Do GPS satellites use the earth's magnetic field in any way?

Question

There's a lot of speculation about how changes or flips in the Earth's magnetic field would affect us, our machines, and sea turtles.

I'm curious about the GPS satellites themselves. In one way they are basically an atomic clock and transmitter. But it's silly to break it down to that level. They aren't over 2000kg without significant brains.

That leads me to wonder what sensors modern GPS (block III) satellites use. Do they even have a magnetometer? Most cell phones do, so it seems reasonable they might. Do they have a star tracker? What is used for standard stationkeeping, and what else might they have in this vein?

I'm not talking about "second order effects", like "the atmosphere will be affected, so the signals might get attenuated", or changes in solar radiation, etc.

Answer 1

tl;d: At only a handful of milliGauss, the Earth's field out there is so weak that it probably wouldn't be very useful. It's doubtful that the critical GPS satellites would depend on it.

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What's the Earth's field like out where the GPS satellites are?

First of all, where are they? The approximate period of a satellite with semimajor axis $a$ is given by (from here)

$$T = 2 \pi \sqrt{a^3 / GM_E},$$

where Earth's standard gravitational parameter is about 3.986E+14 m^3/s^2. Flip that around and you get

$$a = \left(T^2 \frac{GM}{4 \pi^2} \right)^{1/3}.$$

Put in a period of a half-sidereal day (about 43082 seconds) and you get a distance from the center of the Earth of about 26,560 kilometers give or take, or about 4.2 Earth radii.

A dipole field drops as $1/r^3$. For example

$$\mathbf{B} = B_0 \frac{3(\mathbf{\hat{p}} \cdot \mathbf{\hat{r}}) \mathbf{\hat{r}} - \mathbf{\hat{p}}}{r^3} $$

where $\mathbf{\hat{p}}$ is the dipole vector of the field and $\mathbf{\hat{r}}$ is the vector from the dipole to the field point. Here $B_0$ is about 3.12E-5 Tesla, or about 0.312 gauss.

If we ignore that Earth's field is tipped by about 11.5 degrees, and put in two points at one and 4.2 earth radii, we get about 0.31 gauss and 0.0042 gauss, which is only about 1.3% as strong as the field near the Earth's equator.

At the poles the field is double that, but the ratio is the same.

This is an incredibly weak field, there's not much you can do with a handful of milliGauss, and GPS is so critical that they'd never depend on something so weak.

That doesn't mean that they don't have some backup systems available in an emergency, they might exist. But I don't think they will depend on Earth's field for torque.