Equation 17

The Redshift-Distance and the Lensing equations 6 and 16 together yield a derivation for the Antipode length L for the universe.

This derivation depends only on measured redshifts and measured apparent distances derived from measured apparent magnitudes.

As shown in the extensive calculations here: -

A value of L close to 1.23 e metres emerges in every case, within the limits of observational inaccuracies in apparent magnitude observations. This corresponds to 13 billion light years.

The substitution of this value for L into equation 1 gives the exact value of the mass of the universe M at 8 e52 kilograms, eighty octillion metric tonnes.

The substitution of this value for L into equation 2 gives the exact value of A the spacetime curvature of the universe expressed as an acceleration of 7.317 e-10 metres per second squared.

The substitution of this value for L into equation 5 gives the exact angular velocity of megastructures around the universe as 0.005 arcseconds per century on the basis that they rotate around the great circles of a Hopf Fibration of the hypersphere with a circumference of twice the antipode length L.