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Re: Lost at Sea with a sextant puzzle
From: Roger W. Sinnott
Date: 2019 Jun 24, 23:51 +0000
From: Roger W. Sinnott
Date: 2019 Jun 24, 23:51 +0000
Greg mentioned that Polaris's sextant altitude gives your latitude to within ±40'. That uncertainty can shrink to ±10' or better as follows.
A line from Polaris to Kochab (the only other Little Dipper star as bright) goes almost exactly through the north celestial pole (NCP). During 2018 thru 2020 Polaris is indeed 39' or 40' from the NCP. Call it 40'. Now, think of Kochab as the hour hand of a clock, with Polaris at the clock center.
If Kochab is at 12 o'clock, Polaris is 40' BELOW the NCP, so add 40' to its sextant altitude.
Alas, the poor chap in the lifeboat can't wait around for Kochab to reach one of these ideal orientations. He/she must observe between civil and nautical twilight when the two stars AND sea horizon are visible. A simple sketch on that piece of paper will show the correction needed to obtain the latitude from Polaris.
If Kochab is at . . .
12 o'clock, add 40'
1 or 11 o'clock, add 35'
2 or 10 o'clock, add 20'
3 or 9 o'clock, add 0'
4 or 8 o'clock, subtract 20'
5 or 7 o'clock, subtract 35'
6 o'clock, subtract 40'
For improved accuracy, estimate Kochab's angle to a fraction of an hour o'clock and interpolate.
Roger
A line from Polaris to Kochab (the only other Little Dipper star as bright) goes almost exactly through the north celestial pole (NCP). During 2018 thru 2020 Polaris is indeed 39' or 40' from the NCP. Call it 40'. Now, think of Kochab as the hour hand of a clock, with Polaris at the clock center.
If Kochab is at 12 o'clock, Polaris is 40' BELOW the NCP, so add 40' to its sextant altitude.
If Kochab is at 6 o'clock, Polaris is 40' ABOVE the NCP, so subtract 40' from its sextant altitude.
Alas, the poor chap in the lifeboat can't wait around for Kochab to reach one of these ideal orientations. He/she must observe between civil and nautical twilight when the two stars AND sea horizon are visible. A simple sketch on that piece of paper will show the correction needed to obtain the latitude from Polaris.
If Kochab is at . . .
12 o'clock, add 40'
1 or 11 o'clock, add 35'
2 or 10 o'clock, add 20'
3 or 9 o'clock, add 0'
4 or 8 o'clock, subtract 20'
5 or 7 o'clock, subtract 35'
6 o'clock, subtract 40'
For improved accuracy, estimate Kochab's angle to a fraction of an hour o'clock and interpolate.
Roger
