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Right ascension is measured eastward up to 24 h along the celestial equator from the primary direction. Right ascension (abbreviated RA; symbol α) is the angular distance of a particular point measured eastward along the celestial equator from the Sun at the March equinox to the (hour circle of the) point in question above the Earth. [1]
In this case, the longitude is also called the right ascension of the ascending node (RAAN). 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.
The vector algebra to derive the standard formula is equivalent to the calculation of the long derivation for the compass course. The sign of the angle is basically kept, north over east in both cases, but as astronomers look at stars from the inside of the celestial sphere, the definition uses the convention that the q is the angle in an image that turns the direction to the NCP ...
Vega's proper motion is 202.03 ± 0.63 milliarcseconds (mas) per year in right ascension—the celestial equivalent of longitude—and 287.47 ± 0.54 mas/y in declination, which is equivalent to a change in latitude. The net proper motion of Vega is 327.78 mas/y, [83] which results in angular movement of a degree every 11,000 years.
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).
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.
The values of sine and cosine of 30 and 60 degrees are derived by analysis of the equilateral triangle. In an equilateral triangle, the 3 angles are equal and sum to 180°, therefore each corner angle is 60°. Bisecting one corner, the special right triangle with angles 30-60-90 is obtained.
Newcomb gives the Right ascension of the fictitious mean Sun, affected by aberration (which is used in finding mean solar time) as [10] τ = 18 h 38 m 45.836 s + 8 640 184.542 s T + 0.0929 s T 2. Authors citing this expression include McCarthy & Seidelmann (p. 13) and the Nautical Almanac Offices of the United Kingdom and United States (p. 73).