Part of a high school course on astronomy, Newtonian mechanics and spaceflight
by David P. Stern
This lesson plan supplements: "Navigation," section #5a: on disk Snavigat.htm, on the web |
Goals: The student will|
Terms: Global Positioning System (GPS), sextant, chronometer
Stories and extras: A verse from "Sea Fever" by John Masefield. The existence and use of the Global Positioning System The story of finding longitude and John Harrison's chronometers. The story of Nansen and his "Fram" expedition, and how he let his chronometer run down. Also the story of Robert Wood devising a crude navigation instrument to overcome wartime secrecy and deduce their ship's position in mid-ocean
Start class by setting up the background:
Today's astronomy is "pure research," aimed at extending our understanding and exploring of the universe. But in the days of the sailing ships, it was a very practical field--even one of strategic importance.
Between 1500 and 1800, when trading monopolies on spices, tea, chinaware, silk and other precious goods were hotly contested, and the navies of Spain, Britain, France, Holland and other countries competed for mastery of the oceans--in those days, sea-captains needed astronomy for finding their way at sea.
Great Britain established and supported the Royal Observatory in Greenwich (outside London), headed by the "Astronomer Royal," while the French king created a rival institution, the Observatory of Paris. Sea officers learned to measure the positions of the Sun and of stars, and to use them in determining position in mid-ocean.
To measure latitude measuring (or deducing) the highest point in the Sun's daily motion across the sky gave the required information. We will come to that. (Note: An early instrument for such measurements, the cross staff, is described elsewhere in "Stargazers.").
To measure longitude, however, navigators needed to accurately know the time. Some used a small telescope to observe eclipses of the moons of Jupiter, whose times could be tabulated in advance, enabling them to set their clocks and thus determine their longitude. This method worked well on land, allowing geographers to accurately derive latitudes and longitudes on land and helping map the known world.
It was much harder in mid-ocean, however. The problem was finally solved by John Harrison, a British clockmakers, who constructed the first "chronometers," clocks accurate enough for the job. (They were about as accurate as modern wrist-watches, which count the vibrations of a tiny quartz crystal; but in the 1700s, such accuracy was at the cutting edge of technology.) Anyone looking for more of the story may read the book [put on blackboard] "Longitude" by Dava Sobel, or look up on the web: The Discovery of Longitude by Jonathan Medwin.
This brief survey can only give a very quick overview of methods used in navigation.
Then go over section 5a of "Stargazers." The questions below may be used in the presentation, the review afterwards or both
-- How can the help you find your latitude λ at night?
If the question arises: we can also calculate the small difference between the positions of the pole and the pole star, and take it into account
-- Suppose the date is the equinox, March 21 or September 22. How can the noontime Sun give you your latitude λ?
-- How would you measure that angle of the noonday Sun?
-- Suppose the date is the winter solstice, December 21. How can the noontime Sun give you your latitude λ?
-- What if this formula for latitude in the Northern Hemisphere gives a negative number?
-- Suppose the date is the summer solstice, June 21. How can the noontime Sun give you your latitude λ.
-- What if this formula gives an angle greater than 90 degrees?
Mention to the class that for other dates, formulas and tables exist which derive the local latitude from the height above the horizon of the noontime Sun.
-- Besides observations of the Sun, what additional information is needed to measure longitude?
-- What is a chronometer?
--How did Robert Wood, sailing across the North Atlantic in World War 1, determine his ship's latitude, even though it was kept secret?
--How did Robert Wood determine his ship's secret longitude, knowing the date was that of the Fall equinox, and having noted the time of sunset on the ship's clock? The ship was sailing east, from America to England, and its clock was presumably set (by time zones) a known number of hours ahead of the time at its port of departure.
(The teacher might fill in the details below)
Suppose that by the clock, when the Sun set at the ship, the time at the port of departure was 3:28 pm. The Earth rotates 360° in 24 hours, which comes to 360/24 = 15° per hour. Wood knew that it would only set 2:32 = 2.5333 hours later at the port of departure. During that time, the Earth would rotate
Therefore the longitude of the ship was 38° further east than the longitude of the port from which it started, which could be looked up on an atlas.
The light was channeled inside a 42-foot wooden tube, about 6 inches across, but spiders got inside and spun their webs. So Wood cleaned the tube: he opened the door at one end, shoved the family cat into it ("not without a struggle"), then quickly shut the door again. The poor cat had no choice but to run to the other end, in the process brushing away the cobwebs.)
--Who was Fridtjof Nansen?
Have a student find out about Nansen and report on it before the class.
[In addition to leading the "Fram" expedition, Nansen also crossed Greenland on skis, alone, was active in establishing the independence of Norway (from Sweden) and earned the Nobel peace prize for his work in resettling refugees from a bitter war between Greece and Turkey in the years after World War I.]
--How can a radio help in determining longitude?
-- What is the Global Positioning System (GPS)?
Has anyone used or seen a GPS receiver? What is it like? What does it show? (It can show latitude and longitude, your changing position on a small map, and much more.)
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Author and Curator: Dr. David P. Stern
Mail to Dr.Stern: stargaze("at" symbol)phy6.org .
Last updated: 28 August 2004