**Authors:** Bernard Riley

The length and mass scales of cosmology and astrophysics are shown to derive from quantum scales. The Quantum/Classical connection maps the Bohr radius, the reduced Compton wavelength and the classical electron radius – three ‘quantum’ length scales that lie in geometric progression with common ratio α, the fine structure constant – onto three ‘classical’ length scales: the radius of the observable universe; the radius of the stellar halo of the geometric-mean-sized galaxy that is typified by the Milky Way; and the radius of the planetary system of the geometric-mean-sized star that is typified by the sun. By way of the Quantum/Classical connection, the three classical length scales lie in geometric progression with common ratio equal to alpha^5/2 (=4.55E-6). This observation has opened up a framework of multiplicative relationships between cosmological and astrophysical scales based on powers of alpha^5/2. The astrophysical scales of the model refer to the geometric mean values of distributions of scales. ‘Local’ scales take very nearly ideal (geometric mean) values. The baryonic mass of the Milky Way and the mass of the sun approximate very closely to the baryonic mass of the Hubble sphere multiplied by alpha^5 and alpha^10, respectively. The total mass of the Milky Way, the mass of the supermassive black hole Sgr A* at the centre of the Milky Way and the geometric mean mass of black hole-black hole gravitational wave event progenitors approximate very closely to the total mass/energy of the Hubble sphere multiplied by alpha^5, alpha^15/2 and alpha^10, respectively. The results indicate that the total mass/energy of the Hubble sphere increases with time and that black holes grow at Hubble rate. The Schwarzschild radius of the ‘ideal’ star equals the radius of the star multiplied by alpha^5/2. By way of the Quantum/Classical connection, the radius and mass of the ‘ideal’ star map onto the mass and atomic radius, respectively, of the stable nuclide iron-56. The nearly-ideal sun is the counterpart of the stable nuclide chromium-53.

**Comments:** 11 Pages. Typos corrected

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