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 (23.5o 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 (66.5o N) is 24 hours
- daylength in the southern hemisphere is less than 12 hours
- daylength south of the Antarctic Circle (66.5o S) is 0 hours
- December Solstice (December 21 or 22)
- latitude of the subsolar point (declination of the sun) is the Tropic of Capricorn (23.5o 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 (66.5o N) is 0 hours
- daylength in the southern hemisphere is more than 12 hours
- daylength south of the Antarctic Circle (66.5o 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 (0o)
- 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:
http://esminfo.prenhall.com/science/geoanimations/animations/01_EarthSun_E2.html
Copyright © Kevin Mulligan, Texas Tech University
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
Calculating the Noon Sun Angle
- the noon sun angle can be calculated for any latitude, for any day of the year
noon sun angle = 90o – 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
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 = 90o – 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 15th and we measure the noon sun angle as 40o above the southern horizon,
then what is our latitude?
Calculating Longitude from Time
- recall from the previous lecture that the Earth rotates 360o in 24 hours
- if we divide 360o by 24 hours, the Earth rotates 15o 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 (0o)
- for example, if you measure the noon sun where you are, and it is 4 p.m. in Greenwich (0o), then you must 60oW
- this longitude is calculated by multiplying the time difference (4 hours) by the rate of Earth rotation (15o per hour)
- in this case we have 4 hours difference x 15o/hour = 60o
- 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
Copyright © Kevin Mulligan, Texas Tech University
GIST 3300 / 5300
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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
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Earth-Sun Relationships
Two components to the Earth’s motion
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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
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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
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Earth-Sun Relationships
Two components to the Earth’s motion
- also note that the Earth’s polar axis is tilted 23.5o
relative to a line that is perpendicular to the Plane
of the Ecliptic
23.5o
23.5o
Plane of the Ecliptic
SUN
polar axis
polar axis
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Earth-Sun Relationships
Summer: northern hemisphere
tilted toward from the Sun
Winter: northern hemisphere
tilted away from the Sun
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Earth-Sun Relationships
Circle of Illumination
declination of the sun
(latitude of the subsolar point)
Equator 0o
Spring or Fall Equinox
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Earth-Sun Relationships
Circle of Illumination
declination of the sun
(latitude of the subsolar point)
Tropic of Cancer 23.5o N
June Solstice
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Earth-Sun Relationships
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Earth-Sun Relationships
Declination of the sun varies between the Tropic of Cancer and Capricorn
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Earth-Sun Relationships
Apparent Movement of the Sun
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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
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Earth-Sun Relationships
Noon Sun Angle = 90o – arc distance
- where the arc distance is the number of degrees between
your latitude and the latitude of the subsolar point
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Earth-Sun Relationships
Noon Sun Angle = 90o – arc distance
- where the arc distance is the number of degrees between
your latitude and the latitude of the subsolar point
Lubbock Summer Solstice
o
- the latitude of Lubbock is 34 N
- the latitude of the subsolar point is 23.5o N
arc distance = 34o - 23.5o = 10.5o
NSA = 90o – arc distance
X 34o N
X
23.5o N
0o
NSA = 90o – 10.5o = 79.5o above the southern horizon
23.5o S
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Earth-Sun Relationships
Noon Sun Angle = 90o – arc distance
- where the arc distance is the number of degrees between
your latitude and the latitude of the subsolar point
Lubbock Winter Solstice
o
- the latitude of Lubbock is 34 N
- the latitude of the subsolar point is 23.5o S
X 34o N
23.5o N
arc distance = 34o + 23.5o = 57.5o
0o
NSA = 90o – arc distance
NSA = 90o – 57.5o = 32.5o above the southern horizon
X
23.5o S
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Earth-Sun Relationships
Noon Sun Angle = 90o – 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
o
- the latitude of Lubbock is 34 N
- the latitude of the subsolar point is 0o (equator)
X 34o N
23.5o N
arc distance = 34o - 0 = 34o
NSA = 90o – arc distance
X
0o
NSA = 90o – 34o = 56o above the southern horizon
23.5o S
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Earth-Sun Relationships
The analemma
A graph showing the declination
of the sun (or subsolar point) for
any day of the year
October 15
8o S
NSA in Lubbock on October 15
arc distance = 34o + 8o = 42o
NSA = 90o – 42o = 48o
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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
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Calculating Latitude
If the date is October 15 and we measure the noon sun angle as
40o above the southern horizon, what is our latitude?
From the analemma, we know that the sun is 8o S on October 15
X ?
Noon Sun Angle = 90o – arc distance
23.5o N
40o = 90o – arc distance
50o
re-arrange the equation and solve for the arc distance
arc distance = 90o - 40o = 50o
0o
X 8o S
23.5o S
we must be located 42o N
50o – 8o = 42o
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Calculating Latitude
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Calculating Longitude
1707 – two thousand men went down
John Harrison
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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. …
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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.
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Longitude and Time
Royal Observatory
- established to find a way
to calculate longitude
Royal Observatory, Greenwich, England
Prime Meridian
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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 60o W of Greenwich.
4 hours x 15o / hr = 60o
John Harrison’s
H5 Marine Chronometer
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Longitude and Time
If it’s noon where you are - and it’s 4 p.m. in Greenwich,
then you must be located 60o W of Greenwich
4 hours x 15o / hr = 60oW
Your Location
Noon
60oW
Greenwich
1:00 p.m.
45oW
2:00 p.m.
3:00 p.m.
30oW
15oW
4:00 p.m.
0o
meridian of the noon sun “moves” from east to west
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Longitude and Time
Today – the official time in the U.S. is maintained by the U.S. Naval Observatory.
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