On 15 December in DR position LAT 23°24.0'N, LONG 55°36.0'W, you take an ex-meridian observation of the Sun's lower limb. The chronometer time of the sight is 03h 45m 19s, and the chronometer error is 00m 00s. The sextant altitude (hs) is 43°02.3'. The index error is 2.6' on the arc, and your height of eye is 65.0 feet. What is the latitude at meridian transit?

Question

On 15 December in DR position LAT 23&deg;24.0'N, LONG 55&deg;36.0'W, you take an ex-meridian observation of the Sun's lower limb. The chronometer time of the sight is 03h 45m 19s, and the chronometer error is 00m 00s. The sextant altitude (hs) is 43&deg;02.3'. The index error is 2.6' on the arc, and your height of eye is 65.0 feet. What is the latitude at meridian transit?

Accepted Answer

Option A: LAT 23&deg;33.5'N. Compute Greenwich Mean Time (GMT) from chronometer time, extract local hour angle, and apply index error, dip, and semi-diameter to sextant altitude. Per Bowditch, apply the ex-meridian reduction formula to calculate latitude at meridian transit, yielding LAT 23°33.5'N.