One need not have something as expensive as Hubble to have such angle sensitivity.
This instrument can resolve an angle change of < 0.3 millionths of a degree in one second.
https://arxiv.org/abs/1309.4828
Disclaimer -- am an author.
Edit: and this instrument, using the autocollimator above, can do the same thing for inertial sensing. Same disclaimer applies. https://aip.scitation.org/doi/10.1063/1.4862816
