Dynamical tomography of gravitationally bound systems

We study the inverse problem of deducing the dynamical characteristics (such as the potential field) of large systems from kinematic observations. We show that, for a class of steady-state systems, the solution is unique even with fragmentary data, dark matter, or selection (bias) functions. Using spherically symmetric models for simulations, we investigate solution convergence and the roles of data noise and regularization in the inverse problem. We also present a method, analogous to tomography, for comparing the observed data with a model probability distribution such that the latter can be determined.