ie-Physics

Experiment II-2

Early Greek Astronomy

Thales of Miletos (b 624 BC, d 545 BC) was regarded as one of the Seven Wise Men of Ancient Greece!  Thales believed that the earth was a disk floating on the world ocean, surrounded by the rotating celestial sphere carrying the stars and other heavenly objects.  Legend (perhaps false?) has it that he predicted the loss of daylight (a solar eclipse) in 585 BC based on either Babylonian or Egyptian astronomical records and by doing so caused the end to the long war between the Lydians and Persians.  Whether the legend was true or not, both the Babylonians and Egyptians did for many centuries made accurate records of such astronomic events and noted their periods of occurrence.

The development of science and religion were parallel, contiguous, and interrelated in many ways.  That development often took place in the same minds!  Pythagoras (←statue at left, b 566 BC, d 497 BC), after studying perhaps with Thales then in Egypt and Babylon, developed a religious order in Croton which viewed the universe as a logically connected, knowable cosmos.  The group chose to live very ascetic, austere, vegetarian lives, partially in response to their belief that human souls could inhabit other people or animals.  Mathematics was an intimate part of their universe.  They used an a priori scientific method which presumed how the universe must be arranged, then looked for confirming evidence.  Their study of mathematics suggested the most perfect geometric shape was a sphere.  So they presumed the earth and all the other major parts of the universe must be spherical.  They then looked for supporting evidence:

• Stars move as if there are attached to a celestial sphere.
  
  
• Both the sun and full moon are circles, the expected visible shape of spheres.
  
  
• If the moon is lit by sunlight, then the phases of the moon would match a half lit sphere viewed from varying angles.
  
  
• During a lunar eclipse, the moon grew dark as if it were passing through the earth's shadow.  The round shape of the shadow during the lunar eclipse was evidence that the earth too was round.
  
  
• When ships sailed to sea, the tops of their masts were the last visible parts.  When the lower portion of the ship went over the horizon, this too was evidence that the earth was a sphere.

So all peoples who learned from the Pythagoreans have known convincing evidence that the earth and all heavenly bodies are spherical.  But the earth itself is not a perfect sphere.  The Pythagoreans established a dualism where the celestial heavens were eternal, divine, perfect, and unchangeable with only perfect circular motion.  The imperfect sublunar earth was endlessly changing, decaying, mortal, dying with irregular, capricious motions.

Plato, famous teacher in Athens, noted that planets seem to wander while all else in the sky moves in the uniform motion of a rotating sphere.  He suggested that the planets must somehow also have perfect circular motion and probably challenged his students to save the phenomena by determining the planets' true motions.

• The stars and all other spheres were carried daily around the earth by the celestial sphere.
  
  
• The Sun moved slowly on its own sphere in the reverse direction, completing one revolution in about 365 days.  The Sun's sphere was tipped 23.5° to the celestial equator so as the sphere rotated the Sun moved gradually north and south of the celestial equator creating the seasons.
  
  
• Each of the other planets was carried daily around by the celestial sphere.  The planets first sphere would carry it backwards past the stars in a period characteristic of that planet.  (Venus and Mercury are faster than the Sun but slower than the Moon.  Mars, Jupiter, and Saturn take longer than the Sun)  a planet's second sphere rotated in the forward direction so when its motion was combined with that of its first sphere, the planet would occasional retrograde.

So the Greeks successfully explained the observed motions of all heavenly objects!  As more accurate observation found small imperfections, they found additional spheres could be added to account for these details.  What remained was for a complete cataloging of all stars, the determination of the sizes of each heavenly body, and their spacings.

Relative Sizes and Spacings of the Earth, Sun and Moon.

1. The Moon receives its light from the Sun;
   
   
2. The earth is in center of the sphere that carries the Moon.
   
   
3. 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.
   
   
4. 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°].
   
   
5. The breadth of the Earth's shadow when the Moon passes through the shadow during a lunar eclipse is two Moons.
   
   
6. 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°].

From these measurements and assumptions, Aristarchos deduced the following:

1. Using the first four, Aristarchos determine the other angles and constructed an accurate scale triangle (conceptualized at right→).  From the diagram he was able to determine that the Sun was 19 times more distant than the Moon.
   
   
2. But since the Sun and Moon appear the same size in the sky, the Sun must be 19 times the diameter of the Moon.
   
   
3. Because the Sun was much further away than the Moon, during a lunar eclipse the size of the Earth's shadow is approximately the same size as the Earth.  Therefore observation five required the Earth to be twice the diameter of the Moon.
   
   
4. From the angular size of the Moon, Aristarchos calculated that the moon's (orbit) sphere was 26 times greater than the Moon's diameter.
   
   
5. Finally, because the Sun is much larger than either the Earth or Moon, Aristarchos proposed the Earth likely moved around the Sun rather than the converse which had been assumed up to this time.

Experiment

While Aristarchos pioneered a procedure which we still find valid, we now know his measurements were inaccurate.  The actual angle between the Moon and Sun at the time of Half Moon is about 89° 50'.  And the Sun and Moon each subtend about 0.5° in the sky.  Use these better measurements to recalculate the relative sizes and distances.  It may be easier to use the law of sines which states the lengths of triangle sides are proportional to the sines of the opposite angles (a / sine A = b / sine B = c / sine C) rather than attempt to construct accurate scale triangles.

We note that the Greeks relied heavily on careful observations, the a priori method, and deductive logic to understand astronomy.  These tools of science are still widely used today.

Finally, record your procedures, measurements, and findings in your journal.  If you need course credit, use your observations recorded in your journal to construct a technical report.

References

• George Sarton, A History of Science: Ancient Science Through the Golden Age of Greece, Wiley, 1952.
• George Sarton, A History of Science: Hellenistic Science and Culture in the Last Three Centuries B.C., Wiley, 1959.
• O. Neugebauer, The Exact Science in Antiquity, Princeton U. Press, 1952.