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NASA has confirmed that the Transiting Exoplanet Survey Satellite (TESS) has recovered from a reaction wheel problem and resumed making observations. The spacecraft dropped into safe mode on April 23 following an issue that occurred earlier in the month. The latest safe mode was triggered by a failure to dump momentum from …
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I think you're confusing them with gyroscopes. Both relate to the attitude of the instrument but gyros are constantly running and measure changes in attitude. They're also small and comparatively easy to arrange spares for. Since in operation they are always running that's a good idea since they do wear out, essentially they are a spinning disk with the bearing wear that implies.
Reaction wheels in contrast are large, weighty components. They are rotated when the instrument needs to actively change orientation, the instrument then moves in the opposite direction: no propellant is needed for that operation. You don't have such a free hand with spares and their placement though, since the axis of rotation is always related to the particular set of wheels in question.
Things like solar wind will exert force upon a spacecraft causing it to spin, so reaction wheels are also used to prevent the craft from changing orientation by spinning to resist the external forces. They do not stop spinning after resisting external forces (as slowing down to a stop would transfer the rotational energy to the spacecraft causing it to spin), so in practice they are always spinning.
Countering the effects of induced spin on the craft is what manoeuvring thrusters are for, for a persistent effect the reaction wheels would have to remain in motion constantly. The reaction wheels are used when the craft is not rotating, rather you want to change the orientation, i.e. you are currently pointing over "here" but want to switch to pointing over "there". The wheels spin up and the craft starts to rotate in the required direction, stop the wheels and the craft's rotation in turn stops. It's conservation of angular momentum.
"Countering the effects of induced spin on the craft is what manoeuvring thrusters are for"
Valves have a high failure rate so you don't want to be opening and closing them constantly. The attitude control system will transfer any unwanted angular momentum from the spacecraft to the reaction wheels, and then when the reaction wheels are saturated you spin them down and burn the thrusters in one long burn to de-saturate them. This allows you to make constant tiny corrections for the effects of solar wind whilst minimising the amount of time you need to actuate the thrusters.
Other setups include using a combination of reaction wheels and magnetorquers like the Hubble, attitude is controlled by the reaction wheels and then once they are saturated the Hubble shuts down it's instruments and turns on its magnetorquers clamping it to the Earth's magnetic field, this allows it to spin down its reaction wheels without going into a spin.
I'm replying to myself here, which I usually try to avoid.
NASA's Roman telescope will have six reaction wheels.
They must have built a time machine, read my comment and then modified their design. Cheeky devils.
I believe its predecessor, the Greek telescope had six banks of oars.