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One of the fundamental tasks of dynamical astronomy is to infer the distribution of mass in a stellar system from a snapshot of the positions and velocities of its stars. The usual approach to this task (e.g., Schwarzschilds method) involves fitting parametrized forms of the gravitational potential and the phase-space distribution to the data. We review the practical and conceptual difficulties with this approach and describe a novel statistical method for determining the mass distribution that does not require determining the phase-space distribution of the stars. We show that this new estimator out-performs other distribution-free estimators for the harmonic and Kepler potentials.
Cluster mass profiles are tests of models of structure formation. Only two current observational methods of determining the mass profile, gravitational lensing and the caustic technique, are independent of the assumption of dynamical equilibrium. Bot
In this chapter, we review some historical understanding and recent advances on the Initial Mass Function (IMF) and the Core Mass Function (CMF), both in terms of observations and theories. We focus mostly on star formation in clustered environment s
Mass-to-light versus colour relations (MLCRs), derived from stellar population synthesis models, are widely used to estimate galaxy stellar masses (M$_*$) yet a detailed investigation of their inherent biases and limitations is still lacking. We quan
Halo stars orbit within the potential of the Milky Way and hence their kinematics can be used to understand the underlying mass distribution. However, the inferred mass distribution depends sensitively upon assumptions made on the density and the vel
Most globular clusters have half-mass radii of a few pc with no apparent correlation with their masses. This is different from elliptical galaxies, for which the Faber-Jackson relation suggests a strong positive correlation between mass and radius. O