MadSci Network: Astronomy |
The relationship between the mass of a black hole and the radius of its event horizon is a linear one:
R = (2G/c^2) M
Here R is the radius, M is the mass, and G is the gravitational constant.
But as you probably know, the force you feel at the event horizon is proportional to the mass divided by the distance squared, or M/R^2.
So, because R scales linearly with M, you can plug the first equation into the second one and find that the force you feel actually scales as 1/M! Larger masses make for smaller gravitational forces at the event horizon.
Tidal forces are even better; those scale as M/R^3, or (after plugging in the first equation), 1/M^2. So you're much better off falling into a more massive black hole (assuming you have to pick one or the other!)
The amazing thing is that you can keep imagining larger and larger black holes, where the gravitational force at the event horizon is the same gravitational force we feel on the surface of the Earth! (It would have to be a *very* big black hole...)
Here's a good Black Hole FAQ
Try the links in the MadSci Library for more information on Astronomy.