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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 .
Given the different Sun incidence in different positions in the orbit, it is necessary to define a standard point of the orbit of the planet, to define the planet position in the orbit at each moment of the year w.r.t such point; this point is called with several names: vernal equinox, spring equinox, March equinox, all equivalent, and named considering northern hemisphere seasons.
3D visualization of a sphere and a rotation about an Euler axis (^) by an angle of In 3-dimensional space, according to Euler's rotation theorem, any rotation or sequence of rotations of a rigid body or coordinate system about a fixed point is equivalent to a single rotation by a given angle about a fixed axis (called the Euler axis) that runs through the fixed point. [6]
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 ...
In astronomy, the rotation period or spin period [1] of a celestial object (e.g., star, planet, moon, asteroid) has two definitions. The first one corresponds to the sidereal rotation period (or sidereal day), i.e., the time that the object takes to complete a full rotation around its axis relative to the background stars (inertial space).
The formula above indicates that the angular motion is multiplied by a factor k = 1/ √ n, so that the apsidal angle α equals 180°/ √ n. This angular scaling can be seen in the apsidal precession, i.e., in the gradual rotation of the long axis of the ellipse (Figure 3).
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Despite being correct in saying that the planets revolved around the Sun, Copernicus was incorrect in defining their orbits. Introducing physical explanations for movement in space beyond just geometry, Kepler correctly defined the orbit of planets as follows: [1] [2] [5]: 53–54 The planetary orbit is not a circle with epicycles, but an ellipse.