For the mathematical details of this post, see Dr. Satz’s paper “Calculation of the Gravitational Limits and Hubble Constant for the Local Group” on this site.

Advocates of the Reciprocal System do *not* accept the conventional theories of the “Big Bang” and “dark energy.” The source of the recession of distant galaxies and clusters is the *space-time progression*. As the counterforce, gravitation, weakens with the inverse square of the distance, the acceleration *increases*. Inside the first gravitational limit, the motion is inward; between the first and second gravitational limits, the motion is outward, with increasing speed and acceleration with distance. At the second gravitational limit, the recession speed maxes out at speed c; this is a boundary limit. However, before reaching this limit in space, the *upper age limit *of matter is reached, causing the destruction of the galaxy or cluster.

For the Local Group, the second gravitational limit is at 3877 Mpc (12.639 billion light years), and it would take 102 billion years to get there. But the destruction of the Local Group will occur in a lifetime of approx. 50 billion years, so the Local Group will not make it to the second gravitational limit.

For the largest cluster of galaxies, containing the equivalent of approx. 10^15 x the mass of our Sun, the second gravitational limit is 68.852 billion light years, so this could represent the *maximum* possible radius of “the universe.” However, the mean radius, averaging over all *large* clusters, would be, say, 50 billion light years.

Therefore, assuming roughly a time limit of 50 billion years for matter in our sector, and a space limit of 50 billion light years, the *period* of our cyclical universe would be double this amount, or 100 billion years. *Cosmic* galaxies and clusters in the cosmic sector have a space progression *inward* of roughly 50 billion light years, and an equivalent time limit of 50 billion years, completely reversing the 50 billion light years *outward* in our sector. The two sectors of the universe, our material sector and the cosmic (inverse) sector, are in precise balance.

Study the Reciprocal System and prove it for yourself! *The Reciprocal System: Microcosmos Database* is now available from http://www.amazon.com and http://www.reciprocalsytem.guru. *The Reciprocal System: Macrocosmos Database *is currently in preparation.