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The Schwarzschild radius or the gravitational radius is a physical parameter in the Schwarzschild solution to Einstein's field equations that corresponds to the radius defining the event horizon of a Schwarzschild black hole. It is a characteristic radius associated with any quantity of mass.
The sizes and masses of many of the moons of Jupiter and Saturn are fairly well known due to numerous observations and interactions of the Galileo and Cassini orbiters; however, many of the moons with a radius less than ~100 km, such as Jupiter's Himalia, have far less certain masses. [5]
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 ...
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]
Since the Schwarzschild metric is expected to be valid only for those radii larger than the radius R of the gravitating body, there is no problem as long as R > r s. For ordinary stars and planets this is always the case. For example, the radius of the Sun is approximately 700 000 km, while its Schwarzschild radius is only 3 km.
The moon’s gravity slightly bent Juice’s path so it received a much larger gravity assist from Earth. The flyby of Earth reduced Juice’s speed by 10,737 miles per hour (4.8 kilometers per ...
Ganymede is the only Galilean moon of Jupiter named after a male figure—like Io, Europa, and Callisto, he was a lover of Zeus. In English, the Galilean satellites Io, Europa and Callisto have the Latin spellings of their names, but the Latin form of Ganymede is Ganymēdēs , which would be pronounced / ˌ ɡ æ n ɪ ˈ m iː d iː z / . [ 38 ]
To calculate the changes in frequency in a nearly static gravitational field, only the time component of the metric tensor is important, and the lowest order approximation is accurate enough for ordinary stars and planets, which are much bigger than their Schwarzschild radius.