On 2 January your 1759 zone time DR...

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Question 1 of 2066636eea28f7522a1c51ac2b

On 2 January your 1759 zone time DR longitude is 45°17.6' W. At that time you observe Polaris with a sextant altitude (hs) of 24°16.5'. The chronometer time of the sight is 08h 57m 10s, and the chronometer error is 02m 16s slow. The index error is 3.5' on the arc, and the height of eye is 42.5 feet. What is your latitude by Polaris?

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🔍 Key Concepts

• Polaris latitude formula (using observed altitude of Polaris and applying corrections) • Altitude corrections: index error, height of eye (dip), and refraction (use standard Nautical Almanac Polaris tables conceptually) • Distinction between zone time and chronometer time (and how time affects GHA/longitude vs. Polaris latitude)

💭 Think About

• First, carefully reduce the sextant altitude (hs) to an observed altitude (Ho): how do you apply index error and dip, and in what sign? • Think about what extra small corrections are applied specifically for Polaris to convert its altitude to latitude (for example, how close Polaris is to the celestial pole and how that varies with LHA Aries). • Ask yourself: does the exact time of the sight significantly change the basic Polaris-latitude relation, or is it mainly used to look up small corrections in the Polaris tables?

✅ Before You Answer

• Be sure you apply index error in the correct direction ("on the arc" vs. "off the arc"). • Confirm you are using height of eye to compute dip with the right sign (dip always lowers the apparent horizon). • After you get your final latitude, check whether it is reasonable compared to the raw Polaris altitude: Polaris altitude in the Northern Hemisphere should be close to your latitude.

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