Question

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

Since this distance is more than 600 AU ,so we can expect one such black hole in every solar system and hence seems to be a possible hypothesis for dark matter.