An automated Spamazon delivery starship suffers a catastrophic system failure and finds itself hurtling towards a black hole on a direct collision course. In particularly dramatic fashion, it manages to reignite its STL (0.99c) drives just in time to slowly escape from the black hole's gravitational influence. Any closer and it would be 'treading water' at full thrust, but it is just far enough to slowly increase the distance between it and the event horizon.
The possibility of dropping below a 4 star rating as a result of this delivery has terrified Corporate and they want to know -
How long is this going to take?
Should we wait for the ship to escape, or simply let it sink into the event horizon and just write it off with the insurance company?
(The when is the focus of the question and not the integrity of the starship. It is being assumed here that it will eventually escape intact in most cases. I'm also assuming that time dilation from the singularity will be playing a part here as well.)
Since some want hard numbers:
- The black hole is 5 solar masses
- The ship starts at 100% thrust at 0.99c, moving +1 m/s away relative to the singularity. (I'm not sure what a realistic ship mass looks like so that is up to interpretation)
FTL is only possible once out of the influence of the black hole's gravity well and to make it a hard cutoff, only after you are moving 0.99c relative to the black hole.