Distant of MoonMethod: by Ancient Greeks

Present: So

Leo

Leon

Leong

Introduction

I : UN-AIDED OBSERVERS Imagine a time before satellites, planes,telephones, telesco

pes… What would you conclude about the world using just your o

wn senses? Earth is at rest (i.e., motionless) Earth is flat Sun, Moon, planets, stars move in the sky (from East to W

est) Occasional bizarre things happen (comets, meteors)

Historical Astronomy part1:Ancient (Greek) astronomical measurements of the size of the Earth, Moon, distance to Sun

Aristarchus (c. 280BCE) Use shadow of Earth on Moon

Earth round, Earth 3x size of Moon (actually 3.7x)

Use 1st qtr Moon angle to estimate Sun is ~20x farther than the Moon (actually 400x)

Eratosthenes (c. 200 BCE) Used shadow angle of pole to measure radius

of Earth (6,900 km), actual 6,400km (8% error!)

Cosmology of Eudoxus andAristotle

Fundamental “principles”: Earth is motionless Sun, Moon, planets and stars go around the Earth: geocentric model Eudoxus (408-355 B.C.) & Aristotle (384-322 B.C.) Proposed that all heavenly bodies are embedded in giant, transparent spheres that revolve around the Earth. Eudoxus needed a complex set of 27 interlocking spheres to explain observed celestial motions E.G., need to have 24-hr period =day and 365-day period=year for the Sun

Geocentric-model

Aristarchus of Samos (310-230 B.C.)

Using eclipse data and geometry: Measured relative sizes of Earth, Moon Curvature of Earth’s shadow on Moon during lunar eclipse ⇒ REarth=4×Rmoon Measured distance to Moon (duration of eclipse)÷(1 month)= (2REarth)÷(circumf. of Moon’s orbit) Attempted to measure distance to Sun Need to measure (using time interval ratios) the angle of Sun when Moon is exactly at 1st or 3rd quarter Then use trigonometry and known Earth-Moon distance to get Sun’s distance Meaured angle was too small, but still concluded Sun was very distant from Earth (20×Moon’s distance) and larger than the Earth (5×Earth’s diameter) Note: true distance & size 20×larger http://www.perseus.tufts.edu/GreekScienceduke.usask.ca/~akkerman/ gthought/

Heliocentric model of Aristarchus

Observations implied Sun is much larger than Earth Therefore proposed the first heliocentric model Sun is the center of the Universe Everything goes around the Sun Never accepted by others of his time inconsistent with apparent perception of stationary Earth No apparent shift in stellar positions could be observed over course of seasons Prevailing culture was uncomfortable with the idea that Earth was not central to the Cosmos

More Assumptions

The Moon receives its light from the Sun; The earth is in center of the sphere that carries the Moon. At the time of a Half Moon, our eyes are in the plane of the great circle

that divides the dark from the bright portion of the Moon. At the time of a Half Moon, the Moon's angle from the Sun is less than

a quadrant (90°) by 1/30 of a quadrant [that is, the angle is 90° - 3° = 87°].

The breadth of the Earth's shadow when the Moon passes through the shadow during a lunar eclipse is two Moons.

Both the Moon and the Sun subtend 1/15 of the sign of the zodiac [that is, with 12 signs of the zodiac spaced around the ecliptic, (360° / 12) x 1/15 = 2°].

The Earth is a sphere. The Sun is very far away. The Moon orbits the Earth in such a way that eclipses can occur.

General Method

1. Moon moves (relative to stars) at 360 degrees/month ~ 0.5 degrees/hour.

General Method

2. From duration of lunar eclipse, can infer angular size of Earth as seen from Moon.

General Method

3. Compare to angular size of Moon as seen from Earth.

General Method

4. Aristarchus concluded:

Earth diameter = 3 x Moon diameter (close to true value).

General Method

5. Combine with Eratosthenes measurement of Earth diameter to get Moon diameter in stadia (or km).

i.e. 6300 km

General Method

6. Knowing angular size of Moon (0.5 degrees) and physical size of Moon, find the distance to Moon by:

Q&A

Reference http://www.darkoogle.com http://astronomers.org http://hk.yahoo.com http://www.wikipedia.org http://www.cliffsnotes.com/ http://www.astro.washington.edu/ http://www-ssg.sr.unh.edu/ http://galileoandeinstein.physics.virginia.edu/ http://forum.hkgolden.com

The End