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Partial orbital ring systems [3] – this is essentially a launch loop; In addition, he proposed the concept of "supramundane worlds" such as supra-Jovian and supra-stellar "planets". These are artificial planets that would be supported by a grid of orbital rings that would be positioned above a planet, supergiant or even a star. [9]
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
Every object in a 2-body ballistic trajectory has a constant specific orbital energy equal to the sum of its specific kinetic and specific potential energy: = = =, where = is the standard gravitational parameter of the massive body with mass , and is the radial distance from its center. As an object in an escape trajectory moves outward, its ...
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.
In physics, the most common orbital descriptions are based on the solutions to the hydrogen atom, where orbitals are given by the product between a radial function and a pure spherical harmonic. The quantum numbers, together with the rules governing their possible values, are as follows:
There are many useful features of the effective potential, such as . To find the radius of a circular orbit, simply minimize the effective potential with respect to , or equivalently set the net force to zero and then solve for : = After solving for , plug this back into to find the maximum value of the effective potential .
Benzene, the most widely recognized aromatic compound with six delocalized π-electrons (4n + 2, for n = 1).. In organic chemistry, Hückel's rule predicts that a planar ring molecule will have aromatic properties if it has 4n + 2 π-electrons, where n is a non-negative integer.
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.