Space.com's Hubble Space Telescope Apparently in 'Safe Mode' After Gyroscope Failure says:

"It’s true. Very stressful weekend. Right now HST is in safe mode while we figure out what to do. Another gyro failed. First step is try to bring back the last gyro, which had been off, and is being problematic," Rachel Osten, Hubble's deputy mission head at the Space Telescope Science Institute in Baltimore, said via Twitter Sunday, in response to tweeted questions and comments about the gyroscope's rumored failure.

Hubble has six gyroscopes, all of which were replaced by spacewalking astronauts during a servicing mission in May 2009. The telescope needs three working gyroscopes to "ensure optimal efficiency," mission team members have written, and the failure brings that number down to two (if the "problematic" one that had been off can't be brought back online).

"IF the third doesn't spin back up, I wouldn't be surprised if they drop to 1 gyro mode, keeping the second as reserve. @rachelosten might know, but I imagine it's a stressful, difficult decision. Let's just hope the brilliant people at @STScI can recover the third."

This tweet by Dr. Rachel Osten, Deputy Mission Head for HST says (replies):

It’s not a difficult decision, @astrogrant: the plan has always been to drop to 1-gyro mode when two remain. There isn’t much difference between 2- and 1, and it buys lots of extra observing time. Which the Astro community wants desperately.

I like that there was a plan in place to run Hubble in one-gyro mode when the point in time arrives that Hubble had only two left.

But I don't understand how that's possible. Kepler is in a heliocentric orbit almost 1 AU from Earth, while Hubble is in LEO, and so could possibly face torques from things like gravity gradient and atmospheric drag in addition to any residual torques from unbalanced solar photo-pressure that both telescopes could experience.

Question: How does the Hubble Space Telescope's one-gyro mode of stabilization, attitude control and slewing work? How does it work exactly to keep Hubble pointed during measurements, then rapidly slew to the next target? For bright object, measurements can be a minute or less, so time-to-next target can be a serious consideration. This answer describes a sequence of short, six minute exposures to get astrometric data on MU69, the object that New Horizons will be visiting soon. exposure sequence in proposal.

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    $\begingroup$ "Which the Astro community wants desperately." - there's an understatement if ever I heard one! $\endgroup$ – Martin Bonner supports Monica Oct 17 '18 at 14:48

Some of the confusion may arise in that the gyros under discussion are not used to actually change the attitude of the HST...that is done by Reaction Wheel Assemblies, (separate spinning devices) and magnetic torquers. The gyros in question are sensors only.

Knowing that, it makes sense that.

Both the FHST and the FGS measure two degrees-of-freedom of star position, and the addition of a single gyro provides the minimum number of sensor measurements necessary to successfully control HST rates.

FHST = Fixed Head Star Tracker

FGS = Fine Guidance Sensor

(both of these are optical devices)

A wonderfully detailed writeup on how it all works can be found here, the source of the quote. A more general reference on the attitude control system is here.

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