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The Schwarzschild radius was named after the German astronomer Karl Schwarzschild, who calculated this exact solution for the theory of general relativity in 1916. The Schwarzschild radius is given as =, where G is the gravitational constant, M is the object mass, and c is the speed of light.
Vesta (radius 262.7 ± 0.1 km), the second-largest asteroid, appears to have a differentiated interior and therefore likely was once a dwarf planet, but it is no longer very round today. [74] Pallas (radius 255.5 ± 2 km ), the third-largest asteroid, appears never to have completed differentiation and likewise has an irregular shape.
For example, the Schwarzschild radius r s of the Earth is roughly 9 mm (3 ⁄ 8 inch); at the surface of the Earth, the corrections to Newtonian gravity are only one part in a billion. The Schwarzschild radius of the Sun is much larger, roughly 2953 meters, but at its surface, the ratio r s / r is roughly 4 parts in a million.
For example, if a TNO is incorrectly assumed to have a mass of 3.59 × 10 20 kg based on a radius of 350 km with a density of 2 g/cm 3 but is later discovered to have a radius of only 175 km with a density of 0.5 g/cm 3, its true mass would be only 1.12 × 10 19 kg.
The Jupiter radius or Jovian radius (R J or R Jup) has a value of 71,492 km (44,423 mi), or 11.2 Earth radii (R 🜨) [2] (one Earth radius equals 0.08921 R J). The Jupiter radius is a unit of length used in astronomy to describe the radii of gas giants and some exoplanets. It is also used in describing brown dwarfs.
Some planets might have a radius that would be hard to compare to Jupiter. So the option to compare the planet to Earth is possible. {{ Planetary radius | base = <!--base planet (between Jupiter and Earth [Jupiter automatic])--> | radius = <!--simplified number of the radius (Jupiter or Earth equals 100px)--> }}
In such a spacetime, a particularly important kind of coordinate chart is the Schwarzschild chart, ... is the standard Riemannian metric on the unit radius 2-sphere.
is the definition of the Schwarzschild radius for an object of mass , so the Schwarzschild metric may be rewritten in the alternative form: d s 2 = ( 1 − r s r ) − 1 d r 2 + r 2 ( d θ 2 + sin 2 θ d ϕ 2 ) − c 2 ( 1 − r s r ) d t 2 {\displaystyle ds^{2}=\left(1-{\frac {r_{s}}{r}}\right)^{-1}dr^{2}+r^{2}(d\theta ^{2}+\sin ^{2}\theta ...