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The cosine of the hour angle (cos(h)) is used to calculate the solar zenith angle. At solar noon, h = 0.000 so cos(h) = 1, and before and after solar noon the cos(± h) term = the same value for morning (negative hour angle) or afternoon (positive hour angle), so that the Sun is at the same altitude in the sky at 11:00AM and 1:00PM solar time. [5]
A culminating star on the observer's meridian is said to have a zero hour angle (0 h). One sidereal hour (approximately 0.9973 solar hours) later, Earth's rotation will carry the star to the west of the meridian, and its hour angle will be 1 h. When calculating topocentric phenomena, right ascension may be converted into hour angle as an ...
LHA = GHA + L is the local hour angle (+W/-E), Dec and GHA are the declination and Greenwich hour angle of the star observed. And Ho is the true or observed altitude, that is, the altitude measured with a sextant corrected for dip, refraction and parallax.
Angles in the hours ( h), minutes ( m), and seconds ( s) of time measure must be converted to decimal degrees or radians before calculations are performed. 1 h = 15°; 1 m = 15′; 1 s = 15″ 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 ...
This involves resolving a spherical triangle. Given the three magnitudes: local hour angle (LHA), observed body's declination (dec), and assumed latitude (lat), the altitude Hc and azimuth Zn must be computed. The local hour angle, LHA, is the difference between the AP longitude and the hour angle of the observed object. It is always measured ...
, the Greenwich hour angle of the body observed; L H A = G H A + L o n {\displaystyle LHA=GHA+Lon} , the local hour angle of the body observed. First calculate the altitude of the celestial body H c {\displaystyle Hc} using the equation of circle of equal altitude :
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Time sight is a general method for determining longitude by celestial observations using a chronometer; these observations are reduced by solving the navigational triangle for meridian angle and require known values for altitude, latitude, and declination; the meridian angle is converted to local hour angle and compared with Greenwich hour angle.