Stellar dynamics

Stellar dynamics is the branch of astrophysics which describes in a statistical way the collective motions of stars subject to their mutual gravity. The essential difference from celestial mechanics is that each star contributes more or less equally to the total gravitational field, whereas in celestial mechanics the pull of a massive body dominates any satellite orbits. Stellar dynamics is the branch of astrophysics which describes in a statistical way the collective motions of stars subject to their mutual gravity. The essential difference from celestial mechanics is that each star contributes more or less equally to the total gravitational field, whereas in celestial mechanics the pull of a massive body dominates any satellite orbits. Historically, the methods utilized in stellar dynamics originated from the fields of both classical mechanics and statistical mechanics. In essence, the fundamental problem of stellar dynamics is the N-body problem, where the N members refer to the members of a given stellar system. Given the large number of objects in a stellar system, stellar dynamics is usually concerned with the more global, statistical properties of several orbits rather than with the specific data on the positions and velocities of individual orbits. The motions of stars in a galaxy or in a globular cluster are principally determined by the average distribution of the other, distant stars. Stellar encounters involve processes such as relaxation, mass segregation, tidal forces, and dynamical friction that influence the trajectories of the system's members. Stellar dynamics also has connections to the field of plasma physics. The two fields underwent significant development during a similar time period in the early 20th century, and both borrow mathematical formalism originally developed in the field of fluid mechanics. Stellar dynamics involves determining the gravitational potential of a substantial number of stars. The stars can be modeled as point masses whose orbits are determined by the combined interactions with each other. Typically, these point masses represent stars in a variety of clusters or galaxies, such as a Galaxy cluster, or a Globular cluster. From Newton's second law an equation describing the interactions of an isolated stellar system can be written down as, m i d r i d t = ∑ i = 1 i ≠ j N G m i m j ( r i − r j ) ‖ r i − r j ‖ 3 {displaystyle m_{i}{frac {dmathbf {r_{i}} }{dt}}=sum _{i=1 atop i eq j}^{N}{frac {Gm_{i}m_{j}left(mathbf {r} _{i}-mathbf {r} _{j} ight)}{left|mathbf {r} _{i}-mathbf {r} _{j} ight|^{3}}}} which is simply a formulation of the N-body problem. For an N-body system, any individual member, m i {displaystyle m_{i}} is influenced by the gravitational potentials of the remaining m j {displaystyle m_{j}} members. In practice, it is not feasible to calculate the system's gravitational potential by adding all of the point-mass potentials in the system, so stellar dynamicists develop potential models that can accurately model the system while remaining computationally inexpensive. The gravitational potential, Φ {displaystyle Phi } , of a system is related to the gravitational field, g → {displaystyle mathbf {vec {g}} } by: g → = − ∇ Φ {displaystyle mathbf {vec {g}} =- abla Phi } whereas the mass density, ρ {displaystyle ho } , is related to the potential via Poisson's equation: