APPENDIX C

OTHER CORRECTIONS IN THE FIELDS OF FORCES

At the end of section 3.1 is outlined the possibility that the fields of the forces could have other corrections. This means that the definitions of the fields corrected in Section 2.2 could have yet another modification not mentioned there.

A) Reachability of the fields

The author believes in the possibility that the forces considered in Section 3.1 do not extend to infinite.

It should be considered that a "reachability factor" could exist for each field similar to the factor "s" introduced in Section 2.2.

The factor would be a function of the distance "f(r)" which for some R_max would verify:

f(r) > 0 for r ≤ R_max

f(r) = 0 for r ≥ R_max

Note that this formulation determines continuity of order 1 in the fields but an unavoidable discontinuity at the derivative of some order necessary to have a finite limit.

Also note that the factor needs to be approximately "1" at relatively small distances, where the classical prediction is valid and at large distances it could become greater or smaller than "1" to finally be "0" at R_max. 

In the case of the Gravitational Field the "reachability factor" could imply that it does not go farer than the region of the galaxies and that there is no gravitational attraction between well separated ones. One argument for this assumption is that all observed galaxies are finite in their extent what would be caused by a Gravitational Field restricted to a finite region in Space.

B) Gravitational Field Formula

The recent observations of the dynamics of spiral galaxies show an apparent invariance in the shape of the arms of the spiral what implies a constancy of the angular rotation in the stars of the arms. This dynamic does not agree with the classical prediction where stars more distant from the center would move slower.

The author believes in the possibility that the real Gravitational Field formula could be different. After all, Newton didn't have the information of the behaviour of galaxies to be considered in his formulation of the Gravitational Field.

The classical approach could be an approximation valid at the scale of the solar planetary system but not at galactic scale.

If the Gravitational Field would be proportional to 1/r at galactic scale stars would have a constant angular rotation.

It is possible to find a right function that could make the Gravitational Field both approximately proportional to 1/r² at the distances of a planetary system ("planetary scale") and approximately proportional to 1/r at the distances of galaxies' arms ("galactic scale") for example with two factors each one being the relevant one and the other with negligible effect in each case.