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To find some of the phasing orbital parameters, first one must find the required period time of the phasing orbit using the following equation. = where T 1 is defined as period of original orbit; T 2 is defined as period of phasing orbit; t is defined as time elapsed to cover phase angle in original orbit
For some objects, such as the Moon (see lunar phases), Venus and Mercury the phase angle (as seen from the Earth) covers the full 0–180° range. The superior planets cover shorter ranges. For example, for Mars the maximum phase angle is about 45°. For Jupiter, the maximum is 11.1° and for Saturn 6°. [1]
In astronomy, a phase curve describes the brightness of a reflecting body as a function of its phase angle (the arc subtended by the observer and the Sun as measured at the body). The brightness usually refers the object's absolute magnitude , which, in turn, is its apparent magnitude at a distance of one astronomical unit from the Earth and Sun.
Parametrically, ω is the angle from the body's ascending node to its periapsis, measured in the direction of motion. For specific types of orbits, terms such as argument of perihelion (for heliocentric orbits ), argument of perigee (for geocentric orbits ), argument of periastron (for orbits around stars), and so on, may be used (see apsis for ...
Phase angle may refer to: Phase (waves), the angular displacement of a sinusoid from a reference point or time; Phasor angle, angular component of the complex number representation of a sinusoid; Analytic representation phase, instantaneous phase of an analytic signal representation; Phase angle (astronomy), the angle between the incident light ...
In mathematics, a phase portrait is a geometric representation of the orbits of a dynamical system in the phase plane. Each set of initial conditions is represented by a different point or curve. Phase portraits are an invaluable tool in studying dynamical systems. They consist of a plot of typical trajectories in the phase space.
In applied mathematics, the phase space method is a technique for constructing and analyzing solutions of dynamical systems, that is, solving time-dependent differential equations. The method consists of first rewriting the equations as a system of differential equations that are first-order in time, by introducing additional variables.
Conversely, a phase reversal or phase inversion implies a 180-degree phase shift. [ 2 ] When the phase difference φ ( t ) {\displaystyle \varphi (t)} is a quarter of turn (a right angle, +90° = π/2 or −90° = 270° = −π/2 = 3π/2 ), sinusoidal signals are sometimes said to be in quadrature , e.g., in-phase and quadrature components of a ...