Search results
Results from the WOW.Com Content Network
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.
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]
This definition allows a polytope to be neither bounded nor finite. Polytopes are defined in this way, e.g., in linear programming. A polytope is bounded if there is a ball of finite radius that contains it. A polytope is said to be pointed if it contains at least one vertex. Every bounded nonempty polytope is pointed.
Solute atoms should have a smaller radius than 59% of the radius of solvent atoms. [5] [6] The solute and solvent should have similar electronegativity. [7] Valency factor: two elements should have the same valence. The greater the difference in valence between solute and solvent atoms, the lower the solubility.
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 ...
Below are few ultrarelativistic approximations when .The rapidity is denoted : Motion with constant proper acceleration: d ≈ e aτ /(2a), where d is the distance traveled, a = dφ/dτ is proper acceleration (with aτ ≫ 1), τ is proper time, and travel starts at rest and without changing direction of acceleration (see proper acceleration for more details).
The most likely radii for a given neutron star mass are bracketed by models AP4 (smallest radius) and MS2 (largest radius). BE is the ratio of gravitational binding energy mass equivalent to observed neutron star gravitational mass of M with radius R , B E = 0.60 β 1 − β 2 {\displaystyle BE={\frac {0.60\,\beta }{1-{\frac {\beta }{2}}}}} β ...
Some specific values of n correspond to particular cases: = for an isobaric process, = + for an isochoric process. In addition, when the ideal gas law applies: = for an isothermal process,