they just orbit around the equator, with their normal along the radial direction (plane of the coil tangent to the trajectory), for example, it won't be much current induced, the field is along the meridian, the normal along the radius, angle is pretty much the same. This is, unless there are some field inhomogeneities along the way, where the direction of the field changes rapidly in space.
Maybe there are some regions of magnetic storms on the way?

ImaLooser

The Io flux tube carries a huge amount of electrical current, twice as much produced artificially to today's Earth. The other moons in all likelyhood have current like this too. Not as much, but plenty. They could build two tall towers and use the potential difference between them.

AJ Bentley

Heck - it'll never work, for a thousand reasons.

But why let facts get in the way of a good story?

wagons-east

Maybe my understanding is faulty or fuzzy, but why would generating power on an orbiting satellite force that satellite to lose it's orbit and enter the atmosphere (i.e. crash, unless I'm reading it wrong)?

Ryan_m_b

I've read this in a Sci-Fi story. There's a novel called Accelerando in which some of the protagonists build huge coils of wire from a small Jovian satellite which produces energy by slowing down the orbit of the satellite as it passes through Jupiter's magnetic field. This energy is used to power a laser array for an interstellar starwisp.

mfb

Current flow in the coil in the magnetic field of Jupiter would give a force - this is opposite to the direction of motion, thus slowing the object*.

*the velocity would actually increase due to orbital mechanics, but that energy comes from the reducing orbital radius.

Redbelly98

Your formula is for a coil spinning in a fixed magnetic speed. For an orbiting coil above the equator, but not spinning, there is no change in magnetic flux hence no emf is generated.

Instead you could put the coil in a polar orbit, so that the flux did change. But any motion that causes a change in flux and induces a current in the coil -- whether by spinning the coil, or using a polar orbit -- would be opposed by the magnetic force acting on that current. The orbital or spinning motion would soon stop, and thus the power generation would stop as well.

Looks like you'll have to break some law of physics in order to make this story work.

EDIT: I see matterwave and mfb have already thought of this objection.

vemvare

Both Io and Europa have considerably tidal forces heating them. Since a heat differential means that power can be extracted, why bother with the magnetic field?

SteamKing

Robert L. Forward used this idea to generate electricity from a neutron star in Dragon's Egg.