AGM Home	Behaviour	Evidence	Simulations	Investigation	Objections	Problems
				Maths with AGM Pressure

This page describes an analysis of the behaviour of anti-gravity matter around a small central normal matter object when AGM Pressure is involved. This analysis is much simplified by the observation described in Investigation that for small scale phenomena anti-gravity between anti-gravity matter particles can be ignored. In the analysis we assume that Gaa = 0.

Definitions and Assumptions

Gravitational constant for normal matter to normal matter attraction = Gnn = conventional G

Gravitational constant for normal matter to anti-gravity matter repulsion = Gna

Gravitational constant for anti-gravity matter to anti-gravity matter repulsion = Gaa = 0

The background density of anti-gravity matter = Dab

The AGM Exclusion Density = Dnx

The background pressure of anti-gravity matter = Pab

Assume monatomic adiabatic expansion where = 5/3

What’s the relationship between anti-gravity matter pressure and radius?

Assume anti-gravity matter is arranged spherically symmetrically around a central normal matter object of mass M.

Radius variable = r

Anti-gravity matter density at any radius =

Anti-gravity matter pressure at any radius = p

For any thin concentric spherical shell weight (outwards) is supported by change of pressure.

1)

The equation for adiabatic expansion of anti-gravity matter as pressure decreases

2) where k is a constant

Therefore

3)

But from 1) and 2)

4)

Integrate

5)

When r = p = Pab and from 3)

6)

At the AGM Boundary let r = R, p = 0 and from 5) and 6)

7)

8) R =

and

9) AGM Exclusion Density = Dnx =

and therefore

10)

Therefore from 8) the radius of the AGM Boundary is proportional to M, and from 10) inversely proportional to the square root of AGM Exclusion Density.

© Copyright Tim E Simmons 2010 to 2015. Last updated 27^th July 2015. Major changes are logged in AGM Change Log.