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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 ...
Orbital mechanics is a core discipline within space-mission design and control. Celestial mechanics treats more broadly the orbital dynamics of systems under the influence of gravity, including both spacecraft and natural astronomical bodies such as star systems, planets, moons, and comets.
Unlike the two-body problem, the three-body problem has no general closed-form solution, meaning there is no equation that always solves it. [1] When three bodies orbit each other, the resulting dynamical system is chaotic for most initial conditions .
The rate of precession depends on the inclination of the orbital plane to the equatorial plane, as well as the orbital eccentricity. For a satellite in a prograde orbit around Earth, the precession is westward (nodal regression), that is, the node and satellite move in opposite directions. [1] A good approximation of the precession rate is
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 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.
Unlike standard orbits which are classified by their orbital eccentricity, radial orbits are classified by their specific orbital energy, the constant sum of the total kinetic and potential energy, divided by the reduced mass: = where x is the distance between the centers of the masses, v is the relative velocity, and = (+) is the standard ...
In orbital mechanics, mean motion (represented by n) is the angular speed required for a body to complete one orbit, assuming constant speed in a circular orbit which completes in the same time as the variable speed, elliptical orbit of the actual body. [1]