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    Re: SHA vs RA
    From: Frank Reed
    Date: 2018 Jan 14, 08:40 -0800

    Good question.

    First of all, just to remind everyone, SHA or "sidereal hour angle" and RA or "right ascension" are fundamentally the same angle. They are both "sky longitude", measured with reference to the same celestial polar axis and starting from the same arbitrary celestial point at the leading edge of the astrological sign of Aries, known quaintly as the "First Point of Aries". One is measured clockwise, the other counter-clockwise, and therefore the mathematical relationship between them is
       SHA = 360° - RA
       RA = 360° - SHA.
    Beyond the fundamental CW vs CCW distinction, it is a matter of historical convention that RA is normally listed, not in degrees, but in hours. So if you have an RA for a star in Orion, e.g., it might be listed as 5h 23m. To convert that to degrees and minutes, multiply each part by 15 and then "clean up" the minutes. In this example, 5·15 is 75 and 23·15 is 345, so you get 75°345'. That doesn't look quite right, so you "clean up" the minutes by taking out five degrees-worth leaving 80°45'. At this point, the angle is still correctly referred to as a right ascension, an RA value. It has simply been expressed in degrees instead of hours. Finally, we can reverse the direction of measure of this "sky longitude" and get the corresponding SHA by subtracting from 360° (or to make the math a little quicker, subtract from 359°60'). The result is 279°15'. Again, these are two different measures of the same fundamental quantity. A good analogy is east versus west terrestrial longitude. If one group of "easty" geographers expressed all longitudes, all around the globe, as "EL" or east longitude while another competing school of "westy" geographers expressed all longitudes as "WL" or west longitude, then we would convert between them by noting that
       EL = 360° - WL.

    I mentioned above that quoting RA in hours is a historical convention, and that's really what we're seeing here: not navigational necessity, but historical convention. From the beginning of scientific celestial navigation (nautical astronomy) in the late 18th century right through the early 1930s (and longer in some intellectual backwaters, like the UK, Australia, etc. --ha ha), nearly all celestial navigation was done using the RA convention for "sky longitude". That's over 150 years during which navigators did just fine using the historically preferred RA of the astronomers. The transition during the 1930s was motivated by the needs of aerial navigators who welcomed any trick that could save a little time. Quoting sky longitudes in SHA saved one brief step in many calculations, and that was enough to get the ball rolling. The real momentum though was created by the Second World War. Conventions and cultural aspects of navigation became locked in as fixed regimens to be obeyed as navigation became militarized. Huge numbers of navigators had to be trained quickly and efficiently, and that demanded standardization. The adoption of SHA was part of that standardization.

    Frank Reed
    Clockwork Mapping / ReedNavigation.com
    Conanicut Island USA

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