Oort's Limit and the Local Mass Density :
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The problem is to determine the volume mass density
near the Sun,     (in Mo/pc3), and the projected mass
density in the Galactic plane,     (in Mo/pc2).

A direct method (look around and add up) does not
really work, since some (much?) of the mass may be
unseen.  The gravity is still there, though.

The basic dynamical method is due to Oort.  It uses 
a population of stars as tracers (test particles).
The density is evaluated from the Poisson eq.:




where     is the vertical component of the force,
and     is the potential.  The boundary conditions
are:



If energy is the only integral of motion, then:




The density can be represented as a sum of several
isothermal components:



The projected density is simply:


One starts with an observed density run for the
tracer population,         , and its velocity
dispersion, derives the potential or the     ,
and from there the total density.