GEOGRAPHIC INFORMATION SYSTEMS Lecture 07: Earth-Sun Relationships

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1 GEOGRAPHIC INFORMATION SYSTEMS Lecture 07: Earth-Sun Relationships Earth-Sun Relationships - there are two components to the Earth s motion - the Earth rotates on its polar axis - counterclockwise when viewed from above the North Pole - the motion is west to east - takes one day to complete a rotation - the Earth revolves around the Sun on the Plane of the Ecliptic - counterclockwise when viewed from above the North Pole - takes one year to orbit the Sun - the orbit is elliptical - Perihelion: the Earth is closest to the Sun on January 3rd (147.3 million km) - Aphelion: the Earth is farthest from the Sun on July 4th (152.1 million km) - differences in the distance to the Sun have no significant influence on the seasons Latitude and the Seasons - seasons are caused by the tilt of the Earth s polar axis - polar axis is tilted 23.5 o relative to a line that is perpendicular to the Plane of the Ecliptic - this tilt of the polar axis causes variations in: 1) the angle of incoming solar radiation (controls the intensity of surface radiation per unit area) 2) variations in daylength (seasonal changes in the Circle of Illumination) - in summer (warmer months), the angle of incoming solar radiation is higher and daylength in longer - in winter (cooler months), the angle of incoming solar radiation is lower and daylength is shorter - the declination of the sun (latitude of the subsolar point or direct sun) varies between the tropics (see the analemma) - June Solstice (June 21 or 22) - latitude of the subsolar point (declination of the sun) is the Tropic of Cancer (23.5 o N) - Circle of Illumination extends from Arctic Circle to the Antarctic Circle - daylength in the northern hemisphere is more than 12 hours - daylength north of the Arctic Circle (66.5 o N) is 24 hours - daylength in the southern hemisphere is less than 12 hours - daylength south of the Antarctic Circle (66.5 o S) is 0 hours - December Solstice (December 21 or 22) - latitude of the subsolar point (declination of the sun) is the Tropic of Capricorn (23.5 o S) - Circle of Illumination extends from Arctic Circle to the Antarctic Circle - daylength in the northern hemisphere is less than 12 hours - daylength north of the Arctic Circle (66.5 o N) is 0 hours - daylength in the southern hemisphere is more than 12 hours - daylength south of the Antarctic Circle (66.5 o S) is 24 hours - March Equinox (March 20 or 21) and September Equinox (September 22 or 23) - latitude of the subsolar point (declination of the sun) is the Equator (0 o ) - Circle of Illumination extends from pole to pole - daylength is 12 hours at every latitude * note that the daylength on the Equator is 12 hours every day of the year - also, at the north and south poles, the sun is up continuously for 6 months - the animation used in lecture can be found at: Copyright Kevin Mulligan, Texas Tech University

2 Apparent Movement of the Sun - the sun angle varies throughout the day and throughout the year - between the March and the September Equinox (for places north of the Tropic of Cancer) - the sun will rise north of due east and set north of due west - the sun will reach its highest point in the sky at solar noon (due south of observer) - the daylength will be more than 12 hours - between the September and the March Equinox (for places north of Tropic of Cancer) - sun will rise south of due east and set south of due west - the sun will reach its highest point in the sky at solar noon (due south of observer) - the daylength will be less than 12 hours Copyright Kevin Mulligan, Texas Tech University

3 Calculating the Noon Sun Angle - the noon sun angle can be calculated for any latitude, for any day of the year noon sun angle = 90 o the arc distance - where the arc distance is defined as the number of degrees between your latitude and the latitude of the subsolar point - to calculate the noon sun angle for on any other day of the year, we need an analemma, - the analemma is a graph that gives you the latitude of the subsolar point for any day of the year Copyright Kevin Mulligan, Texas Tech University

4 Calculating Latitude from the Noon Sun Angle - in the previous examples we calculated the noon sun angle for a given latitude - similarly, your latitude can be calculated from measurement of the noon sun angle - in this case, a sextant is used to measure the noon sun angle - knowing the noon sun angle, the equation is rearranged to solve for the arc distance, and then the latitude arc dist = 90 o measured noon sun angle - if we measure the noon sun angle on an equinox or solstice, it is relatively easy to calculate your latitude because we know the latitude of the subsolar point on those four days - to calculate your latitude on any other day of the year, we need an analemma, - with an analemma, you can calculate your latitude from a noon sun angle measurement on any day of the year - for example, if the date is October 15 th and we measure the noon sun angle as 40 o above the southern horizon, then what is our latitude? Calculating Longitude from Time - recall from the previous lecture that the Earth rotates 360 o in 24 hours - if we divide 360 o by 24 hours, the Earth rotates 15 o per hour - developing a way to calculate longitude was one of the greatest scientific problems of the 1700 s - in fact, the Greenwich Observatory was built to try to solve the problem of calculating longitude - the problem was eventually solved by John Harrison who developed a chronometer (a mechanical clock) - to calculate your longitude, you need to know what time it is in Greenwich on the Prime Meridian (0 o ) - for example, if you measure the noon sun where you are, and it is 4 p.m. in Greenwich (0 o ), then you must 60 o W - this longitude is calculated by multiplying the time difference (4 hours) by the rate of Earth rotation (15 o per hour) - in this case we have 4 hours difference x 15 o /hour = 60 o - also, if the time in Greenwich is p.m., then the noon meridian has past Greenwich - and you are W of Greenwich - if the time in Greenwich is a.m., then the noon meridian has not past Greenwich - and you are E of Greenwich Copyright Kevin Mulligan, Texas Tech University

5 Copyright Kevin Mulligan, Texas Tech University

6 GIST 3300 / 5300 Earth-Sun Relationships Calculating Latitude from the Sun - two components of Earth s motion - latitude and the seasons - calculating latitude from the sun - the analemma Calculating Longitude in Relation to Time - John Harrison - solving the greatest scientific problem of his time - invention of the chronometer - calculating longitude from time

7 Earth-Sun Relationships Two components to the Earth s motion

8 Earth-Sun Relationships Two components to the Earth s motion 1) the Earth rotates on it s polar axis - counterclockwise when viewed from above the North Pole - takes one day to complete a rotation - the motion is west to east

9 Earth-Sun Relationships Two components to the Earth s motion 2) the Earth revolves around the Sun on the Plane of the Ecliptic - counterclockwise when viewed from above the North Pole - takes one year to orbit the Sun - the orbit is elliptical

10 Earth-Sun Relationships Two components to the Earth s motion - also note that the Earth s polar axis is tilted 23.5 o relative to a line that is perpendicular to the Plane of the Ecliptic 23.5 o 23.5 o Plane of the Ecliptic SUN polar axis polar axis

11 Earth-Sun Relationships Summer: northern hemisphere tilted toward from the Sun Winter: northern hemisphere tilted away from the Sun

12 Earth-Sun Relationships Circle of Illumination declination of the sun (latitude of the subsolar point) Equator 0 o Spring or Fall Equinox

13 Earth-Sun Relationships Circle of Illumination declination of the sun (latitude of the subsolar point) Tropic of Cancer 23.5 o N June Solstice

14 Earth-Sun Relationships

15 Earth-Sun Relationships Declination of the sun varies between the Tropic of Cancer and Capricorn

16 Earth-Sun Relationships Apparent Movement of the Sun

17 Earth-Sun Relationships Sun s position in the sky at solar noon over one year Athens view looking due south 180 o Summer Solstice Winter Solstice horizon

18 Earth-Sun Relationships Noon Sun Angle = 90 o arc distance - where the arc distance is the number of degrees between your latitude and the latitude of the subsolar point

19 Earth-Sun Relationships Noon Sun Angle = 90 o arc distance - where the arc distance is the number of degrees between your latitude and the latitude of the subsolar point Lubbock Summer Solstice - the latitude of Lubbock is 34 o N - the latitude of the subsolar point is 23.5 o N arc distance = 34 o o = 10.5 o NSA = 90 o arc distance NSA = 90 o 10.5 o = 79.5 o above the southern horizon X 34 o N X 23.5 o N 0 o 23.5 o S

20 Earth-Sun Relationships Noon Sun Angle = 90 o arc distance - where the arc distance is the number of degrees between your latitude and the latitude of the subsolar point Lubbock Winter Solstice - the latitude of Lubbock is 34 o N - the latitude of the subsolar point is 23.5 o S arc distance = 34 o o = 57.5 o NSA = 90 o arc distance NSA = 90 o 57.5 o = 32.5 o above the southern horizon X 34 o N X 23.5 o N 0 o 23.5 o S

21 Earth-Sun Relationships Noon Sun Angle = 90 o arc distance - where the arc distance is the number of degrees between your latitude and the latitude of the subsolar point Lubbock Spring or Fall Equinox - the latitude of Lubbock is 34 o N - the latitude of the subsolar point is 0 o (equator) arc distance = 34 o - 0 = 34 o NSA = 90 o arc distance NSA = 90 o 34 o = 56 o above the southern horizon X 34 o N X 23.5 o N 0 o 23.5 o S

22 Earth-Sun Relationships The analemma A graph showing the declination of the sun (or subsolar point) for any day of the year October 15 8 o S NSA in Lubbock on October 15 arc distance = 34 o + 8 o = 42 o NSA = 90 o 42 o = 48 o

23 Calculating Latitude If we know what day of the year it is, we can calculate our latitude by measuring the noon sun angle with a sextant

24 Calculating Latitude If the date is October 15 and we measure the noon sun angle as 40 o above the southern horizon, what is our latitude? From the analemma, we know that the sun is 8 o S on October 15 Noon Sun Angle = 90 o arc distance X? 40 o = 90 o arc distance re-arrange the equation and solve for the arc distance 50 o 23.5 o N 0 o arc distance = 90 o - 40 o = 50 o we must be located 42 o N 50 o 8 o = 42 o X 8 o S 23.5 o S

25 Calculating Latitude

26 Calculating Longitude 1707 two thousand men went down John Harrison

27 Excerpts from Longitude: The True Story of a Lone Genius Who Solved the Greatest Scientific Problem of His Time, by Dava Sorbel, Walker Publishing Company, Inc.,1995. Any sailor worth his salt can gauge his latitude well enough by the length of day, or the height of the sun, or known guide starts above the horizon. Christopher Columbus followed a straight path across the Atlantic when he sailed the parallel on his 1492 journey For lack of a practical method to determining longitude, every great captain in the Age of Exploration became lost at sea despite the best available charts and compasses. From Vasco da Gama to Vasco Balboa, from Ferdinand Magellan to Sir Francis Drake they all got where they were going willy-nilly, by forces attributed to good luck and the grace of God. As more and more sailing vessels set out to conquer or explore new territories, to wage war, or to ferry gold between foreign lands, the wealth of nations floated upon the oceans. And still no ship owned a reliable means for establishing her whereabouts. In consequence, untold numbers of sailors died when their destinations suddenly loamed out of the sea and took them by surprise. In a single such accident, on October 22, 1707, at the Scilly Isles, near the southwest tip of England, four home-bound warships ran aground and nearly two thousand men lost their lives.

28 Excerpts from Longitude: The True Story of a Lone Genius Who Solved the Greatest Scientific Problem of His Time, by Dava Sorbel, Walker Publishing Company, Inc.,1995. The active quest for a solution to the problem of longitude persisted over four centuries and across the whole continent of Europe. Most crowned heads of state eventually played a part in the longitude story, notable King George III of England and King Louis XIV of France.... Renowned astronomers approached the longitude challenge by appealing to the clockwork universe: Galileo, Cassinni, Sir Isaac Newton, and Edmond Halley, all looked to the moon and stars for help. Palatial observatories were founded in Paris, London, and Berlin for the express purpose of determining longitude by the heavens. As time passed and no method proved successful, the search for the solution to the longitude problem assumed legendary proportions, on par with the discovery of the Fountain of Youth, the secret of perpetual motion, or the formula for transforming lead into gold. The governments of great maritime nations including Spain, the Netherlands, and certain city-states of Italy offered huge rewards for a workable method. The British Parliament, in the famed Longitude Act of 1714, set the highest bounty of all, naming a prize equal to a King s ransom for a Practicable and Useful means of determining longitude.

29 Longitude and Time Royal Observatory - established to find a way to calculate longitude Royal Observatory, Greenwich, England Prime Meridian

30 Longitude and Time John Harrison recognized that longitude was related to time. If you know what time it is in Greenwich you can calculate your longitude. Invented the chronometer (mechanical clock) If it s noon where you are, and it s 4 p.m. in Greenwich, then you must be 60 o W of Greenwich. 4 hours x 15 o / hr = 60 o John Harrison s H5 Marine Chronometer

31 Longitude and Time If it s noon where you are - and it s 4 p.m. in Greenwich, then you must be located 60 o W of Greenwich Your Location 4 hours x 15 o / hr = 60 o W Greenwich Noon 1:00 p.m. 2:00 p.m. 3:00 p.m. 4:00 p.m. 60 o W 45 o W 30 o W 15 o W 0 o meridian of the noon sun moves from east to west

32 Longitude and Time Today the official time in the U.S. is maintained by the U.S. Naval Observatory.

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