The Earth Really is Flat! The Globe and Coordinate Systems Intro to Mapping & GIS The Earth is Flat Long History of Mapping • Day to day, we live life in a flat world • Prehistoric Renderings, Rock – sun rises in east, sets in west Paintings from the KhoiSan – sky is above, ground is below People in South Africa – we orient travel by north-south, east-west thinking • Ex. Philly is “north west” of Glassboro • Map = Representation or Model of landscape • Traditional Australian Aboriginal Art Symbols • A Flat map (ie model of space) is a perfectly Communicated Place rational model for a local or regional scale Long History of Mapping Mapping on a flat surface is • Ancient tablet from the 7th Century BC relatively easy depicting the world at the time of Sargon (2300 BC) as a circle surrounded by water, with Babylon at its center. (British Museum) graphic symbols • Map of known world by Hecataeus store – about 500 BC – Greeks believed world a sphere abstraction house reality map 1 Map Making • Cartographic Symbology – Abstracting spatial reality with graphic representation • Extent – The area being mapped • Scale – relationship of size of realworld to map – Fraction 1/24,000 – Ratio 1:24,000 – Written statement “1 inch equals 1 mile” – Bar style 0 1 2 3 4 • Generalization – The amount of detail included in the map – Depends on the scale Coordinate Systems Cartesian Coordinates (knowing where it’s at) II Y I • Origin P 1 • Numerical systems that y1 specify location in space. • Abscissa or X Axis P 2 y • Ordinate or Y Axis 2 • Types of coordinate • Position X,Y systems: • Quadrants I through IV – Plane coordinates x x (i.e. FLAT Surface) • Point Locations: 2 1 X • Cartesian Point X Y 1 x y • Angular / polar 1 1 – Global or spherical 2 x2 y2 coordinates • Used for most projections. III IV Distance Calculation for Points Most Flat Maps Utilize a Measured in Cartesian Coordinates Cartesian Coordinate System Y • Point Locations: I P 1 Point X Y y1 1 x1 y1 2 x2 y2 y - y • Distance Formula: 1 2 – Distance from Point 1 to Point P 2: 2 SOUTH AXIS y2 – x1 - x2 2 2 (X1 – X2) + (Y1 – Y2) NORTH EAST – WEST AXIS x x 2 1 X Ancient Plan of Jerusalem 2 The Flat Earth Model Doesn’t Work at a Large Scale. Defining Location on a Spear, the Global Coordinate System Long distance travel required a better model. Basis of Global Coordinate System Terms to Specify Position on Globe • Earth’s rotation gives poles and axis as two • Latitude:degrees north and south of equator. natural points of reference on the sphere. • Longitude:degrees east and west of Greenwich, – Equator: locus of points on sphere’s surface that England. are equidistant from the poles. • Meridian = line of constant longitude. – Great Circle: • Pass a plane through a sphere’s center. • Parallel = line of constant latitude • Connect the points along which plane intersects sphere’s • Great circle = circle inscribed on surface by a surface. plane passing through earth’s center. • Line defined by the points is a great circle. • Small circle = circle inscribed on surface by a – Equator is only great circle perpendicular to axis plane that passes through earth, but misses the of rotation. center. Global Coordinate System Units of Measure All meridians are • Angular Measure: • Great Circle Degree great circle arcs. Distances: – Degrees: 360 per – Degree = 69 miles. circle. – Minute = 1.15 miles. – Minutes: 60 per degree. – Second= .02 miles – Seconds: 60 per – One tenth second = minute. 10.12 feet – One hundredth second All parallels, except = 1.012 feet. for the equator, are small circles. 3 Units of Measure Decimal Degrees • Traditional Angular • Based on decimal fraction • Decimal Degree Measure: of a degree Conversion: – Degrees: 360 per • Easier to work with – Multiply minutes by 60 circle. • can express angles to – Add seconds to results – Minutes: 60 per any precision - to of minutes multiplied degree. hundredths of a degree, by 60. to thousandths of a – Seconds: 60 per – Divide total by 3,600 degree, and so on minute. – Add result to degrees • Better for digital mapping Example of Decimal Conversion Global Grid Properties Traditional Measure: 45°20’30” 1. All meridians equal length Convert minutes to seconds: * 60 = 1200” 2. All meridians converge at poles (true north orientation) Add seconds to + = 1230” 3. All lines of latitude are parallel to the equator converted minutes: 4. All parallels maintain the same spacing Convert seconds / 3600 = .3416667 5. Meridians and parallels intersect at right to degree fraction: angles 6. The scale on a globe is the same everywhere Add whole degree 45.3416667 ° (unlike a map) to fraction: Arc and Great Circle Distance Great Circle Arc Distance • Proper measure for long distances Given the latitude and the longitude of two locations on the globe. How do you • Data required: measure the distance in degrees – Latitude in decimal degrees of each place. of great circle arc? – Longitude in decimal degrees of each place. • Procedure: – Calculate angular distance over the great circle route. q° = Arccos (Sine(Lat )*Sine(Lat )) + – Convert angular distance into miles or 1 2 kilometers. (Cosine(Lat1)*Cosine(Lat2)* Cosine(|Long1 - Long2|)) 4 Great Circle Arc Distance Given the great circle arc distance between two locations on the on the globe. How do you measure the distance in miles? Distance in miles = 69*q° Windows Calculator Seasonal Variation of Solar Angle Tropics and Polar Circles Earth-Sun Relations 5 Arctic Circle Polar Axis Northern Limit Tropic of Cancer Prime Meridian Southern Limit Tropic of Capricorn Equator Earth’s Shape What Shape is the Earth? Question: What kind of argument is this? • Earth’s shape in history: Inductive – Aristotle: Deductive • Humans are nearly perfect animals. Empirical • Home of humans should be as perfect as they are. • Most perfect shape is the sphere • Therefore the Earth must be a sphere. – He was almost perfectly correct!!! Earth’s Shape Question: What kind of argument is this? Shape of the Earth • Earth’s shape in history: Inductive – Isaac Newton: Deductive • Earth rotates about axis. Empirical • This implies greater centrifugal force is exerted on material near equator where movement is faster than near poles. • This force pulls on the Earth and causes it to deviate from a perfect sphere. • Therefore the Earth must be an oblate spheroid. – He also was almost perfectly correct!!! 6 Shape of the Earth Earth Ellipsoid • Ellipsoid: Earth as slightly flattened ball b • Ellipse of Earth's shape: – Semi-major axis = 6,378,137 meters a – Semi-minor axis = 6,356,733 meters – 1/298th difference pole to pole versus equatorial – Resulting ellipsoid provides mathematical model of planet’s shape. – Used for creating accurate large scale maps Does It Matter? Which Ellipsoids Are Used? • Small scale maps. No, go ahead and use • NAD 1927: Based on calculations by the sphere as model. British geodesist Alexander Clark. • Large scale maps. Yes, use ellipsoid as • NAD 1983: Based on Geodetic model. Referencing System of 1980. • Difference in length of a degree of latitude due to flattening: • Conversion from NAD27 to NAD83 can be troublesome – 0° = 68.708 miles – 45° = 69.054 miles – 90° = 69.403 miles The Geoid Represents mean sea level The Geoid Diverges from the Ellipsoid which varies due to gravity anomalies by as much as 100 meters Geoid highs - max. +73 m Geoid lows - min. -105 m Earth is actually lumpy – proper term Oblate Geoid 7 Who cares about the Geoid? Earth’s Surface varies from the Geoid Size of the Earth: • We all do • Maximum Vertical Surface – It is the reference level against which elevations are Difference: measured – Greatest ocean depth = 36, 161 feet [Mariana – It skews the orbit of satellites Trench]. – Greatest mountain height = • Earth scientists do 29, 028 feet [Mount Everest]. – It tells us about the deep interior of Earth – Difference = 65, 189 feet. • Maximum Elevation • Surveyors do Difference as Proportion of – It purturbs leveling measurements Diameter – .001558 which on a 12” – That is, it changes the direction of "straight down" globe is equal to .0186 inches. Who First Measured Earth? Size of the Earth Alexandria • Eratosthenes in 250 B.C. NP Class survey • q = q’= 7.2° • 7.2 = 1/50 0f 360° Which of the following closest to • Arc length = 5,000 q’ the circumference of the earth? stadia. • 5,000 x 50 = q 250,000 stadia – He was very close!! Well at A)9,000 miles Syene B)12,500 miles C) 25,000 miles D) 50,000 miles E) 120,000 miles SP Earth’s Size Earth’s Rotational Speed Size of the Earth: Rotation Earth: • Diameter: • Circumference: – 12, 756,370 meters. – 24, 901 miles. – 41, 851, 607 feet. Divide by 24 hours – 7, 926 miles. = 1,038 mph • Circumference: Faster than – 40, 075, 318 meters. commercial jet – 131,480, 703 feet. (580 mph) – 24, 901 miles. Faster than sound (769 mph) 8 Time and Time Zones Mean Solar Time • A sundial keeps apparent solar time and it will differ from the time on your watch during the course of a year. • This means that the true Sun is not always on the meridian at exactly noon. – Sometimes the Sun is on the meridian before noon and sometimes after noon. – The difference, called the equation of time, can be as much as 17 minutes. Sundial Apparent Solar Time – The path of the Sun at noon during the year makes a figure 8 shape called the analemma. • The north-south motion is due to the 23.5 degree tilt of the celestial sphere with respect to the ecliptic. • The east-west motion is primarily caused by the varying speed of Earth in its orbit around the Sun.