On 30 October an ex-meridian altitude of the Sun's lower limb at upper transit was observed at 1144 ZT. Your DR position is LAT 22°42.0'S, LONG 137°16.0'W, and your sextant altitude (hs) is 80°59.4'. The index error is 2.5' off the arc, and your height of eye is 42.5 feet. The chronometer time of the observation is 08h 46m 15s, and the chronometer error is 02m 12s fast. Find the latitude at meridian transit from the ex-meridian observation.

Question

On 30 October an ex-meridian altitude of the Sun's lower limb at upper transit was observed at 1144 ZT. Your DR position is LAT 22&deg;42.0'S, LONG 137&deg;16.0'W, and your sextant altitude (hs) is 80&deg;59.4'. The index error is 2.5' off the arc, and your height of eye is 42.5 feet. The chronometer time of the observation is 08h 46m 15s, and the chronometer error is 02m 12s fast. Find the latitude at meridian transit from the ex-meridian observation.

Accepted Answer

Option A: LAT 22&deg;31.4'S. Calculate the time of meridian passage and the Sun's declination. Apply the ex-meridian reduction formula to the observed altitude, adjusting for the time difference from local apparent noon. This process yields the latitude at meridian transit, which is 22°31.4'S, consistent with standard Bowditch celestial navigation reduction methods.