This section was edited by Kenneth Foote, Department of Geography, University of Texas Austin.

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- This unit provides an overview of latitude and longitude, including:
- Earth rotation, the North and South Poles, and the Equator
- Parallels of latitude and meridians of longitude
- Determination of north or south position with latitude
- The use of longitude to determine east or west position
- The measurement of latitude and longitude with degrees, minutes, and seconds

- After learning the material covered in this unit, students should gain an
appreciation for:
- The relationship between plane and earth coordinate geometries
- The importance of the earth's rotation and poles to measurement and point location
- The use of latitude and longitude to determine locations on the earth's surface
- The differences and relationships between latitude and longitude
- Using latitude and longitude to measure distances

Unit 014 - Latitude and Longitude

- Throughout history, many methods of keeping track of locations have been developed.

*Plane coordinate geometry*was developed as an abstract frame of reference for flat surfaces.

- Once the earth's round, three-dimensional shape was accepted, a spherical coordinate system was created to determine locations around the world.

- René Descartes' contributions to mathematics were developed
into
*cartesian coordinate geometry.*

- This is the familiar system of equally-spaced intersecting perpendicular lines in a single plane.
- The two principal axes are the horizontal (x) and the vertical (y) .
- Any point's position can be described with respect to its corresponding x and y values (x,y).
- Figure 1. The position (5,3) is a unique location easily plotted on the cartesian plane.
- The position of one point relative to another can also be shown with the cartesian coordinate system.

- The earth's spherical shape is more difficult to describe than a plane surface.

- Concepts from cartesian coordinate geometry have been incorporated into the earth's coordinate system.

- The spinning of the earth on its imaginary axis is called
*rotation*.

- Aside from the cultural influences of rotation, this
spinning also has a physical influence.
- The spinning has led to the creation of a system to determine points and directions on the sphere.
- The North and South poles represent the axis of spin and
are fixed reference points.
- If the North Pole was extended, it would point to a fixed star, the North Star (Polaris).

- Any point on the earth's surface moves with the rotation
and traces an imaginary curved line:
*Parallel of Latitude*

- If a plane bisected the earth midway between the axis of
rotation and perpendicular to it, the intersection with the surface would form
a circle.
- This unique circle is the
*equator*. - The equator is a fundamental reference line for measuring the position of points around the globe.

- This unique circle is the

- Figure 2. The equator and the poles are the most important parts of the earth's coordinate system.

- The spherical coordinate system with latitudes and longtitudes used for
determining the locations of surface features.
- Parallels: east-west lines parallel to the equator.
- Meridians: north-south lines connecting the poles.
- Figure 3. The Geographic Grid

- Parallels are constantly parallel, and meridians converge at the poles.

- Meridians and parallels always intersect at right angles.

*Parallels of latitude*are all small circles, except for the equator.

- True east-west lines
- Always parallel
- Any two are always equal distances apart
- An infinite number can be created
- Parallels are related to the horizontal x-axes of the cartesian coordinate system.
- Figure 4. Parallels of Latitude

*Meridians of longitude*are halves of great circles, connecting one pole to the other.- All run in a true north-south direction
- Spaced farthest apart at the equator and converge to a point at the poles
- An infinite number can be created on a globe
- Meridians are similar to the vertical y-axes of the cartesian coordinate system.
- Meridians of Longitude - Figure 4.

- Angular measurement must be used in addition to simple plane
geometry to specify location on the earth's surface.
- This is based on a
*sexagesimal scale:* - A circle has 360 degrees, 60 minutes per degree, and 60 seconds per minute.
- There are 3,600 seconds per degree.
- Example: 45° 33' 22" (45 degrees, 33 minutes, 22 seconds).

- This is based on a

- It is often necessary to convert this conventional angular
measurement into decimal degrees.
- To convert 45° 33' 22", first multiply 33 minutes by 60, which equals 1,980 seconds.
- Next add 22 seconds to 1,980: 2,002 total seconds.
- Now compute the ratio: 2,002/3,600 = 0.55.
- Adding this to 45 degrees, the answer is 45.55°.

- The earth rotates on its axis once every 24 hours,
therefore:
- Any point moves through 360° a day, or 15° per hour.

- A
*great circle*is a circle formed by passing a plane though the exact center of a sphere.- The largest circle that can be drawn on a sphere's surface.
- An infinite number of great circles can be drawn on a sphere.
- Great circles are used in the calculation of distance between two points on a sphere.

- A
*small circle*is produced by passing a plane through any part of the sphere other than the center.

- Figure 5 - Great and Small Circles

- Arcs of great circles are very important to navigation since
they represent the shortest route between two points.
- A loxodrome, or rhumb line, intersects each meridian at the same angle (constant compass bearing).
- Unfortunately, this route traced by a loxodrome is not the
shortest distance.
- Maintaining a constant heading or azimuth traces a sprial on the globe called a loxodromic curve.

- To approximate the path of a great circle, which constantly changes azimuth, navigators plot courses along a series of loxodromes.

- The Mercator projection was developed especially for
navigators, and presents straight lines as loxodromes.
- Because of the great distortion of parallels and meridians on this projection, great circles appear as deformed curves.
- Figure 6 - Loxodrome and Great Circle Comparison on Mercator Projection

**Authalic Latitude**is based on a spherical earth:- Measures the position of a point on the earth's surface in terms of the angular distance between the equator and the poles.
- Indicates how far north or south of the equator a particular point is situated.
*North latitude*: all points north of the equator in the northern hemisphere*South latitude*: all points south of the equator in the southern hemisphere

- Latitude is measured in angular degrees from 0° at the
equator to 90° at either of the poles.
- A point in the northern hemisphere 40 degrees north of the equator is labeled Lat. 40° N.
- Forty degrees south of the equator, the label changes to Lat. 40° S.

- The north or south measurement of latitude is actually
measured along the meridian which passes through that location
- It is known as an
*arc*of the meridian.

- It is known as an

**Geodetic Latitude**is based on an ellipsoidal earth:- The ellipsoid is a more accurate representation of the earth than a sphere since it accounts for polar flattening.
- Refer to the Shape of the Earth (Unit 015) for more information.
- Modern large-scale mapping, GIS, and GPS technology all require the higher accuracy of an ellipsoidal reference surface.
- Refer to the Coordinate Systems Overview (Unit 013) for more information.

- When the earth's shape is based on the WGS 84
Ellipsoid:
- The length of 1° of latitude is not the same everywhere as it is on the sphere.
- At the equator, 1° of latitude is 110.57 kilometers (68.7 miles).
- At the poles, 1° of latitude is 111.69 kilometers (69.4 miles).
- Table 1 - Length of a Degree of Geodetic Latitude

- Parallels of latitude decrease in length with increasing latitude.
*Mathematical expression*: length of parallel at latitude x = (cosine of x) * (length of equator)- The length of each degree is obtained by dividing the length of that parallel by 360.
- Example: the cosine of 60° is 0.5, so the length of the parallel at that latitude is one half the length of the equator.

- Since the variation in lengths of degrees of latitude varies
by only 1.13 kilometers (0.7 mile), the standard figure of 111.325 kilometers
(69.172 miles) can be used.
- For example, anywhere on the earth, the length represented by 3° of latitude is (3 * 111.325) 333.975 kilometers.

- Longitude measures the position of a point on the earth's surface east or
west from a specific meridian, the
*prime meridian*.- The longitude of a place is the arc, measured in degrees along a parallel of latitude from the prime meridian.
- The most widely accepted prime meridian is based on the
*Bureau International de l'Heure (BIH) Zero Meridian*:- Defined by the longitudes of many BIH stations around the world..
- Passes through the old Royal Observatory in Greenwich, England.
- The prime meridian has the angular designation of 0° longitude.
- All other points are measured with respect to their position east or west of this meridian.
- Longitude ranges from 0° to 180°, either east or west.

- Since the placement of a prime meridian is arbitrary, other countries
have often used their own.
- For the purposes of measurement, no one prime meridian is better than another
- Having a widely accepted meridian allows comparison between maps published in different areas.

- The distance represented by a degree of longitude varies
upon where it is measured.
- The length of a degree of longitude along a meridian is not constant because of polar flattening.
- At the equator, the approximate length is determined by dividing the earth's circumference (24,900 miles) by 360 degrees: 111.05 kilometers (69 miles).
- The meridians converge at the poles, and the distance represented by one degree decreases.
- At 60° N latitude, one degree of longitude is equal to about 55.52 kilometers (34.5 miles).

- Because the earth is not a perfect sphere, the equatorial circumfererence does not equal that of the meridians.

- On a perfect sphere, each meridian of longitude equals one-half the
circumference of the sphere.
- The length of each degree is equal to the circumference divided by 360.
- Each degree is equal to every other degree.

- Measurement along meridians of longitude accounts for the earth's polar
flattening:.
- Degree lengths along meridians are not constant:
- 111.325 kilometers (69.172 miles) per degree at the equator
- 16.85 kilometers (10.47 miles) per degree at 80° North
- 0 kilometers at the poles

- Degree lengths along meridians are not constant:

- The distance between meridians of longitude on a sphere is a function of
latitude:
*Mathematical expression*: Length of a degree of longitude = cos (latitude) * 111.325 kilometers- Example: 1° of longitude at 40° N = cos (40°) * 111.325
- Since the cosine of 40° is 0.7660, the length of one degree is 85.28 kilometers.

- Table
2 - Length of a Degree of Geodetic Longitude
- These lengths are based on an ellipsoid and are similar to the lengths computed with the spherical formula.

- Calculating distance on a sphere based on latitude and
longitude is a complicated task.
- The calulation of the distance between two points on a plane surface is a relatively simple task and has promoted the use of two-dimensional maps throughout history.
- When calculating distances over large areas, the authalic sphere can be
used as a reference surface.
- The shortest distance between two points on a sphere is the arc on the surface directly above the true straight line.
- The arc is based on a great circle.
- Table 3 - Great Circle Distance Calculation
- See the Web References section for online examples.

- The difference betwen the sphere and ellipsoid is important when working
with large areas.
- At a scale of 1:40,000,000, a 23 kilometer error in distance would equal a pen line (0.5 mm) on paper.

- Complex geodetic models based on ellipsoids are necessary for precise
meaurement.
- Long range radio navigation requires precise distances.
- Loran-C requires range computations with better than 10 meter accuracy over 2,000 kilometers.
- Geodetic measurements using satellites requires very accurate range computations.
- Table 4 - Ellipsoidal Distance Calculation

- Describe the relationship between the cartesian coordinate system and the geographic grid.

- Convert 35.40° into degrees, minutes, and seconds.

- Explain why the length of a degree of longitude decreases as one approaches the poles.

- The equator can also be called a:
- Prime Meridian
- Parallel of Latitude
- Great Circle
- Both 1 and 2
- Both 2 and 3

- Which of the following is
**not**true of parallels of latitude?- They are true east-west lines
- Any two are always equal distances apart
- Always meet at the poles
- Related to the x-axis of the cartesian coordinate system

- Which of the following is
**not**true of meridians of longitude?- They always meet at the poles
- True north-south lines
- Each is equal to half the length of a great circle
- Always begin with the Prime Meridian through Greenwich, England

- Dent, Borden D.
*Cartography: Thematic Map Design*, William C. Brown Publishers, 1990.

- Muehrcke, Phillip C., and Juliana O. Muehrcke.
*Map Use: Reading-Analysis-Interpretation,*4th ed. Madison, WI: J.P. Publications, 1998.

- Robinson, Arthur H., et al.
*Elements of Cartography*, New York: John Wiley & Sons, 1995.

- Strahler, Arthur N., and Alan H. Strahler.
*Elements of Physical Geography: Fouth Edition*, New York: John Wiley & Sons, 1989.

- Strahler, Arthur N., and Alan H. Strahler.
*Modern Physical Geography: Third Edition*, New York: John Wiley & Sons, 1987.

- Bali Online: How far is it? - This service calculates the distance between two places.

- Geographic Names Information System (GNIS) - This database can be used to locate the longitude and latitude of over 1,233,933 features in the U.S.

- Bureau of the Census Gazetteer - Search for latitude and longitude data by entering a zip code or town and state information.

- Kirvan, Anthony P. (1997) Latitude/Longitude,

The correct URL for this page is: http://www.ncgia.ucsb.edu/giscc/units/u014/u014_f.html

Created: October 29, 1997. Last revised: July 7, 2000.

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