N-body units

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Quantity Expression
Length (R) Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://api.formulasearchengine.com/v1/":): {\displaystyle \frac{1}{R} = \frac{2}{M^2} \sum_{i,j \ne i}^{N} \frac{m_i m_j}{\left| \vec{r_j}-\vec{r_i} \right| }}
Mass (M) Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://api.formulasearchengine.com/v1/":): {\displaystyle M = \sum_{i=1}^{N} m_i}

N-body units are a completely self-contained system of units used for N-body simulations of self gravitating systems in astrophysics. In this system, the base physical units are chosen so that the total mass, M, the gravitational constant, G, and the virial radius, R, are normalised. The underlying assumption is that the system of N objects (stars) satisfies the virial theorem. The consequence of standard N-body units is that the velocity dispersion of the system is Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://api.formulasearchengine.com/v1/":): {\displaystyle \scriptstyle v = 1/\sqrt{2} } and that the dynamical -crossing- time scales as Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://api.formulasearchengine.com/v1/":): {\displaystyle \scriptstyle t = 2\sqrt{2} } . The first mention of standard N-body units was by Michel Hénon (1971).[1] They were taken up by Haldan Cohn (1979)[2] and later widely advertised and generalized by Douglas Heggie and Robert Mathieu (1986).[3]

References