November 26, 2014

Determine Your Longitude: the Lunar Eclipse Method Part I

Eclipse.

A Ruddy Lunar Eclipse. (All photos by Author).

We’re back now with a new look! Hopefully, it’s less of an eyestrain for our loyal legion of readers… and just in time for this months’ Lunar Eclipse!

Getting an accurate fix on your position has long been a bane of the world traveler. Long before Global Positioning Systems, a way was sought for navigators to calculate their location using the stars. Latitude was easy enough; in the Northern Hemisphere, you simply have to measure the angle of Polaris, also known as the North Star, above the horizon. Polaris is over head at the Earth’s rotational pole, and on the horizon at the equator. This gives you your local latitude accurate to about a degree. But what about longitude? A much more complicated set of observations and calculations now come into play. To calculate your local position, one needs to know the local time, along with a specific event that will occur at a predicted time. For ages, keeping accurate time was the real kicker. The modern world is divided up into 24 time zones, but in earlier times, time was determined locally by each hamlet or village. As for celestial events, circumstances such as conjunctions, eclipses, and transits of the moons of Jupiter were proposed. Planetary conjunctions closer than one degree are fairly rare; also, it would be difficult to judge closest approach by more than 6 hours or so. Phenomena of Jupiter’s moons would also be difficult; first, a telescope would be required and it would be extremely difficult to sight from to pitching deck of a ship!
That leaves eclipses. As any Eclipse chaser can attest, total solar eclipses are extremely rare from any given location. A spot on Earth may go centuries before totality graces the skies. In theory, a partial would be much more common. And of course, this would require something such as smoked glass to observe first contact.
That leaves us with lunar eclipses. Any given eclipse can easily span more than one full hemisphere of the Earth. Also, while contact with the diffuse outer cone of Earth’s shadow, or penumbra, is rather subtle, contact with the inner core, or umbra, is not. Such an event can be defined by eye to a span of time of about five minutes.
Up until the time of the invention of the telescope, eclipse timing was the only semi reliable way to judge longitude. The idea is simple; observe the local time of first contact with the umbra, then compare it with the known time from a separate fixed location. The Earth rotates 15 degrees per hour, (360/24=15) or 1 degree every 4 minutes. If umbral contact was said to begin at 2:05AM at a given location and you observed it to begin at 1:05AM, you are 15 degrees west of the first location.
The Greeks first noted this during an eclipse on September 20th, 331BC. Alexander the Great in Mesopotamia recorded the eclipse as beginning two hours after sunset, while on the north shores of Africa, the city of Carthage it was seen to start at sunset. Ptolemy correctly deduced that Alexander’s position was 30 degrees or 2 hours east of Carthage.
None other than Christopher Columbus was a student of the works of Ptolmey. He attempted to use this method to judge his position on his second and third voyage to the new world. The eclipses concerned were on September 14th, 1494 (part of saros cycle #119) and February 29, 1504 (saros cycle #109).
Incidentally, saros is the period of eclipse cycles approximately 18 years 11 days and 8 hours long. At this point, the Earth, sun, and moon return to the same relative geometry and a similar eclipse occurs with an 120 degree displacement along the Earth’s surface.
Historians differ on how Columbus kept time; some claim he used a device known as a Nocturlabe, others state he simply used an hourglass to measure the time that had lapsed after sunset. A Nocturlabe is a rather unwieldy device which measures the angle of the star Kochab during upper and lower culmination. This is the point of transiting the meridian; any star that is circumpolar from your location does this twice a day.

The concept is simple; if say, lower culmination occurs at your locale at 5:15PM on a certain date, and the angle of Kochab is seen to be 15 degrees past this point, the local time is approximately 6:15PM. Some Nocturlabes were quite ornate in design.

I personally favor the sunset method; Its simpler to utilize, especially from the tropics that Columbus generally preferred. Perhaps he used both!
So, how did Chris do? Unfortunately, not very well. He favored a smaller model of the Earth than reality presented him; remember, he stubbornly thought he had landed in the Far East until the day he died. Consequently, his calculations were of by several hundred miles. Otherwise, he would have got it right.
So, what’s the moral of the story? I’d say that don’t let your wishes conflict with reality. The good news is, this is a calculation that anyone can easily duplicate! And to top it off, North American Observers can observe a total lunar eclipse in its entirety on the night of February 20th, 2008. Part of saros cycle 133, this eclipse promises 50 minutes of totality starting at 10:01PM Eastern Time. An excellent page with all the specifics can be seen at;

http://sunearth.gsfc.nasa.gov/eclipse/LEmono/TLE2008Feb21/TLE2008Feb21.html

As seen below, the moon will pass through both the Earths’ Umbra and Penumbra;

The Moon’s passage through the Earth’s shadow.

(Credit: NASA/GSFC/Fred Espenak).

Penumbral ingress is very diffuse; at most only subtle yellowish shading may be observed. Umbral entry is more distinct and can be judged usually with in five minutes or so. I intend to duplicate the Columbus observation using simple tools, and encourage others to do the same. My “nocturlabe” will be a transparent protractor with a plumb line weight;

Homemade “Nocturlabe”.

My “hourglass” will be something somewhat more modern; my wristwatch or ipod timer. I intend to judge the time of first umbral contact, totality and then the reverse egress for a total of four measurements. My almanac to judge Kocab culminations will be the yearly Sky Gazers’ Almanac published by Sky & Telescope. Kochab transits approximately twelve hours opposite of Polaris. Just remember that upper culmination for Polaris is close to lower for Kocab and vice versa. Incidentally, the “offset” of time for this transit is -19 minutes; subtract this from any reading made. I suggest using the homemade nostrolabe first on screen with a planetarium program (preferably free!) such as Stellarium or HN Sky, and then test it out of doors to see how accurate it is. As always, some guesswork is involved as to the precise reading; just imagine doing it from the deck of a rolling ship! Take at least three readings and compute an average for better results.
As for sunset timings, do not forget that we’re talking local timings! You may think you can cheat simply by looking at your watch, but remember, the sun rises and sets locally at different times across your time zone. Elevation can also play a factor. Ideally, a flat, sea level western horizon (think Pacific) would work best. I intend to head to the eastern shore of St. Froid Lake and deal with the 200 meters of elevation. Good point forecasts for your local sunrise/sunset times can be found at the respective websites for Heavens Above, Sky & Telescope, and ye ole Farmer’s Almanac. The times we are calculating against are Greenwich Mean Time, also known as Universal to scientists or Zulu to the military. This is the time at zero longitude. They are as follows;

Partial Eclipse begins: 01:43 AM
Total Eclipse begins: 03:01 AM
Total Eclipse ends: 03:51 AM
Partial Eclipse ends: 05:09 AM

Granted, GMT only came into vogue as a standard convention in the late 19th century; its most likely that Columbus used a known position published in an almanac by one of the major observatories of the day.
Finally, don’t forget to consider our friend, the equation of time! This is the amount of time in minutes that the sun is running “fast” or “slow”. It’s caused by a combination of the eccentricity of the Earths’ orbit and its obliquity to the ecliptic. Who knew time was so complicated! It also causes the mysterious figure eights we all noticed on the globe in elementary school. Set up a year long time exposure, and you get what’s called an analemma.

Note that the sun runs about 15 minutes “slow” through mid February; this will have to be corrected for as well.

In closing, don’t forget to note the color and brightness of the moon during totality. This can range from a bright orange to a very dark copper, and is another scientific bit of data that any one can contribute. This is rated on the Danjon scale, which is as follows;

L=0 Very dark eclipse. Moon almost invisible
L=1 Dark, grayish or brownish eclipse. Details distinguishable only with difficulty
L-2 Deep red or rust colored eclipse. Very dark central shadow, while outer edge of umbra is relatively bright.
L=3 Brick red eclipse. Umbral shadow usually has a bright or yellow rim.
L=4 Very bright copper-red or orange eclipse. Umbral shadow has a bluish, very bright rim.

A painters strip or wheel can help judge the exact shades of red. This can be a fairly subjective measurement; several observers quietly jotting down their impressions during totality may yeild a more objective result.

In the (very probable) event of cloudy skies, I will conduct observations via the web. A quick search yields no links as of yet, but generally someone is broadcasting the eclipse live. And as always, I’ll be shooting video and pics through-out.

Next week: stay tuned for the results! Also; Columbus didn’t just use eclipses to gauge longitude; the curious account of the Eclipse of 1504.

Last August’s Eclipse (photo by author).

Trackbacks

  1. [...] of the Moon in the sky from one location versus a known longitude during an event— such as first contact of the Moon with the Earth’s umbra during an eclipse —you can gauge your relative longitude east or west [...]

  2. [...] occasion to get him and his crew out of a jam, and also attempted to use a lunar eclipse to gauge his position at sea using a method first described by Ptolemy while studying the lunar eclipse of September 20th, 331 [...]

  3. [...] This is known as totality, and it’s also the time that’ll you’ll see a hallmark of a total lunar eclipse. Does the eclipsed Moon appear reddish to you? What you’re seeing is the sunlight of a thousand sunsets worldwide, streaming through the Earth’s atmosphere into the shadow. This color can vary considerably from eclipse to eclipse, causing it to appear anywhere from a dark tea-stained color to a bright cherry red. This variation is due to the amount of dust currently in the Earth’s atmosphere, and is measured on what is known as the Danjon scale. [...]

  4. [...] Thanks to Dave Dickinson, the lunar phenomenon is broken down into laymen’s terms, in shades of red. “Does the eclipsed Moon appear reddish to you? What you’re seeing is the sunlight of a thousand sunsets worldwide, streaming through the Earth’s atmosphere into the shadow. This color can vary considerably from eclipse to eclipse, causing it to appear anywhere from a dark tea-stained color to a bright cherry red. This variation is due to the amount of dust currently in the Earth’s atmosphere, and is measured on what is known as the Danjon scale.” [...]

  5. [...] This is famous as totality, and it’s also a time that’ll you’ll see a hallmark of a sum lunar eclipse. Does a eclipsed Moon seem reddish to you? What you’re saying is a object of a thousand sunsets worldwide, streaming by a Earth’s atmosphere into a shadow. This tone can change extremely from obscure to eclipse, causing it to seem anywhere from a dim tea-stained tone to a splendid cherry red. This movement is due to a volume of dirt now in a Earth’s atmosphere, and is totalled on what is famous as a Danjon scale. [...]

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