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The numerical action variational principle is used to find fully nonlinearsolutions for the orbits of the mass tracers given their present redshifts andangular positions and the cosmological boundary condition that the peculiarvelocities are small at high redshift. A solution predicts the distances of themass tracers, and is tested by a comparison with measured distances. Thecurrent numerical results use 289 luminosity-linewidth distance measurementsdesigned to be close to unbiased. A catalog of 1138 tracers approximates theluminosity distribution of galaxies in the vicinity of the Local Supercluster,at redshifts cz < 3000 km/s. These mass tracers include groups with crossingtimes less than the Hubble time and isolated galaxies. The measure of merit ofa solution is the sum of the mean square differences between the predicted andobserved distance moduli. In the 3000 km/s sample, this reduced $\chi^2$statistic has a well-defined minimum value at M/L=175 and $t_0 = 10.0$ Gyr, and$\chi^2$ at the minimum is about 1.29 times the value expected from just thestandard deviation of the distance measurements. We have tested for the effectof the mass at greater distance by using the positions of Abell clusters as amodel for the large-scale mass distribution. This external mass model reducesthe minimum value of $\chi^2$ by about 10\% ($\sim 1 \sigma$). The value of thecosmological density parameter $\Omega_0$ is determined by the global meanmass-to-light ratio. Our preliminary analysis yields $\Omega_0= 0.17 \pm 0.10$at one standard deviation. A tighter bound is expected to come out of a largersample of measured distances now available.Comment: Replaced with shorter record size for machines with limits set by  their maile

Action Principle Solutions for Galaxy Motions within 3000 Kilometers per Second