Geostationary Space Based Solar Power

The geostationary orbit is a seemingly attractive place to put Space Based Solar Power arrays. It is also already full of valuable satellites, and the orbital dynamics are more complicated than a naive two body Kepler orbit without light pressure modification.

The most important thing to know is that international law and common decency require that the hundreds of GEO satellites up there stick to their assigned angular slot, and must not deviate from their assigned position more than 0.1° or so, north-south or east-west. They also must not create radio interference with those other satellites.

Earth antennas for GEO communication services are usually fixed, and have narrow angular apertures, but they are not perfect and will receive off-axis sidelobe power, creating interference. SBSP satellites will produce millions to billions of times more power than a communication satellite, so even tiny amounts of sidelobe leakage may swamp ground receivers, even receivers intended for other frequency bands.

If an SBSP can interfere with existing services, it will not be allowed to launch. If it is launched and does not perform within licensed limits, it will be shut down, disabled, or destroyed, whatever it takes to get it off the air and out of the way of other licensed satellites. If your hypothetical solar power satellite cannot operate within these constraints, go back to the drawing board and figure out something that will.

For this analysis, I will ignore the effects of eclipse, the Earth's axial tilt, higher order gravitational harmonics, special relativity, and perturbations from Jupiter and other planets. These effects are not trivial, but they require a book-length treatment (such as Soop and Piscane and Wertz, referenced below).

I will also not reference closed-source computer programs such as AGI's Satellite Toolkit. These programs can be useful, but they are opaque. You can't see the math behind the pretty GUI, so you don't know when you've taken the models beyond their range of applicability. Before using any computer-aided design tool, you must learn the underlying math and physics, or you will almost certainly misapply it. CAD tools automate understanding, they do not replace it.

Effects Discussed

We will assume that the orbit is near circular, but will be slightly elliptical. It will be perturbed away from that orbit, which will require appropriate choice of eccentricity (zero eccentricity is far too expensive) and quite a bit of \Delta V ~~~ thrust to keep the inclination near zero, in spite of out of plane perturbations by lunar and solar tides. A related analysis is on this wiki, for lower and more stable MXXX orbits.

• Precession of the argument of periapsis by J₂ earth oblateness.

• Precession of the argument of periapsis by light pressure.

• Inclination perturbation of the north-south alignment by the Moon and the Sun.

• Radio sidelobe interference caused by off-axis power.

Simplified Orbits

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Precession of the argument of periapsis by J₂ earth oblateness.

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Precession of the argument of periapsis by light pressure

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Inclination perturbation of the north-south alignment by the Moon and the Sun

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Radio Sidelobe interference caused by off-axis power

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References

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