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Earth radius (denoted as R 🜨 or R E) is the distance from the center of Earth to a point on or near its surface. Approximating the figure of Earth by an Earth spheroid (an oblate ellipsoid), the radius ranges from a maximum (equatorial radius, denoted a) of nearly 6,378 km (3,963 mi) to a minimum (polar radius, denoted b) of nearly 6,357 km (3,950 mi).
The Hill sphere, or the sphere of gravitational influence, of Earth is about 1.5 million km (930,000 mi) in radius. [164] [n 11] This is the maximum distance at which Earth's gravitational influence is stronger than that of the more distant Sun and planets.
e r is the radial unit vector, r is the radius, |r|. M is the mass of the particle, which is assumed to be a point mass located at the origin. A proof using vector calculus is shown in the box below. It is mathematically identical to the proof of Gauss's law (in electrostatics) starting from Coulomb's law. [2]
The curvature of the Earth is evident in the horizon across the image, and the bases of the buildings on the far shore are below that horizon and hidden by the sea. The simplest model for the shape of the entire Earth is a sphere. The Earth's radius is the distance from Earth's center to its surface, about 6,371 km (3,959 mi). While "radius ...
It is a generalisation of the vector form, which becomes particularly useful if more than two objects are involved (such as a rocket between the Earth and the Moon). For two objects (e.g. object 2 is a rocket, object 1 the Earth), we simply write r instead of r 12 and m instead of m 2 and define the gravitational field g(r) as:
As the Schwarzschild radius is linearly related to mass, while the enclosed volume corresponds to the third power of the radius, small black holes are therefore much more dense than large ones. The volume enclosed in the event horizon of the most massive black holes has an average density lower than main sequence stars.
Because the definition of r SOI relies on the presence of the Sun and a planet, the term is only applicable in a three-body or greater system and requires the mass of the primary body to be much greater than the mass of the secondary body. This changes the three-body problem into a restricted two-body problem.
For Earth-orbiting satellites, the reference plane is usually the Earth's equatorial plane, and for satellites in solar orbits it is the ecliptic plane. The intersection is called the line of nodes , as it connects the reference body (the primary) with the ascending and descending nodes.