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)

Geography 104 - “Physical Geography of the World’s Oceans”

Greek mathematician, poet, athlete, geographer and astronomer

Eratosthenes of Cyrene (c.275-192):

http://www.livius.org/aj-al/alexander/alexander_t33.html

Interesting to know

http://epod.usra.edu/archive/epodviewer.php3?oid=61280

800 km

Alexandria & Syene

(Aswan)

Eratosthenes’ estimate of earth’s diameter

http://www.nos.noaa.gov/education/kits/geodesy/media/supp_geo02a.html

360º x 800 km 7.2º

C =

C = earth’s circumference = 40,000 km

= 7.2°

Eratosthenes’ estimate of earth’s diameter

http://www.nos.noaa.gov/education/kits/geodesy/media/supp_geo02a.html

7.2 º360º =

800 km C

C = earth’s circumference = 40,000 km (stadia)

= 7.2°

Modern estimate of Earth’s radius,re = 6371 kmC=2re = 40,030 km

Eratosthenes

polar radius = 6357 kmequatorial radius = 6378 = 0.9967

radius of sphere with Earth’s volume is 6371 km

non-spherical shape important for satellite orbits

Latitude and Longitude – Mollweide projection

latitude line (equator only great circle latitude) longitude line (great circle)

zonal

meridional

Latitude and Longitude – Mollweide projection

latitude line longitude line

360 deg/1 day = 15 deg/hr

special latitude & longitude lines

axial tilt of the Earth with respect to the sun is 23° 26′ 21.41″

circle – subtends angle of 360°1° = 60’ (minutes)1’ = 60” (seconds)

nautical mile = distance of 1° latitude

distance / degree latitude is constantnot true for longitude

re = 6371 km

circumference = 2πre = 40,030 km

r e =

637

1 kmc lat

1° / 360° = Clat / 40,030 km

Clat = 40,030 km / 360° = 111 km/°lat = 60 nm/°lat

= 69 mi/°lat

distance per degree of latitude

distance / degree not constant for longitude

re = 6371 km

Φ = latitude

circumference = 2πrecosΦ = 40,030km cosΦ

r e =

637

1 km

1° / 360° = Clon / 40,030km cosΦ

Clon = 111 km cosΦ km/°lon

distance per degree of longitude

ϕ

re cos Φ

A

B

d

x

y

- can use Pythagorean Theorem to obtain accurate distance estimate between two points- accurate for distances around 100 km or less

34° 20’

34° 10’

120° 10’ 120°

A

B

A = 34° 20’ = 34° + 20/60° = 34.333°

B = 34° 10’ = 34° + 10/60° = 34.167°

A - B = 0.166°

A =

B = y

34° 20’

34° 10’

120° 10’ 120°

A

B

y = (111 km/°lat)(0.166 °lat) = 18.3 km

A =

B = y

120° 10’ 120°

A

B

=AB =

x

x = (111*cos(34+15/60) km/°lon)(0.167 °lon) = 15.2 km

34° 15’

A

B

d

x

y

d = (x2+y2)1/2 = (18.42+15.22)1/2 = 23.9 km

early Pacific navigation

early Pacific navigation

early Pacific navigation

early Atlantic navigation

Latitude determination

antique navigational instruments

horizon

North Star

latitude

using a cross staff

sextant

using a sextant

Gemma Frisius 1508 – 1555

mathematician, cartographer, instrument maker, first to describe how an accurate clock could be used to determine longitude

Longitude determination

rotation rate = 360 deg in 24 hr = 15 deg per hr

15°

Set clock on boat before departing from Greenwich.

Longitude determination

What is longitude if clock on boat reads 16:18 at local noon?

Longitude determination

Local noon is behind clock => boat is west of Greenwich

Longitude determination

time difference = 4+ hr = 4.3 hr longitude difference = 4.3 hr x 15°/hr = 64.5° W

1860

Longitude determination

John Harrison (1693-1776)

Clocks for measuring longitude

global sea surface temperature from satellite observations

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”