Earth – Maps and Navigation size/shape/rotation of Earth is fundamental to ocean dynamics

2. Geography 104 - “Physical Geography of the World’s Oceans” • Earth – Maps and Navigation • size/shape/rotation of Earth is fundamental to ocean dynamics • interesting to know history of Earth’s geometry • need to know how to describe location and size of features • bit of navigational history (can use oceans/celestial)

3. Eratosthenes of Cyrene (c.275-192): Greek mathematician, poet, athlete, geographer and astronomer Interesting to know http://www.livius.org/aj-al/alexander/alexander_t33.html

4. Alexandria & Syene 800 km (Aswan) http://epod.usra.edu/archive/epodviewer.php3?oid=61280

5. Eratosthenes’ estimate of earth’s diameter  = 7.2° 360º x 800 km 7.2º C = C = earth’s circumference = 40,000 km http://www.nos.noaa.gov/education/kits/geodesy/media/supp_geo02a.html

6. Eratosthenes’ estimate of earth’s diameter  = 7.2° 7.2 º 360º 800 km C = C = earth’s circumference = 40,000 km (stadia) Modern estimate of Earth’s radius, re = 6371 km C=2pre = 40,030 km http://www.nos.noaa.gov/education/kits/geodesy/media/supp_geo02a.html

7. Eratosthenes

8. non-spherical shape important for satellite orbits polar radius = 6357 km equatorial radius = 6378 = 0.9967 radius of sphere with Earth’s volume is 6371 km

9. Latitude and Longitude – Mollweide projection zonal meridional latitude line (equator only great circle latitude) longitude line (great circle)

10. Latitude and Longitude – Mollweide projection 360 deg/1 day = 15 deg/hr latitude line longitude line

11. special latitude & longitude lines axial tilt of the Earth with respect to the sun is 23° 26′ 21.41″

12. distance per degree of latitude circle – subtends angle of 360° 1° = 60’ (minutes) 1’ = 60” (seconds) nautical mile = distance of 1° latitude distance / degree latitude is constant not true for longitude clat re = 6371 km re = 6371 km circumference = 2πre = 40,030 km 1° / 360° = Clat / 40,030 km Clat = 40,030 km / 360° = 111 km/°lat = 60 nm/°lat = 69 mi/°lat

13. distance per degree of longitude re = 6371 km Φ = latitude circumference = 2πrecosΦ = 40,030km cosΦ re = 6371 km ϕ re cos Φ 1° / 360° = Clon / 40,030km cosΦ Clon = 111 km cosΦ km/°lon distance / degree not constant for longitude

14. A Dd Dy Dx B - can use Pythagorean Theorem to obtain accurate distance estimate between two points - accurate for distances around 100 km or less

15. fA= A 34° 20’ Dy fB= 34° 10’ B 120° 10’ 120° fA= 34° 20’ = 34° + 20/60° = 34.333° fB = 34° 10’ = 34° + 10/60° = 34.167° fA - fB = 0.166°

16. fA= A 34° 20’ Dy fB= 34° 10’ B 120° 10’ 120° Dy = (111 km/°lat)(0.166 °lat) = 18.3 km

17. A 34° 15’ B Dx = qA qB= 120° 10’ 120° Dx = (111*cos(34+15/60) km/°lon)(0.167 °lon) = 15.2 km

18. A Dd Dy Dx B Dd = (Dx2+Dy2)1/2 = (18.42+15.22)1/2 = 23.9 km

19. early Pacific navigation

20. early Pacific navigation

21. early Pacific navigation

22. early Atlantic navigation

23. Latitude determination

24. antique navigational instruments

25. using a cross staff North Star latitude horizon

26. sextant

27. using a sextant

28. Gemma Frisius 1508 – 1555 mathematician, cartographer, instrument maker, first to describe how an accurate clock could be used to determine longitude

29. Longitude determination 15° rotation rate = 360 deg in 24 hr = 15 deg per hr

30. Longitude determination Set clock on boat before departing from Greenwich.

31. Longitude determination What is longitude if clock on boat reads 16:18 at local noon?

32. Longitude determination Local noon is behind clock => boat is west of Greenwich

33. Longitude determination 18 60 time difference = 4+ hr = 4.3 hr longitude difference = 4.3 hr x 15°/hr = 64.5° W

35. Clocks for measuring longitude John Harrison (1693-1776)

36. global sea surface temperature from satellite observations

37. Readings for next time (Seafloor): • Read Chapter 4 “Seafloor Features”; article “Emergence of Complex Societies After Sea Level Stabilized”; article “Risk of Rising Sea Level to Population and Land Area”