On 15 March in DR position LAT 21°42.0'N, LONG 55°26.0'W, you take an ex-meridian observation of the Sun's lower limb. The chronometer time of the sight is 04h 02m 40s, and the chronometer error is 02m 24s fast. The sextant altitude (hs) is 66°15.6'. The index error is 2.8' on the arc, and your height of eye is 56 feet. What is the latitude at meridian transit?
• Ex-meridian sun sight: using an altitude taken a few minutes before/after meridian passage to find the meridian altitude and then latitude • Full altitude corrections: converting hs → Ha → Ho using index error, dip (height of eye), and main sun corrections (LL, refraction, semi‑diameter) • Latitude at meridian transit relationship: combining Ho at LAN with the Sun’s declination (same name vs contrary name)
• First, work the sight to get the observed altitude Ho from the given hs (include index error, dip for 56 ft, and lower‑limb sun corrections). Is this altitude reasonable for your DR latitude? • Use the corrected chronometer time and its error to find GMT of the sight, then compare it with the meridian passage time of the Sun from the Nautical Almanac for 15 March. How many minutes before/after meridian passage was your sight taken? • Use that time difference and the ex‑meridian tables (or formula) to find the small correction from Ho to the meridian altitude Hm. Then combine Hm with the Sun’s declination to decide whether to add or subtract the zenith distance when solving for latitude.
• Make sure you apply index error correctly: "on the arc" is subtracted from hs to get ha. • Confirm the sign and size of dip for a 56‑ft height of eye (it should reduce the apparent altitude). • Before choosing an option, ask: does the resulting latitude make sense with both the DR latitude (21°42'N) and the fact that the Sun is near the March equinox (small declination near the equator)?
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