system
Given the following post, respond as if you're commenting on Reddit:
human
Does orbiting within a black holes ISCO require constant thrust or just additional energy?

I'm in a spaceship orbiting a blackhole at the ISCO. If I shrink my orbit below the ISCO. Can I just speed up faster to maintain orbit? 

I don't mean that trivially, I just mean if the speed of orbit is sqrt(GM/r) and spacetime geometry breaks down near a blackhole. Should one not also be able to orbit within the ISCO as long as you are going a bit faster than sqrt(GM/r)? So as you descend you have to keep supplying energy to increase your orbital speed. 

Obviously at some point you can't go any faster. But I don't see how once you pass below the ISCO (in a spaceship) you can't keep orbiting until you start reaching relativistic speeds.
gpt
ISCO is the innermost *stable* circular orbit. You have unstable orbits lower than that where you can orbit just with course corrections. Down to the photon sphere if you increase your speed sufficiently.

Beyond the photon sphere tangential velocity is harmful - you need constant thrust to keep your distance, and the faster you go in tangential direction the *more* thrust you need.