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Time sight practice: Joshua Slocum's lunar
From: Frank Reed
Date: 2011 Mar 22, 15:54 -0700

Here's an exercise in latitude by noon Sun and longitude by time sight using a famous mariner for a model. The goal here, if you decide to play, is to work up the latitude and longitude the way it would have been done in that era. Of course, I can't force you to play by the rules, so no doubt there will be other solutions. The more the merrier! The items marked by asterisks (*) below are the key data points that you'll need to get the job done. The rest is more or less background and explanation.

It is the afternoon of June 17, 1896, and you are Joshua Slocum. Congratulations! You are sailing alone around the world aboard the sloop Spray. You have been 43 days from land, having left Isla Juan Fernandez (known today in 2011 as Isla Robinson Crusoe) on May 6. To set the scene, it's a beautiful sunny day in the tropics, and you believe you're approaching the Marquesas, if everything is going well. You're keeping an eye out for the southernmost island of the Marquesas, which you think is Nuka Hiva (and that's how you'll name it in your book in a few years) but it's really Fatu Hiva. You're sailing due west at 4 knots. Since it's the middle of June, the Sun is near the solstice. It's about as far north of the equator as it can get.

* The estimated latitude of the Spray is 11d 00' S. The estimated (dead reckoning) longitude is 138d 35' W. These are the coordinates near local noon on June 17, 1896 (by the normal "civil" reckoning of days).

* At local noon, you measure the maximum altitude of the Sun (to the north of you!) to be 55d 19'. That's the reading right off the instrument. Your index correction is -2.0'. What was your latitude at that time based on this observation? (note: if it's noon in this longitude, the approximate time in Greenwich is 2100 --you'll need that to interpolate the Sun's declination).

As the afternoon continues, you note the Sun and Moon are nicely placed on opposite side of the sky. The Moon and the Sun are separated by some 83 degrees with the Moon, nearly half full, about 43 degrees high in the east and the Sun about 39 degrees high in the northwest. The Moon "being in distance with the Sun", you will determine Greenwich Mean Time using the Moon as a chronometer in the sky. You will also at nearly the same time measure the Sun's altitude to determine the local time and by comparing local with GMT, you'll get your longitude. We'll talk about the "lunar observation" for GMT another day. But for now, let's do the "time sight" for local time. Your tin clock, which you've been resetting every day to show local time, tells you that it's about 2:45 in the afternoon.

* From working up the lunar, you now know Greenwich Time: it is 23:50:48 (on June 17).

Just knowing that you took these sights around two hours and forty-five minutes after your Noon Sun sight, you can already make a rough check on the longitude. It's nearly midnight or 2400 in Greenwich while it's 1445 here in the Pacific. That's a nine and a quarter hour difference. At 15 degrees per hour, that would put you close to 139 degrees west of Greenwich. So far so good. That's at least consistent.

* Your observed altitude for the Sun is 38d 39', and since it was almost simultaneous with the lunar observation, the GMT for this sight is as above, 23:50:48. The IC, again, is -2.0'. So what is the local apparent time from that altitude? And what is the local mean time? And finally what is your longitude? Some hints below.

You'll be happy to know that the real Joshua Slocum sighted the peaks of Fatu Hiva on the northern horizon just a short while later confirming both his dead reckoning and his longitude calculations and making him very happy. But after that he apparently never again bothered with lunars in his solo-circumnavigation and sailed by good old-fashioned dead reckoning for longitude the rest of the way around the world.

HINTS:
For the noon sight, your zenith distance should be 34d 31' S.
For the afternoon time sight, the "half sum" should be 81d 40'.
For the afternoon time sight, the four logarithms should be:
9.83259
10.03735
10.00820
9.16095
And the resulting LAT (Local Apparent Time) should have 34 minutes it. That is, ??:34:??.
Don't forget to add 12 hours to the time since it's in the afternoon.
Your final longitude should be within five ot ten miles of your estimated DR longitude for 2:45pm.

I'm posting this for some of the students from this past weekend's "Celestial Navigation: 19th Century Methods" class, but I figured there might be some other folks on NavList who would like to give it a try. You can get the required declinations and equation of time from various tables, including the famous tables published by ReedNavigation.com. There are also some online sources :).

-FER

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