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Therefore, as the body accumulates matter at a given fixed density (in this example, 997 kg/m 3, the density of water), its Schwarzschild radius will increase more quickly than its physical radius. When a body of this density has grown to around 136 million solar masses (1.36 × 10 8 M ☉), its physical radius would be overtaken by its ...
We can convert a mass expressed in kilograms to the equivalent mass expressed in metres by multiplying by the conversion factor G/c 2. For example, the Sun's mass of 2.0 × 10 30 kg in SI units is equivalent to 1.5 km. This is half the Schwarzschild radius of a one solar mass black hole. All other conversion factors can be worked out by ...
Estimates from an IAU question-and-answer press release from 2006, giving 800 km radius and 0.5 × 10 21 kg mass as cut-offs that normally would be enough for hydrostatic equilibrium, while stating that observation would be needed to determine the status of borderline cases. [50]
A special type of area density is called column density (also columnar mass density or simply column density), denoted ρ A or σ. It is the mass of substance per unit area integrated along a path; [ 1 ] It is obtained integrating volumetric density ρ {\displaystyle \rho } over a column: [ 2 ] σ = ∫ ρ d s . {\displaystyle \sigma =\int \rho ...
Dimensionless numbers (or characteristic numbers) have an important role in analyzing the behavior of fluids and their flow as well as in other transport phenomena. [1] They include the Reynolds and the Mach numbers, which describe as ratios the relative magnitude of fluid and physical system characteristics, such as density, viscosity, speed of sound, and flow speed.
The Wigner–Seitz radius, named after Eugene Wigner and Frederick Seitz, is the radius of a sphere whose volume is equal to the mean volume per atom in a solid (for first group metals). [1] In the more general case of metals having more valence electrons, r s {\displaystyle r_{\rm {s}}} is the radius of a sphere whose volume is equal to the ...
Approximate specific stiffness for various materials. No attempt is made to correct for materials whose stiffness varies with their density. Material Young's modulus Density (g/cm 3) Young's modulus per density; specific stiffness (10 6 m 2 s −2) Young's modulus per density squared (10 3 m 5 kg −1 s −2) Young's modulus per density cubed ...
Using the number density as a function of spatial coordinates, the total number of objects N in the entire volume V can be calculated as = (,,), where dV = dx dy dz is a volume element. If each object possesses the same mass m 0 , the total mass m of all the objects in the volume V can be expressed as m = ∭ V m 0 n ( x , y , z ) d V ...