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An orbital ring is a concept of an artificial ring placed around a body and set rotating at such a rate that the apparent centrifugal force is large enough to counteract the force of gravity. For the Earth , the required speed is on the order of 10 km/sec, compared to a typical low Earth orbit velocity of 8 km/sec.
The Bohr–Sommerfeld model was fundamentally inconsistent and led to many paradoxes. The magnetic quantum number measured the tilt of the orbital plane relative to the xy plane, and it could only take a few discrete values. This contradicted the obvious fact that an atom could be turned this way and that relative to the coordinates without ...
In quantum mechanics, the case of a particle in a one-dimensional ring is similar to the particle in a box. The Schrödinger equation for a free particle which is restricted to a ring (technically, whose configuration space is the circle S 1 {\displaystyle S^{1}} ) is
Classically we have for the angular momentum =. This is the same in quantum mechanics considering and as operators. Classically, an infinitesimal rotation of the vector = (,,) about the -axis to ′ = (′, ′,) leaving unchanged can be expressed by the following infinitesimal translations (using Taylor approximation):
In mathematics and physics, the term generator or generating set may refer to any of a number of related concepts. The underlying concept in each case is that of a smaller set of objects, together with a set of operations that can be applied to it, that result in the creation of a larger collection of objects, called the generated set .
Hydrogen atomic orbitals of different energy levels. The more opaque areas are where one is most likely to find an electron at any given time. In quantum mechanics, a spherically symmetric potential is a system of which the potential only depends on the radial distance from the spherical center and a location in space.
An orbital ring is a dynamically elevated ring placed around the Earth that rotates at an angular rate that is faster than orbital velocity at that altitude, stationary platforms can be supported by the excess centripetal acceleration of the super-orbiting ring (similar in principle to a Launch loop), and ground-tethers can be supported from ...
In astrodynamics, the vis-viva equation is one of the equations that model the motion of orbiting bodies.It is the direct result of the principle of conservation of mechanical energy which applies when the only force acting on an object is its own weight which is the gravitational force determined by the product of the mass of the object and the strength of the surrounding gravitational field.