Basically the ``Bohr radius'' for the dark matter is
rB=ℏ^2 / GN M m^2
where m is the dark matter mass, M is the total amount of dark matter mass contained inside the ``gravitational atom'', and ℏ and GN are constants as usual.
Taking the dark matter to be of constant density ρ0=1.3×10−22 kg/m3, calculate the lower bound on the dark matter mass m. To do this, you will need to calculate how much mass M is inside this atom using the given density. Give your answer to two significant figures.