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Longitude

Longitude. North - South Meridians base point of world system is Greenwich, England Iowa - approximately 93 0 West. Latitude. Measured from the Equator Iowa - approximately 42 0 North. Great circle distances (assume a round world).

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Longitude

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  1. Longitude • North - South Meridians base point of world system is Greenwich, England Iowa - approximately 930 West

  2. Latitude • Measured from the Equator • Iowa - approximately 42 0 North

  3. Great circle distances(assume a round world) • Along a longitudinal line the Radius of the earth is approximately • R = 3959 miles or • R = 6371 kilometers • Distance along 1 degree of longitude: • L = R * theta where theta is in radians • L = 3959 * (1 deg/ 57.2958 deg/rad) • L = 69.09 miles

  4. Great circle distances(assume a round world) • Along a latitudinal line the Radius of the earth about the poles is a function of the latitude: • Radius(at Lat. y) = Radius *cos(Latidude) • Distance =( R at Lat Y) * theta • At 420 , lat, R = 3959 miles * Cos (420) • =2942 miles • In 1 deg, Dist = 2942 *1/57.29 =51.35 mi

  5. Navigational GPS at ISU • Records to nearest 0.001 minute • ___________________ • A) What is the distance in feet for 0.001 minute change in the longitude at a latitude of 420? • What is the distance in feet for 0.001 minute change in the latitude of 420 (or any other latitude)?

  6. Bearings from flat-earth society Spherical trigonometry is used to obtain precise assessment of distance. HOWEVER, over short distances, Eastings and Northings from surveying will give good estimates: Point 1: Latitude 42d 17.369’ N, Longitude: 93d 43.614’ W Point 2 Latitude 42d 18.749’ N Longitude: 93d 44.865’ W Angular change Delta North = 1.380’ (minutes) to north Delta West = 1.251’ to west

  7. Bearings from flat-earth society Delta North = 1.380’ (minutes) to north Delta West = 1.251’ to west Distance north: Radius = 3959 miles along meridian L = R * theta where theta is the central angle L = 3959 mi * 5280 ft/mi * 1.380’/ (60’/deg) / (57.2958d per radian) L = 8391 feet Distance West - consider using average latitude of the two points Average latitude = 42d 18.059’ Radius = 3959 * cos (42d 18.059’) = 2928 miles L = 2928 mi *5280 ft/mi * 1.251min/ (60’/deg) / (57.2958d per radian) L = 5626 feet

  8. Bearing of line Dist north = 8391 feet Dist. West = 5626 feet Bearing = atan( 5626/ 8391) or N 33d 50’ W Total Distance = 10,103’ This estimate of distance is in error by less than 0.00002 feet compared to spherical trigonometry.

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