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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 case of a particle in a one-dimensional ring is an instructive example when studying the quantization of angular momentum for, say, an electron orbiting the nucleus. The azimuthal wave functions in that case are identical to the energy eigenfunctions of the particle on a ring.
For example, the orbital 1s (pronounced as the individual numbers and letters: "'one' 'ess'") is the lowest energy level (n = 1) and has an angular quantum number of ℓ = 0, denoted as s. Orbitals with ℓ = 1, 2 and 3 are denoted as p, d and f respectively.
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 ...
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.
The localized orbital corresponding to one O-H bond is the sum of these two delocalized orbitals, and the localized orbital for the other O-H bond is their difference; as per Valence bond theory. For multiple bonds and lone pairs, different localization procedures give different orbitals.
The speed (or the magnitude of velocity) relative to the centre of mass is constant: [1]: 30 = = where: , is the gravitational constant, is the mass of both orbiting bodies (+), although in common practice, if the greater mass is significantly larger, the lesser mass is often neglected, with minimal change in the result.
An example of the first situation is an atom whose electrons only experience the Coulomb force of its atomic nucleus. If we ignore the electron–electron interaction (and other small interactions such as spin–orbit coupling), the orbital angular momentum l of each electron commutes with the total Hamiltonian. In this model the atomic ...