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The Schwarzschild radius of an object is proportional to its mass. Accordingly, the Sun has a Schwarzschild radius of approximately 3.0 km (1.9 mi), [8] whereas Earth's is approximately 9 mm (0.35 in) [8] and the Moon's is approximately 0.1 mm (0.0039 in).
Schwarzschild solution in Schwarzschild coordinates, with two space dimensions suppressed, leaving just the time t and the distance from the center r. In red the incoming null geodesics. In blue outcoming null geodesics. In green the null light cones on which borders light moves, while massive objects move inside the cones.
The Jupiter mass, also called Jovian mass, is the unit of mass equal to the total mass of the planet Jupiter. This value may refer to the mass of the planet alone, or the mass of the entire Jovian system to include the moons of Jupiter. Jupiter is by far the most massive planet in the Solar System. It is approximately 2.5 times as massive as ...
In general relativity, Schwarzschild geodesics describe the motion of test particles in the gravitational field of a central fixed mass , that is, motion in the Schwarzschild metric. Schwarzschild geodesics have been pivotal in the validation of Einstein's theory of general relativity .
Static mass increase is a third effect noted by Einstein in the same paper. [6] The effect is an increase in inertia of a body when other masses are placed nearby. While not strictly a frame dragging effect (the term frame dragging is not used by Einstein), it is demonstrated by Einstein that it derives from the same equation of general relativity.
A Schwarzschild black hole is described by the Schwarzschild metric, and cannot be distinguished from any other Schwarzschild black hole except by its mass. The Schwarzschild black hole is characterized by a surrounding spherical boundary, called the event horizon , which is situated at the Schwarzschild radius ( r s {\displaystyle r_{\text{s ...
where is the Schwarzschild radius of the massive object with mass . Thus, even for a non-spinning object, the ISCO radius is only three times the Schwarzschild radius , R S {\displaystyle R_{S}} , suggesting that only black holes and neutron stars have innermost stable circular orbits outside of their surfaces.
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