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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.
For example, the Schwarzschild radius 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 {\textstyle {\frac {r_{\text{s}}}{r}}} is roughly 4 ...
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 the Schwarzschild metric, free-falling objects can be in circular orbits if the orbital radius is larger than (the radius of the photon sphere). The formula for a clock at rest is given above; the formula below gives the general relativistic time dilation for a clock in a circular orbit: [11] [12]
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.
In the Schwarzschild coordinates, the Schwarzschild radius = is the radial coordinate of the event horizon = =. In the Kruskal–Szekeres coordinates the event horizon is given by =. Note that the metric is perfectly well defined and non-singular at the event horizon.
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 ...
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.