So for a homework problem for an astronomy class, we have a cluster of stars passing over a black hole, and need to find the probability that a star in the cluster will pass directly into the black hole's event horizon.
So, I found the number density of stars within the volume of intersection of the star cluster and event horizon.
I think the (mean) number density is almost the same thing as the probability in this case? But I'm not sure.
If the number density was 1 then there would on average be 1 star in the region, however I can't tell how to draw the probability from this.
If anyone could clear this up that would be helpful, thanks
Ok, the question I asked is definitely unclear.
We approximate the star cluster as a sphere, and the black hole as a sphere. The radius of the black hole <<< the radius of the star cluster
Hence if the star cluster is moving, and 'passes over' the black hole, then the volume of intersection is approximated as a cylinder, with height 2 * star cluster radius, and the cross section of the cylinder has radius of the black hole.
We are told the total number of stars in the star cluster (0.5 million)
What i did was found the number density of the entire cluster, N / V, then assumed the density is uniform.
(I have just realised that I made a mistake in wording when i first wrote the question, which becomes clear next:)
Then i found the average number of stars N in the cylinder, by doing number density * cylinder volume.
So what I have found is the average number of stars in the region.
This number is ~10^(-9).
Is this equivalent the probability that a star lies in the region?