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I know that almost every spacecraft uses a gyroscope to determine its orientation, but I don't know if an accelerometer could also be used in addition to a magnetometer to calculate it.

I have been trying to figure it out searching on the internet but all articles say that it can only be done if the accelerometer only reads gravity, in other words, if it is not moving at all. They use a gravity vector as a reference and then calculate the needed rotation to transform body coordinates into fixed ones. Does it mean that this configuration can't be used to determine the orientation of a rocket in motion and have to rely on the gyroscope measurements?

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If multiple accelerometers are spread around the vehicle, their readings can be combined to determine angular speed (from centripetal acceleration) and angular acceleration somewhat easily. There would probably need to be at least 4 or 5 to cover all the degrees of freedom, with one at the CG to cancel out linear acceleration.

To calculate orientation from this, the angular speed would need to be integrated over time. With this integration, the same inaccuracy problems come up as with accelerometer position determination. The position drifts from the true value over time. A gyroscope is more effective in this role.

Magnetometers are useful in space, but need to be used differently than on Earth. Normally on Earth they can be taken as a compass, an inertial frame direction that doesn’t have gyroscope drift, but in orbit, it’s a more complex problem.

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  • $\begingroup$ Rather than centripetal acceleration, it might be more accurate/reliable to measure tangential accelerations and integrate those to derive angular movements than to try to measure radial accelerations resulting from rotations. But your point about drift would still apply. Gyroscopes will be vulnerable to precession, so they will have accuracy issues too. The most accurate way to determine orientation would be to sight known fixed points e.g. stars; either accelerometers or gyros could be used to determine moment-by-moment orientation with periodic sightings to maintain calibration. $\endgroup$
    – Anthony X
    Commented Aug 10, 2019 at 20:05
  • $\begingroup$ @AnthonyX using centripetal acceleration to get angular velocity is not integration, so it is not as susceptible to drift as integrating twice for position on multiple accelerometers and determining attitude that way. The centripetal method involves only one integration to get angular position. Precision would depend on how widely the accelerometers would be placed. $\endgroup$
    – CourageousPotato
    Commented Aug 10, 2019 at 20:31
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    $\begingroup$ @uhoh Oh, right. I’ll edit my answer. I was thinking about my example of the Virtual Reality Trainer onboard the ISS. It’s a modified Oculus Rift, and the tracking had to be replaced by inside-out tracking with a webcam due to a few Earth-based assumptions in the tracking hardware/software. One of those is that the magnetometer is used as an unmoving reference direction for the ground. This doesn’t work in space. $\endgroup$
    – CourageousPotato
    Commented Aug 11, 2019 at 2:04
  • $\begingroup$ fyi I've just asked How could Earth's magnetic field be used to determine a cubesat's attitude in LEO? $\endgroup$
    – uhoh
    Commented Aug 11, 2019 at 2:09
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It depends a bit on what technology you’re referring to.

The original inertial navigation systems used rotating gyroscopes. Those were and are expensive.

Modern MEMS inertial navigation systems (example) don’t use rotating gyroscopes. Instead, they get both linear and angular acceleration (and angular rate) information from their MEMS accelerometer assemblies. That’s not perfect, degree/hour rates are typical, so other systems (including horizon and sun trackers and magnetometers) are used to make long term corrections.

The MEMS systems are based on tiny vibrating elements. Translational and angular motion affect the vibration in various ways, which are sensed and read out electronically. This is an early example from Draper Labs which worked like a large array of tuning forks:

enter image description here

A linear motion affects all the forks the same, while a rotation affects them differently, and the readout and processing electronics used that to make measurements.

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