Celestial Navigation

The calculator performs a classical sun sight reduction using the intercept (Marcq St. Hilaire) method and standard spherical trigonometry. A sextant observation Hs is corrected to true observed altitude Ho by applying index correction, dip correction based on height of eye, atmospheric refraction, and the Sun's semi-diameter:

Ho = Hs + IC - Dip - Refraction + SD

The Sun's declination delta and Greenwich Hour Angle (GHA) are computed from the UTC date and time using astronomical formulas equivalent to nautical almanac data. The Local Hour Angle is then given by LHA = GHA + lon, with longitude positive east in this calculator. From the assumed latitude phi, the calculated altitude Hc is obtained from the navigational triangle:

sin(Hc) = sin(phi) * sin(delta) + cos(phi) * cos(delta) * cos(LHA)

The true azimuth Zn is derived from:

cos(Z) = (sin(delta) - sin(phi) * sin(Hc)) / (cos(phi) * cos(Hc))

with quadrant resolution based on the LHA. The intercept is computed as:

Intercept = (Ho - Hc) * 60

where one minute of arc corresponds to one nautical mile; a positive value indicates position toward the Sun, negative away from it. The resulting Line of Position is constructed perpendicular to the azimuth Zn and offset by the intercept distance. When vessel course, speed, and elapsed time are provided, the Line of Position may be advanced using dead-reckoning:

D = v * dt
phi2 = phi + (D * cos(C)) / 60
lon2 = lon + (D * sin(C)) / (60 * cos(phi))

D is run distance in nm, v is speed in knots, dt is elapsed time in hours, and C is true course. All computations follow standard celestial navigation equations and assumptions.