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    Re: Finding your Position via Lunar Eclipses
    From: Frank Reed
    Date: 2015 Aug 26, 13:39 -0700

    Ed Popko, you wrote:
    "Many countries justified the expense of their expeditions as potential contributions to navigation at sea."

    Ha. Yeah, an early example of scientists lying to governments as a means to funding! The Sun's parallax was sufficiently well known for any navigational purpose before the transits of Venus in the late 18th century. Luckily, European governments were also eager for excuses to practice enlightened imperialism.

    And:
    "Some astronomers, such Swede Anders Planman in Kajana (eastern Finland) and Frenchman Chappe d'Auteroche in Tobolsk (Siberia, Russia) planned to calibrate their clocks and determine the longitude of their observing sites by observing a lunar eclipse that preceded the transit."

    Is it possible that they were talking about eclipses of Jupiter's moons? A common lunar eclipse is a low-accuracy method for determining longitude. But maybe they just threw it into the pot to sweeten the deal. An enlightenment-era monarch (and staff) probably understood lunar eclipses even if they couldn't follow the rest.

    You wondered:
    "how can a lunar eclipse be used to determine longitude? Eclipses tend to slow and gradually evolving events"

    First, you get the local time by any of various methods. For example, you can observe the Sun's altitude in the late afternoon for an accurate determination of local apparent time. Then set a common watch to that time. Similarly, you can observe altitudes of stars towards the east and west and get local time. One could also observe the zenith continually during the eclipse (see below). Next, for absolute time, you watch specific events during the eclipse:

    • First Contact: when the Moon just begins to enter the Earth's umbra and has a small, distinct "bite" taken out of it.
    • Second Contact: when the Moon fully enters the umbra, and the last bright area disappears. After this the Moon is fully eclipsed.
    • Third Contact: when the Moon begins to leave the umbra, and a small bright area appears. This marks the end of the total eclipse.
    • Fourth Contact: the Moon leves the umbra, and the last dark "bite" disappears.

    Before first contact and after fourth, there is a dull shading on one side of the Moon. This penumbral shadow grows/fades gradually, and it is almost un-noticeable. The contact events listed above can be timed, without much trouble, to within about 3-5 minutes of time. By averaging them, we can get the time of the middle of the lunar eclipse within perhaps two minutes of time if we're lucky. Note that this is an absolute event. It occurs "on" the Moon. There's nothing about it that depends on our location on the Earth. If two observers widely separated on the globe could observe a lunar eclipse, even in the era before accurate lunar tables were available, and record their local time at the instant of mid-eclipse, the difference between those local times is the same as the longitude difference (converted to degrees as the usual rate of 15° per hour). Since the times of mid-eclipse can only be observed with an accuracy of a couple of minutes, the longitude differences that result are accurate to about half a degree.

    In historical examples that I have seen where observers actually attempted to determine longitude by lunar phenomena (distances, eclipses, meridian culminations, whatever), I have noticed two common errors in procedure. First, early observers frequently did not understand that the best way to get local time was by altitudes in the east and west. Instead they sometimes measured near meridian altitudes for local time introducing very large errors. Second, when processing the observations, early observers often trusted low-accuracy tables of the era as a source for the eclipse times instead of recognizing that simultaneous observations of eclipses in different longitudes eliminated the need for a theoretical model of the Moon's motion. They just didn't get it...

    Here's a modern "social media" experiment or teaching demo that could be arranged around a predicted lunar eclipse. Convince students at various points around the globe (in the hemisspere scheduled to see a lunar eclipse) to set up a zenith-observing instrument. This can be as simple as a tube strapped to a telephone pole. If the tube has been leveled with a little care, it can be pointed within a fraction of a degree of the local vertical. Then give students a star chart and have them observe the zenith with their zenith tube at each contact event during a lunar eclipse. Plot those points on the star chart. After the eclipse is over, find the mid-point of the four events. That gives the observed zenith from each location at the same absolute time. When all of these mid-eclipse zenith points are collected and plotted on one star chart, they will trace out very nicely a geographic map of the observers' locations on the ground projected out onto the sky. Observers separated by 20° of latitude and 45° of longitude will find that their zenith points plotted on the star chart are separated by 20° of declination and 3 hours of right ascension (or 45° of Sidereal Hour Angle). It's a simple demonstration of mapping the Earth with astronomical position-finding that could have been performed even thousands of years ago.

    By the way, Bob Crawley mentioned longitude by lunar occultations of stars. This is actually quite different and much more complicated. It's much closer to a lunar distance observation than a longitude by lunar eclipse. If you're interested in reading Bowditch on this, here's a link to the index of old Bowditch editions on the NavList web site: http://fer3.com/arc/navbooks2.html.

    Frank Reed
    Conanicut Island USA

       
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