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Orbital mechanics or astrodynamics is the application of ballistics and celestial mechanics to the practical problems concerning the motion of rockets, satellites, and other spacecraft. The motion of these objects is usually calculated from Newton's laws of motion and the law of universal gravitation .
A fundamental physical constant occurring in quantum mechanics is the Planck constant, h. A common abbreviation is ħ = h /2 π , also known as the reduced Planck constant or Dirac constant . Quantity (common name/s)
In astrodynamics, an orbit equation defines the path of orbiting body around central body relative to , without specifying position as a function of time.Under standard assumptions, a body moving under the influence of a force, directed to a central body, with a magnitude inversely proportional to the square of the distance (such as gravity), has an orbit that is a conic section (i.e. circular ...
Early results about relative orbital motion were published by George William Hill in 1878. [3] Hill's paper discussed the orbital motion of the moon relative to the Earth.. In 1960, W. H. Clohessy and R. S. Wiltshire published the Clohessy–Wiltshire equations to describe relative orbital motion of a general satellite for the purpose of designing control systems to achieve orbital rendezvous.
According to the orbital energy conservation equation (also referred to as vis-viva equation), it does not vary with time: = + = = = where v {\displaystyle v} is the relative orbital speed ; r {\displaystyle r} is the orbital distance between the bodies;
In orbital mechanics, Kepler's equation relates various geometric properties of the orbit of a body subject to a central force. It was derived by Johannes Kepler in 1609 in Chapter 60 of his Astronomia nova , [ 1 ] [ 2 ] and in book V of his Epitome of Copernican Astronomy (1621) Kepler proposed an iterative solution to the equation.
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.
Corollary 1 then points out that the centripetal force is proportional to V 2 /R, where V is the orbital speed and R the circular radius. Corollary 2 shows that, putting this in another way, the centripetal force is proportional to (1/P 2) * R where P is the orbital period.