In a cosmological simulation of a high-redshift epoch of the Universe, galaxies are assumed to be distributed uniformly through space. In this simplified model, the average separation between two neighbouring, identical galaxies is 2.4×1022 m2.4 \times 10^{22}\text{ m}2.4×1022 m. Each galaxy is situated at the center of a cubical region of space of volume 1.2×1067 m31.2 \times 10^{67}\text{ m}^31.2×1067 m3.
There are, on average, 8.5×10108.5 \times 10^{10}8.5×1010 stars in each galaxy, and the mass of an average star in this early epoch is estimated to be 2.2×1030 kg2.2 \times 10^{30}\text{ kg}2.2×1030 kg.
Calculate the mass of an average galaxy in this simulation.
Estimate the gravitational force between two neighbouring galaxies.
Calculate the mean density of the Universe in this model.
Suggest why the actual mean density of the Universe might differ from the value calculated in (iii).
