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Celestial mechanics is the branch of astronomy that deals with the motions of objects in outer space. Historically, celestial mechanics applies principles of physics (classical mechanics) to astronomical objects, such as stars and planets, to produce ephemeris data.
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.
The classical method of finding the position of an object in an elliptical orbit from a set of orbital elements is to calculate the mean anomaly by this equation, and then to solve Kepler's equation for the eccentric anomaly. Define ϖ as the longitude of the pericenter, the angular distance of the pericenter from a reference direction.
In time standards, dynamical time is the independent variable of the equations of celestial mechanics. This is in contrast to time scales such as mean solar time which are based on how far the earth has turned. Since Earth's rotation is not constant, using a time scale based on it for calculating the positions of heavenly objects gives errors ...
The equation is the same as the equation for the harmonic oscillator, a well-known equation in both physics and mathematics, however, the unknown constant vector is somewhat inconvenient. Taking the derivative again, we eliminate the constant vector P , {\displaystyle \ \mathbf {P} \ ,} at the price of getting a third-degree differential equation:
In classical mechanics, the Kepler problem is a special case of the two-body problem, in which the two bodies interact by a central force that varies in strength as the inverse square of the distance between them. The force may be either attractive or repulsive.
The distance to the focal point is a function of the polar angle relative to the horizontal line as given by the equation . In celestial mechanics, a Kepler orbit (or Keplerian orbit, named after the German astronomer Johannes Kepler) is the motion of one body relative to another, as an ellipse, parabola, or hyperbola, which forms a two ...
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 .