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Density (normalized to average density) versus radius (normalized to external radius) for a polytrope with index n=3. An index n = 0 polytrope is often used to model rocky planets. The reason is that n = 0 polytrope has constant density, i.e., incompressible interior. This is a zero order approximation for rocky (solid/liquid) planets.
where is a dimensionless radius and is related to the density, and thus the pressure, by = for central density . The index n {\displaystyle n} is the polytropic index that appears in the polytropic equation of state, P = K ρ 1 + 1 n {\displaystyle P=K\rho ^{1+{\frac {1}{n}}}\,} where P {\displaystyle P} and ρ {\displaystyle \rho } are the ...
The above simplified model is not adequate without modification in situations when the composition changes are sufficiently rapid. The equation of hydrostatic equilibrium may need to be modified by adding a radial acceleration term if the radius of the star is changing very quickly, for example if the star is radially pulsating. [9]
Density ( normalized to average density ) versus radius ( normalized to external radius ) for a polytrope with index n=3. Plotted with gnuplot from numerically computed values of the corresponding Lane-Emden function.
For a given L, a lower temperature implies a larger radius, and vice versa. Thus, the Hayashi track separates the HR diagram into two regions: the allowed region to the left, with high temperatures and smaller radii for each luminosity, and the forbidden region to the right, with lower temperatures and correspondingly larger radii.
The convex hull the rectified 5-cell and its dual (of the same long radius) is a nonuniform polychoron composed of 30 cells: 10 tetrahedra, 20 octahedra (as triangular antiprisms), and 20 vertices. Its vertex figure is a triangular bifrustum .
Radius of gyration (in polymer science)(, unit: nm or SI unit: m): For a macromolecule composed of mass elements, of masses , =1,2,…,, located at fixed distances from the centre of mass, the radius of gyration is the square-root of the mass average of over all mass elements, i.e.,
The radius of the radiative zone increases monotonically with mass, with stars around 1.2 solar masses being almost entirely radiative. Above 1.2 solar masses, the core region becomes a convection zone and the overlying region is a radiative zone, with the amount of mass within the convective zone increasing with the mass of the star.