I don't think there exists a system where this would be a feasible experiment.
a)we need a black hole (object with a photonsphere). ordinary objects like stars or clusters there of are just not dense enough.
b) we need to know where it is. there are few that we can really pinpoint
c) distance. Sgr A* is something like 25000 light years away. aka your experiment would take 50000 years to run.
d) aim at distance. The Event Horizon Telescope will be barrely able to resolve its shadow. try aiming a beam that will be strong enough that it is detectable and precise enough that with all the mess in between it is calculated so precise that it hits the right point on earth trajectory in 50000 years time.
Unless we find a black hole close by (max like 10 light years) i don't think this is a feasible experiment