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Angles greater than 360° (2 π) or less than 0° may need to be reduced to the range 0°−360° (0–2 π) depending upon the particular calculating machine or program. The cosine of a latitude (declination, ecliptic and Galactic latitude, and altitude) are never negative by definition, since the latitude varies between −90° and +90°.
Right ascension and declination as seen on the inside of the celestial sphere. The primary direction of the system is the March equinox, the ascending node of the ecliptic (red) on the celestial equator (blue). Right ascension is measured eastward up to 24 h along the celestial equator from the primary direction.
The azimuth is the angle formed between a reference direction (in this example north) and a line from the observer to a point of interest projected on the same plane as the reference direction orthogonal to the zenith. An azimuth (/ ˈ æ z ə m ə θ / ⓘ; from Arabic: اَلسُّمُوت, romanized: as-sumūt, lit.
Azimuth is measured eastward from the north point (sometimes from the south point) of the horizon; altitude is the angle above the horizon. The horizontal coordinate system is a celestial coordinate system that uses the observer's local horizon as the fundamental plane to define two angles of a spherical coordinate system: altitude and azimuth.
Denoted with the symbol Ω, it is the angle from a specified reference direction, called the origin of longitude, to the direction of the ascending node (☊), as measured in a specified reference plane. [1] The ascending node is the point where the orbit of the object passes through the plane of reference, as seen in the adjacent image.
Alternatively to right ascension, hour angle (abbreviated HA or LHA, local hour angle), a left-handed system, measures the angular distance of an object westward along the celestial equator from the observer's meridian to the hour circle passing through the object. Unlike right ascension, hour angle is always increasing with the rotation of Earth.
For example, when the Sun is at an elevation of 10°, it appears to be at 10.1°. The Sun's declination can be used, along with its right ascension, to calculate its azimuth and also its true elevation, which can then be corrected for refraction to give its apparent position. [2] [14] [18]
The value of a solar beta angle for a satellite in Earth orbit can be found using the equation = [ + ()] where is the ecliptic true solar longitude, is the right ascension of ascending node (RAAN), is the orbit's inclination, and is the obliquity of the ecliptic (approximately 23.45 degrees for Earth at present).