4. Longitude North - South Meridians base point of world system is Greenwich, England Iowa - approximately 93 0 West

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

6. 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

7. 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 42 0, lat, R = 3959 miles * Cos (42 0 ) =2942 miles In 1 deg, Dist = 2942 *1/57.29 =51.35 mi

8. 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 42 0 ? What is the distance in feet for 0.001 minute change in the latitude of 42 0 (or any other latitude)?

9. 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

10. 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

11. 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.