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Suppose we have a satellite orbiting Earth in an elliptical orbit, which has an electromagnet inside it. As the satellite goes from its apogee to its perigee (i.e. losing altitude), it turns on the electromagnet. This pulls on Earth's magnetic field, accelerating the satellite downward. Then once it passes perigee and starts climbing again, it turns the electromagnet off. Could this be used to raise the apogee of the satellite?

If yes, could this idea also be used to subsequently circularize the orbit?

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    $\begingroup$ wasn't there some shuttle experiment where they released a large metal sphere from the payload bay and released it on a super long tether. I think the idea was so generate electricity at the cost of speed and vice versa. From what I remember it failed twice because of the tether and it got scrapped. Not sure if it's the same principal or if it's even applicable but could be of interest. $\endgroup$
    – R. Hall
    Commented Dec 1, 2021 at 11:50
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    $\begingroup$ @ReubenFarley-Hall: I think you're referring to the TSS-1 and TSS-1R missions. $\endgroup$
    – Fred Larson
    Commented Dec 1, 2021 at 14:51
  • $\begingroup$ Even if you could somehow generate enough force, wouldn't an electromagnet get hot if run for a long time? And since the only practical way to dissipate the heat is through radiation (which is slow and requires a big heat sink), wouldn't it run the risk of overheating? $\endgroup$
    – flinty
    Commented Dec 1, 2021 at 16:22
  • $\begingroup$ This technique as described would achieve an attitude change and this is exactly what is done with a magnetorquer which is used on lots of satellites as a crude actuator, see the answer by user_1818839, +1 there. For orbit changes see the answer by DrMcCleod, +1there too. $\endgroup$
    – Puffin
    Commented Dec 1, 2021 at 21:49

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You might like to take a look at Electromagnetic Tethers. A spacecraft moving through a magnetic field (such as the Earth's) can deploy a long, trailing wire and run a current through it. This will provide an electromotive force to the wire (and craft) that can be used to raise or lower orbit. It isn't exactly the same as your idea, but it is a practical related system.

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    $\begingroup$ Can you elaborate on why it's not the same as what I suggested? My understanding is that the wire works in "propulsion" mode by the magnetic field of the current in the wire interacting with Earth's field (which is what an electromagnet does). Perhaps you could expand on the workings of the EM tether? $\endgroup$
    – Drake P
    Commented Dec 2, 2021 at 18:47
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    $\begingroup$ @DrakeP that's a great question. Your question begins "we have a satellite... which has an electromagnet inside it." The tether is much much longer than a satellite could be, and it is a wiggly, flexible, thin conductor rather than a rigid satellite structure. That might be the only difference, but at least from a practical point of view, while it's quite related, it's definitely not "the same as" what you suggested. $\endgroup$
    – uhoh
    Commented Dec 3, 2021 at 0:18
  • $\begingroup$ @DrakeP By the way, I think "Can electromagnetic tethers be used to raise and/or circularize low Earth orbits? Can they perform standard orbital maneuvers as well?" would be a fantastic new, follow-up question! $\endgroup$
    – uhoh
    Commented Dec 3, 2021 at 0:18
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The force on the electromagnet will be given by its magnetic moment times the Earth's magnetic field gradient. A large electromagnet might have a magnetic moment of the order of $10^{+6} \,\mathrm{Amp}\cdot\mathrm{meter}^2$. The Earth's field is of the order of $10^{-4} \,\mathrm{Tesla}$ and, at an orbital radius of say $10^{+7}\,\mathrm{meters}$, the field gradient will be something like $10^{-4}/10^{+7} = 10^{-11} \,\mathrm{Tesla}/\mathrm{m}$. The product of these two quantities is of the order of $10^{-5}\,\mathrm{Newtons}$. So it's difficult to get enough force to be useful.

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    $\begingroup$ 1e-5 N is still worth considering, because it doesn't expend anything. $\endgroup$
    – fraxinus
    Commented Dec 1, 2021 at 16:53
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    $\begingroup$ @fraxinus, no it is not. 1) The natural forces on the satellite will far exceed the magnetic force. (solar pressure is 1 example). 2) The added mass, complexity and power requirements of the electromagnet would reduce the performance/lifespan of the satellite. Remember: mass is expensive to launch. The mass & power would be better spent elsewhere. Nice idea, though. $\endgroup$
    – Scottie H
    Commented Dec 1, 2021 at 21:25
  • $\begingroup$ The field outside the coil will almost completely cancel the effect, so the real force is even smaller. $\endgroup$
    – jpa
    Commented Dec 2, 2021 at 15:56
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    $\begingroup$ @RogerWood Ah, hmm, I seem to have misunderstood your calculation at first. $\endgroup$
    – jpa
    Commented Dec 3, 2021 at 6:20
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    $\begingroup$ When SI units are spelled out, they are in lower case - it should be ampere, tesla, newton. $\endgroup$
    – Nayuki
    Commented Dec 3, 2021 at 16:20
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Electromagnets pulling against the Earth's magnetic field are used for the (much lower energy) task of orienting satellites, pointing them in the right direction. This is called a magnetorquer.

As another answer suggests, it's not going to be easy to get any substantial delta-V that way.

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The simplest idea of turning a small electromagnet on and off does not work. An electromagnet has a field both inside and outside the coil:

(Image source: P.Sumanth Naik / Wikipedia)

The field outside the coil has the same flux as the field inside - it is just divided over a larger area. This is true for all types of magnets, except hypothetical magnetic monopoles.

With similarly sized magnets that are close to each other, the outer fields are wide and weak enough that their comparative effect is small:

(Image source: Geek3 / Wikipedia)

Because Earth's magnetic field is so large, it is essentially homogenous in the vicinity of a small electromagnet. Therefore the outer field will almost completely cancel any linear force produced by the inner field. This may sound a bit surprising, but applies in general: uniform magnetic fields do not generate linear forces. Only magnetic torque caused by the dipole moment remains.

In electromagnetic tethers the linear force is generated by electrostatic forces, while the required voltage is generated magnetically.

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