> HST is capable of tracking moving targets with the same precision achieved for fixed targets. This is accomplished by maintaining FGS Fine Lock on guide stars and driving the FGS star sensors in the appropriate path, thus moving the telescope to track the target. Tracking under FGS control is technically possible for apparent target motions up to 5 arcsec/s.
According to JPL Horizons, the current angular motion of 3I/ATLAS across the sky is <0.03 arcsec/s, so it's well within Hubble's capabilities.
My understanding is that the Hubble's one-gyro mode mainly complicates the process of quickly moving from one target to another. Once the telescope is pointed at a target, the stabilization and tracking is done using guide stars without relying on gyros.
Anyway, in absolute terms, 3I/ATLAS isn't moving that fast. Its orbital speed is about 3x that of Mars, but it's farther away, and (for now) much of that motion is directed inward towards the sun.
[1]: https://hst-docs.stsci.edu/hsp/the-hubble-space-telescope-pr...
At even 1 AU of distance, an angular velocity of 1/10 of a degree per second requires a linear speed of about 0.87c. Needless to say, 3I/ATLAS is not moving that fast - if it were, it would be outputting about 100 TW, mostly as heat, just from slamming into the interplanetary medium at relativistic speeds [2].
[1] https://www.pbs.org/deepspace/hubble/diagram.html#:~:text=Th...
[2] https://www.wolframalpha.com/input?i=%2840+*+mass+of+hydroge...
Man, that is a horrible unit. I've never heard of that, but I can only imagine each semester professors every where have to endure an enterprising student using this to be "clever" in some way