Question

Milky Way galaxy has a halo filled with dark matter. The total mass of the dark matter
halo is about 1012 MSun, or 2×1042 kg. To simplify things, let’s assume this dark matter halo
is spherical with a radius of about 100,000 light years, and that it is uniformly filled with
whatever is responsible for dark matter. The following calculations will help you to com-
pare different dark matter hypotheses to see if they are reasonable. You will need to use
the formula for the volume of a sphere and the definition of density as mass per volume.
A. Consider the hypothesis that black holes with a mass of the sun are responsible for
dark matter. If this is true, what is the volume of space in our galaxy within which we
would expect to find one such black hole?
B. Take the cubed root of this volume, which gives you an estimate of approximately how
close we would expect such a black hole to be to our own solar system on average.
Given that the closest black holes that we know of are several thousand light years
away, does this dark matter hypothesis seem possible?
C. What if the dark matter were due to planet-sized black holes, about 10 Earth masses
each? Following the same steps as in part A and B to estimate about how close we
would expect such a black hole to be to Earth. If Planet X is found to be a black hole
about 600 AU from the Sun, would this support this theory explaining dark matter

Answer 1

Given that: