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Lecture# Spherical Systems: Models and Potentials

Description

This lecture covers the theory of spherical systems, focusing on circular speed, circular velocity, circular frequency, and escape speed. It discusses potential-based and density-based models, as well as axisymmetric models for disk galaxies. Examples include potential of flattened systems, infinite thin disks, and spheroidal shells.

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Related concepts (88)

PHYS-401: Astrophysics III : stellar and galactic dynamics

The aim of this course is to acquire the basic knowledge on specific dynamical phenomena related to the origin, equilibrium, and evolution of star
clusters, galaxies, and galaxy clusters.

Escape velocity

In celestial mechanics, escape velocity or escape speed is the minimum speed needed for a free, non-propelled object to escape from the gravitational influence of a primary body, thus reaching an infinite distance from it. It is typically stated as an ideal speed, ignoring atmospheric friction. Although the term "escape velocity" is common, it is more accurately described as a speed than a velocity because it is independent of direction.

Disc galaxy

A disc galaxy (or disk galaxy) is a galaxy characterized by a galactic disc, a flattened circular volume of stars. These galaxies may or may not include a central non-disc-like region (a galactic bulge). Disc galaxy types include: Spiral galaxies: Unbarred spiral galaxies: (types S, SA) Barred spiral galaxies: (type SB) Intermediate spiral galaxies: (type SAB) Lenticular galaxies: (types E8, S0, SA0, SB0, SAB0) Galaxies that are not disc types include: Elliptical galaxies: (type dE) Irregular galaxies: (ty

Spherical harmonics

In mathematics and physical science, spherical harmonics are special functions defined on the surface of a sphere. They are often employed in solving partial differential equations in many scientific fields. Since the spherical harmonics form a complete set of orthogonal functions and thus an orthonormal basis, each function defined on the surface of a sphere can be written as a sum of these spherical harmonics. This is similar to periodic functions defined on a circle that can be expressed as a sum of circular functions (sines and cosines) via Fourier series.

Spherical conic

In mathematics, a spherical conic or sphero-conic is a curve on the sphere, the intersection of the sphere with a concentric elliptic cone. It is the spherical analog of a conic section (ellipse, parabola, or hyperbola) in the plane, and as in the planar case, a spherical conic can be defined as the locus of points the sum or difference of whose great-circle distances to two foci is constant. By taking the antipodal point to one focus, every spherical ellipse is also a spherical hyperbola, and vice versa.

Del in cylindrical and spherical coordinates

This is a list of some vector calculus formulae for working with common curvilinear coordinate systems. This article uses the standard notation ISO 80000-2, which supersedes ISO 31-11, for spherical coordinates (other sources may reverse the definitions of θ and φ): The polar angle is denoted by : it is the angle between the z-axis and the radial vector connecting the origin to the point in question. The azimuthal angle is denoted by : it is the angle between the x-axis and the projection of the radial vector onto the xy-plane.

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