(5) Latitude and Longitude
Part of a high school course on astronomy, Newtonian mechanics and spaceflight
by David P. Stern
This lesson plan supplements: "Latitude and Longitude," section #5: on disk Slatlong.htm, on the web |
Goals: The student will|
Terms: Latitude, longitude, Line of latitude, line of longitude (or meridian), co-latitude, equator, zero meridian ("prime meridian"), eastern and western hemispheres, (local) noon meridian, local time (LT), time zones, international date line, universal time (UT; of "Greenwich Mean Time" GMT), declination, right ascension, "First point in Aries" (or "vernal equinox") on the celestial sphere.
By this stage the student should also know and be able to write at least a few lower-case letters of the Greek alphabet--λ, θ, φ, δ and α, (lambda, theta, phi, delta, alpha), corresponding to (L,T,F,D,A)
Stories and extras: Origin of the word "meridian" and the abbreviations "a.m." and "p.m.". The Royal Observatory in Greenwich. Introduction of time zones.
The teacher may start the class with a map of the US in view, or on a transparency. Ask: what is special about the border between the US and Canada? ("About half of it is a straight line")
Of course, no line on the surface of the Earth is straight. What looks straight on the map follows a line of latitude, a line at a constant distance from the pole. In this case, it is the line of latitude 49 degrees. Any other boundaries that follow lines of latitude?
There are many. The best known ones are probably on the borders of Pennsylvania. The northern border follows the line of latitude 42° which also forms the southern borders of Idaho and Oregon (but not the northern borders of Connecticut and Rhode island--these are parallel, but a short distance further north). But the southern border of Pennsylvania is more famous: it follows latitude 390 43' (39 degrees, 43 minutes--60 "minutes of arc" in each degree). That is the Mason-Dixon line, which before 1860 formed the boundary between the "slave states" (a part of the US still called "Dixie") and the "free states."
One reason many boundaries follow lines of longitude--and the ones perpendicular to them, like boundaries of Utah and Colorado, lines of latitude--is that such boundaries are easy to define. Let us now look at these lines more closely.
Guiding questions and additional tidbits
The questions below may be used in the presentation, the review afterwards or both, and suggested answers are provided. Brackets [ ] enclose comments by the teacher or optional material.
This lesson is rather long, and it might be best to divide it in two parts--half of section 5 of "Stargazers", up to the heading "Local Time," then the other half.
-- What are latitude and longitude used for?
-- Latitude and longitude are angles. What units are used to measure angles?
A right angle contains 90 degrees, written 90°.
-- What is the latitude at the equator, North Pole and South Pole?
The North Pole is at +90 degrees or 90 degrees north.
The South Pole is at –90 degrees or 90 degrees south
--The unit of distance "meter" was originally defined as one part in 10,000,000 of the distance between the pole and the equator. If that distance corresponds to 90°, to what distance does one degree correcpond?
--At what latitude are we halfway between the equator and the pole?
-- How do we define the latitude of a point P on the surface of Earth?
[Illustrate with a drawing on the board and make sure students copy it.]
-- An explorer walked one mile south, one mile east, one mile north, and came back to the original point. Where did this happen?
The next may be a take-home riddle
-- An explorer walked one mile south, one mile east, one mile north, and came back to the original point--and it was not at the north pole. Where did this happen?
[Any other such points? Yes, many. For instance, about 1 1/12 miles from the south pole--same as before, but the explorer makes two circuits around the pole.]
-- Define the longitude of a point P.
The line along which that plane meets the surface of the Earth, on the side of the point P, is called the meridian of P, or its "line of longitude. " Divide the circle of the equator into 360 degrees, with zero at the point where the "Prime Meridian" of Greenwich, England (at the eastern edge of London) crosses it.
The longitude of any point P is the angle at which its meridian cuts the equator. It is measured from 0° to 180° east of Greenwich, or from 0° to 180° west of it (sometimes marked 0° to –180°).
-- The Americas (north and south) are often called "the Western Hemisphere. " Why?
-- Can we specify a point on Mars by its latitude and longitude?
Go over the rest of Section 5, concerned with time measurements.
--How would you define local time on a strict, astronomical basis?
[More accurately, local time does so on the average. It ignores a shift of a few minutes due to the fact the Earth's orbital speed and distance from the Sun vary slightly along its orbit. Because of that variation, the length of time from noon to noon is usually very slightly different from 24 hours.]
-- Is local time the same at all points on a meridian?
-- What are time zones?
Local time inside the strip may then differ by up to half an hour from the "precise" local time.
-- When the time is noon in New York City, it is 9 a.m. in San Francisco and 5 p.m. in London, England. Assuming all these cities are at the same latitude, how would you say the distances from New York--San Francisco and New York--London compare? If London is at longitude zero, what are the approximate longitudes of New York and San Francisco?
-- What is Daylight Savings Time?
-- What is the International Date Line and why is it important?
The International Date Line is a special time zone boundary, most of it following the line of longitude 180°. The line makes sure that in crossing time zones we always match the correct date at each location. Anyone crossing that line gains a day (crossing westward) or loses one day (crossing eastward.
-- Japanese war planes bombed Pear Harbor on Hawaii on December 7, 1941, and in doing so, pushed the US into war against Japan.
Japanese war planes bombed US bases in the Phillipine Islands on December 8. Why did they wait an extra day?
-- What is universal time (UT), and what is it used for?
-- What are declination and right ascension?
Declination- δ (delta--small Greek d) is like latitude, measured in degrees, but from the North Pole, not from the equator, so that the north pole of the heavens has declination 0°, the equator has 90° and the south pole has 180°.
Right Ascension- α (alpha-- small Greek a, or RA) is like longitude, and "meridian lines" of constant RA connect the north and south poles of the sky and are everywhere perpendicular to lines of constant declination.
RA and longitude differ in two ways. First, while the zero meridian on Earth is the one passing Greenwich, England, the celestial meridian on which α = 0 is the one passing one of the two points where the ecliptic crosses the celestial equator, in this case, the "first point in Aries" or "vernal equinox." And second, for historical reasons, RA is measured not in degrees but in hours, each hour equal to 15 degrees (that is, 24 hours = 360 degrees). Hours are subdivided into minutes and seconds, but these are not the same as minutes and seconds into which degrees are divided.
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Author and Curator: Dr. David P. Stern
Mail to Dr.Stern: stargaze("at" symbol)phy6.org .
Last updated: 29 August 2004