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Measuring Earth's Dimensions: Eratosthenes' Method & Latitude-Longitude, Lecture notes of Physics

The ancient greek philosopher eratosthenes' method of measuring earth's dimensions using the angles of shadows during the summer solstice. Additionally, it introduces the latitude-longitude system for describing locations on earth, with a focus on the grid lines (parallels and meridians) and their significance in understanding earth's geography.

Typology: Lecture notes

2021/2022

Uploaded on 09/12/2022

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Earth in Different Dimensions
Round?
Or flat?
Observing the World
observation
the key first step to ALL science
driven by curiosity
a process of discovery
answer questions about how the world works
knowledge improves quality of life
Eratosthenes
(Egypt, 235 B.C.)
On June 21 (summer solstice), midday sun
directly overhead, shining down a deep well in
the city of Syene (Aswan)
Angle of shadow made by sun shining on a
monument at midday on June 21 in Alexandria
was 7o21’
Alexandria lies ~5000 stadia to the north of
Aswan (~500 miles)
Calculate circumference (C) using simple math:
360o/7.2o= C/500 miles; C= 50 x 500 miles =
25,000 miles
Remarkable agreement with actual figure of
24,862 miles (40,010 km) WOW.
a well in Syene
a shadow cast by a
monument in Alexandria
7°12' = 7.2°
~5000 stadia = 500 mi
the Sun's rays
pf3

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Earth in Different Dimensions

Round?

Or flat?

Observing the World

observation

the key first step to ALL science driven by curiosity

a process of discovery answer questions

about how the world works

knowledge

improves quality of life

Eratosthenes

(Egypt, 235 B.C.)

On June 21 (summer solstice), midday sundirectly overhead, shining down a deep well inthe city of Syene (Aswan) Angle of shadow made by sun shining on amonument at midday on June 21 in Alexandriawas

7

o21’

Alexandria lies ~5000 stadia to the north ofAswan (~

500 miles

)

Calculate circumference (

C

) using simple math:

360

o/7.

o^

= C

/500 miles;

C

= 50 x 500 miles =

25,000 miles

Remarkable agreement with actual figure of 24,862 miles

(40,010 km)

a well in Syene^ – WOW.

a shadow cast by a

monument in Alexandria

7

°12' = 7.

°

~5000 stadia = 500 mi

the Sun's rays

Where in the World are we?

How do we describe where weare on the planet?

Latitude (North-South)

Longitude (East-West)

based on

angular relationships

to Earth’s center

grid system

used to precisely describe locations on

the Earth’s surface expressed in

degrees

o) of arc

each degree is divided into 60

minutes

each minute is divided into 60

seconds

Latitude

“parallels” = grid linesthat are parallel to theequator 0

o^

at equator, 90

o^

at

poles 0

o-

oN = N. Hemisphere

o-

oS = S. Hemisphere

Everywhere on Earth’s surface:

o 1

lat. = 60 nautical miles 1’ lat. = 1 nautical mile

°N

(North Pole)

°N 30 °N
0 °^

(Equator)^30

°S 60 °S
S

(South Pole)

Parallels

(Latitude)

Longitude

“meridians” = grid linesthat intersect at poles 0

o^

“Prime Meridian”

(Greenwich, England) 180

o^

= halfway around

Earth 0

o-

o^

to west of

Greenwich = W. Hemisphere 0

o-

o^

to east of

Greenwich = E. Hemisphere

°W
°E)
°W
W
°W
°W

°W^ Meridians

(Longitude)