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The brightness of an object is a function of the phase angle, which is generally smooth, except for the so-called opposition spike near 0°, which does not affect gas giants or bodies with pronounced atmospheres, and when the object becomes fainter as the angle approaches 180°. This relationship is referred to as the phase curve.
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.
The change in position within the orbit is usually defined as the phase angle, ϕ, and is the change in true anomaly required between the spacecraft's current position to the final position. The phase angle can be converted in terms of time using Kepler's Equation: [2]
A planetary phase is a certain portion of a planet's area that reflects sunlight as viewed from a given vantage point, as well as the period of time during which it occurs. The phase is determined by the phase angle , which is the angle between the planet, the Sun and the Earth.
It is expressed as the angle between a reference plane and the orbital plane or axis of direction of the orbiting object. For a satellite orbiting the Earth directly above the Equator, the plane of the satellite's orbit is the same as the Earth's equatorial plane, and the satellite's orbital inclination is 0°.
The angle is measured eastwards (or, as seen from the north, counterclockwise) from the FPA to the node. [2] [3] An alternative is the local time of the ascending node (LTAN), based on the local mean time at which the spacecraft crosses the equator. Similar definitions exist for satellites around other planets (see planetary coordinate systems).
The mean anomaly M is a mathematically convenient fictitious "angle" which does not correspond to a real geometric angle, but rather varies linearly with time, one whole orbital period being represented by an "angle" of 2 π radians.
Phase curve (astronomy) is the brightness of a reflecting body as a function of its phase angle. Phase response curve is the relationship between the timing and the effect of a treatment designed to affect circadian rhythms. Phase diagram is a type of chart used to show conditions at which thermodynamically distinct phases can occur at equilibrium.