On 30 December in DR position LAT 28° 24.0' S, LONG 32° 15.0' W, you take an ex-meridian observation of the Sun's lower limb. The chronometer time of the sight is 02h 09m 16s, and the chronometer error is 00m 00s. The sextant altitude (hs) is 84° 03.3'. The index error is 3.5' off the arc, and your height of eye is 62.0 feet. What is the latitude at meridian transit?
• Ex-meridian sight method and why it’s used when the body is close to, but not exactly on, the meridian • Altitude corrections: index error, dip, and main-altitude corrections to convert hs to Ho before any ex-meridian work • Relationship between latitude, declination, and zenith distance for latitude by (ex-)meridian altitude when latitude and declination are the same name (both South)
• How many minutes of time away from local meridian passage is this sight, and how does that small time difference relate to a small correction in altitude from an ex-meridian table? • After you find the true altitude Ho, ask yourself: if this were taken exactly at meridian transit, what simple formula would link Ho, the Sun’s declination, and your latitude in this hemisphere? • Given the date (30 December), what is the approximate declination of the Sun, and is it the same name or contrary name to your DR latitude? How does that choice affect whether you add or subtract in the latitude formula?
• Apply the index error “off the arc” with the correct sign and include dip for a 62‑ft height of eye before using any tables. • From the Nautical Almanac for 30 December, obtain both the declination and its hourly change for the Sun near the sight time; you will need the rate of change for the ex-meridian correction. • Before settling on an answer, sketch the geometry or write out the rule you are using to combine declination and zenith distance so you don’t mix up the plus/minus signs in the Southern Hemisphere.
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