NCHALADA, February 11, 2006, AM Topic:
Outline and References
Chaired by John Westfall
Working definition (good to ca. 1950): Longitude is the time difference between
two places. (Local mean solar time; one of the places is a standard).
Required: A spherical (or nearly so) Earth model; Pythagoras (c. 580-500 BCE).
Thus logical to use spherical coordinates:
Latitude concept -- Eudoxus of Cnidos (c. 408-355 BCE; klimata); fairly
easy to measure; significant for length of day, climate.
Longitude concept -- Eratosthenes of Cyrene (c. 275-194 BCE).
Either Marinus of Tyre (2nd cent CE) or Ptolemy (c. 90-160 CE) first to
use specific terms (longitude = mekos, “length”; latitude =
platos, “breadth”).
Both latitude and longitude needed to define position on the Earth.
Latitude easy to find, from altitude of the Sun at noon or by altitude of
North Star.
Longitude more difficult; thus the limiting factor in finding position.
Uses of longitude:
Accurate mapping.
Keep from getting lost (e.g., LaSalle expedition).
Calculate sailing distances and times; take more direct routes.
Can relocate discoveries.
Avoid running onto the rocks (e.g., Admiral Shovel).
Fix political boundaries (Treaty of Tordesillas, Treaty of Saragosa; parts
of boundaries of 35 States of US).
Convert local time to that of a Standard Meridian (e.g., Ferro, Paris,
Greenwich).
In (approximate) chronological order:
Lunar eclipse timings.
Galilean satellite eclipse timings.
Lunar distances (from Sun and/or stars).
Celestial sights with chronometer.
Telegraphic longitudes.
Radio navigation (e.g., LORAN).
GPS/Galileo.
Lacking any of the above, fall back on dead reckoning -- the oldest method.
Some methods suitable only on land; others good on both land and sea.
1. Observe same event (lunar eclipse or Jupiter satellite eclipse) from two
different places.
2. Time event at each place in local mean apparent solar time.
3. Find difference in mean apparent solar time between the two places.
4. Multiply time difference by 15° for each hour and 1/4° for each minute to find
difference in longitude.
Oldest method that is potentially accurate.
First reference to total lunar eclipse of BCE 331 Sep 20, observed at Battle of
Arbella and at Carthage at different local times and referred to by
Hipparchus of Nicea (fl. 162-126 BCE).
Several poorly-documented observations during Middle Ages and early modern
times.
Naked-eye timings of lunar eclipse phases before invention of the telescope.
Method continues to be used, with telescopes, until well into 18th century.
How accurate? (i.e., both naked-eye and with a telescope)
Limitation: Lunar eclipses relatively infrequent.
Discovery of four Jupiter satellites by Galileo Galilei on January 7, 1610.
Satellite visibility dependent on telescope.
Galileo’s proposal:
Galileo first observes a satellite eclipse in 1612.
Possibility of using such eclipses to determine longitude.
Two observers at different locations observe same eclipse.
A single observer finds longitude using event ephemerides.
In 1616 Galileo approaches Philip II of Spain, who had offered a prize
for a means of finding longitudes at sea, is turned down.
Why the proposal was premature:
Ephemerides not available.
Thus accurate local time has to be known at two places.
No accurate timekeepers.
Characteristics of Galilean-satellite events:
Types of events: occultations by Jupiter, transits across Jupiter, shadow
transits, mutual satellite conjunctions, satellite eclipses by Jupiter.
Satellite eclipses most accurate to time, particularly those of Io due to its
rapid motion and frequency of its eclipses.
Inherent restrictions with satellite eclipse-timing method:
Timings impractical near solar conjunction or opposition.
Doesn’t work at sea because of magnification needed.
Simultaneous timings difficult over large east-west distances.
Have to wait for a suitable event.
Christian Huygens invents accurate pendulum clock in 1657 (fine on land but
doesn’t work at sea).
Ephemerides:
1614 -- Simon Marius produces tables of the Jovian satellites.
1654 -- Giovanni Battista Odierna produces more accurate tables.
Neither tables sufficiently accurate.
Lunar-eclipse timings continue to be used.
Cassini’s Tables:
Times satellite events from 1652-1667.
Produces Ephemerides Bononienses in 1668.
First use of satellite eclipse timings for longitude -- Jean Picard in 1671-72 finds
Paris-Uraniborg longitude difference (error only 1 m 34 s or 0°.39).
Jean-Baptiste Colbert, Louis XIV’s Finance Minister, an advocate for French
science, founds Académie Royale des Sciences in 1666.
Cassini recruited to direct new Royal Observatory in Paris (founded 1675). Rømer and the Speed of Light
Timing Jupiter-satellite eclipses best means of finding longitudes at the time:
The three prerequisites-- telescopes, pendulum clocks, and ephemerides of
the events -- in place by1670s.
Best if two observers at different places time same event.
Otherwise observer obtains Paris time of event from Cassini’s tables,
corrected by timing an earlier or later eclipse.
G.D. Cassini coordinates the surveying of France in the 1670s:
Uses triangulation and satellite-eclipse timing to remap country’s
shape in 1679.
Moves France’s west coast eastward an entire degree.
Louis XIV complains that he had lost more territory to his
astronomers than to his enemies.
French Academy of Sciences sends expedition to island of Gorée in West Indies
in 1681, first intercontinental longitude determination using satellite-eclipse timings.
During 1680s-1740s numerous expeditions make satellite-eclipse timings
throughout Europe and in Asia, Africa and the Americas.
International cooperation among Britain, Holland, Spain, Portugal, Austria,
Russia and the German and Italian States.
Britain definitely second to France in making longitude determinations.
Cassini plots and updates first accurate world map in Paris Observatory.
Previous maps made obsolete as positions of features are corrected.
Lunar-eclipse timings still used but become less frequent than satellite eclipses.
Accuracy assessment:
Median error using Jupiter-satellite eclipses about 1/6 degree.
Median error using lunar eclipses about 1/4 degree.
Charles Mason and Jeremiah Dixon survey Pennsylvania-Maryland boundary in
1763-67.
James Cook and Charles Green find Tahiti’s longitude within two miles in 1769.
Alexander Mackenzie crosses North America to the Arctic Ocean in 1789 and to
the Pacific in 1793.
Zebulon Pike’s American Southwest expedition in 1806-07.
Benjamin Bonneville’s western expedition of 1832.
Timings of Ganymede and Callisto in Admiralty Instructions for Captain Robert
FitzRoy’s Beagle Voyage of 1839, carrying the young Charles Darwin.
John Charles Fremont in his second western expedition in 1846; satellite eclipses
then a standard method of the U.S. Corps of Topographical Engineers.
Jupiter-satellite eclipse timings never practical at sea.
Lunar distances become practical with sextant, accurate lunar tables and star
positions in the 2nd half of 18th century.
At about the same time, chronometers become practical and become dominant at
sea in 19th century (accuracy of 1 nautical mile becomes feasible).
Jupiter-satellite timings continue in limited use until mid-19th century:
“Lunars” difficult to observe and reduce.
Chronometers impractical to transport overland.
Both lunars and star sights require artificial horizon when used on land.
Satellite method finally discontinued on land with availability of telegraphic time
services (let alone radio time signals and GPS).
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