On 16 June in DR position LAT 50°57.0'S,...

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Question 1 of 2066636eea28f7522a1c51ab1c

On 16 June in DR position LAT 50°57.0'S, LONG 53°03.9'W (ZD+4), you take an ex-meridian observation of Acrux at lower transit. The chronometer time of the sight is 10h 08m 18s, and the chronometer error is 02m 12s fast. The sextant altitude (hs) is 23°49.0'. The index error is 1.1' off the arc, and your height of eye is 26 feet. What is the latitude at meridian transit?

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Question 1 of 20

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🔍 Key Concepts

• Ex-meridian sight for latitude: how it relates to a true meridian altitude and when the body is near transit but not exactly on the meridian • How to correctly reduce sextant altitude: applying index error, dip (height of eye), and refraction/SD to get observed altitude (Ho) • Using star’s declination and its meridian altitude (corrected for not being exactly on the meridian) to find latitude: ( Lat = Dec \pm (90^\circ - H_m) ) for a body south of you in the same hemisphere

💭 Think About

• First, think through each correction step from hs to Ho. What sign do you apply for an index error "off the arc" and for dip with a 26 ft height of eye? • Consider the geometry at lower transit in the Southern Hemisphere: is Acrux (a southern star) to the north or south of your zenith, and how does that affect the sign in the latitude formula? • For an ex-meridian star sight, how does being a few minutes of time away from exact transit change the altitude you would have at true meridian passage—does it need a small increase or decrease?

✅ Before You Answer

• Confirm the corrected altitude (Ho) is reasonable for a star near meridian transit at that latitude (not too low, not too high). • Check the sign of declination for Acrux and whether you should add or subtract ( (90^\circ - H_m) ) when solving for latitude in the same hemisphere. • Verify that your ex-meridian correction is in the correct direction and of the correct order of magnitude (a small change in minutes of arc, not degrees) before selecting among the options.

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