On 15 October an ex-meridian altitude of the Sun's lower limb at upper transit was observed at 1146 ZT. Your DR position is LAT 22°42.0'N, LONG 139°52.0'E, and your sextant altitude (hs) is 58°30.4'. The index error is 3.4' on the arc, and your height of eye is 56.7 feet. The chronometer time of the observation is 02h 45m 06s, and the chronometer error is 01m 06s slow. Find the latitude at meridian transit from the ex-meridian observation.
• Meridian altitude and relationship between observed altitude and latitude when the Sun is on or near your meridian • How to correct sextant altitude: index error, dip, and main altitude corrections from Nautical Almanac • Ex-meridian correction: how to adjust for a sight taken a few minutes before/after meridian passage using LHA and Sun’s declination
• First, reduce the sextant altitude (hs) to get the observed altitude (Ho). Make sure you apply the index error with the correct sign and convert height of eye to dip in minutes of arc. • Next, determine the Sun’s declination and the meridian passage time for your longitude and date, then figure out how many minutes in time before/after meridian transit your sight was taken. • Use the ex-meridian formulas or tables to find the altitude correction due to being off the meridian. Then think about whether this correction will increase or decrease your derived latitude based on whether the sight was taken before or after transit and whether the Sun is north or south of your zenith.
• Confirm that the index error ‘on the arc’ is applied with the correct sign (does it make hs larger or smaller?). • Double-check your dip correction using height of eye in feet and convert properly to minutes, then apply the Nautical Almanac main altitude corrections for the Sun’s lower limb. • Verify whether the Sun’s declination is north or south on 15 October and compare it with your DR latitude to decide if you add or subtract the corrected meridian altitude from 90° to obtain latitude.
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