## 4. A force equation for homogeneous, isotropic distributions in Boltzmann equilibriumIn this section, I derive the force equation and then introduce a Newtonian form for the interaction. The only trick is to apply the operator over expression ( 11 ) and to develop the expression HYPOTHESIS 2: This becomes HYPOTHESIS 3: I rename , , angle between and and assume that (valid in the light of Hypothesis 2) and substitute some expressions using ( 12 ) and ( 14 ), taking into account the isotropy assumed in Hypothesis 3: This is the force equation. It gives us a relationship between
different correlation functions in a distribution that follows our
hypothesis and the force that is represented by means of © European Southern Observatory (ESO) 1997 Online publication: October 15, 1997 |