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Alexandrian Astronomy

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Aristarchus boldly contradicted contemporary wisdom. He pointed out that irregular motion of the planets could be

interpreted much more simply, If all the planets, including the earth were treated as revolving

around the sun. The 54 nestled spheres of Aristotle reduced to 7 circles, a grand

simplification.  It is not the celestial dome which rotates around the earth. The earth spins about its axis. The sun does not move, rise or set. The earth revolves around the sun.

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Mercury

Venus

Earth-Moon

Mars

Jupiter

Saturn

Suin

Mercury

Venus

Earth

Mars

Jupiter

Saturn

Suin

Moon

Earth-Centric to Helio-Centric

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Distance Arrangement

Mercury

Venus

Earth

Mars

Jupiter

Saturn

Suin

Moon

Which of the following takes the longest time to complete its orbit around the zodiac?

(a) Jupiter (b) Saturn (c) Mars (d) Mercury

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The sun-centric scheme could account for an observation not explainable in the scheme of concentric heavenly spheres.

 In the earth-centric scheme, the brightness of

the planets should not change during the year because the distance between all the heavenly bodies and the earth remains consistent.

But if the earth is not at the center, the distance

between the planets and the earth will change, which accounts for the varying brightness in the planets through the year.

Mercury

Venus

Earth

Mars

Jupiter

Saturn

Suin

Moon

Mars is always the same distance from earth

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Mercury

Venus

Earth-Moon

Mars

Jupiter

Saturn

Suin

Mars, Brightness Variations

When does the planet Mars appear brightest to us?

(a) When Mars appears in opposition to the sun

(b) When Mars is near Venus

(c) When Mars appears in conjunction with the sun.

(d) When Mars is farthest from the earth.

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Aristarchus was not just trying to be radical.  He had good reasons to propose the sun-centric theory,

after he made a very important astronomical discovery.

 The sun is much larger in size than the earth.

According to his observations and deductions it was 7 times larger,

Modern measurements show it is 109 times larger in diameter.

 The reason that the sun appears as a small disk in the sky almost the same size disk as the moon is because:

-it is very far away -about 19 times farther away than the moon.  It did not make much sense to Aristarchus that a large

body such as the sun should be orbiting the smaller body, earth.

It was more likely to be the other way around.

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First Quarter

Earth

Sun's raysNew MoonFull Moon

Sun's raysEarth

Moon

degrees

87

The actual time difference is about 20 minutes out of 28 days.

Without an accurate clock, Aristarchus estimated 6 hours out of the 28 days which led him to sun-earth-moon angle of 87 degrees.

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Aristarchus determined the relative size of the sun by applying geometry to astronomy.

Once again we see the role mathematics plays in the description of nature.

1 unit

87 degrees

19 unitsEarth

Sun

Earth-Moon and Earth-Sun Distances

90 degrees

Earth-sun distance = 19 x Earth-Moon distance

Section

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19 h. units

1 v. unit19 v. units

1 h. unit

Eclipse of the Sun

Similar TrianglesDiameter of sun = 19 x diameter of moon

Section

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Moon's Path

Eclipse of the Moon

Appendix and Section: Sun’s diameter = 6.5 x Earth’s diameter

Section

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19th century poet Browning’s exhortation:

“Ah, but a man’s reach should exceed his grasp, Or what is heaven for?”

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Aristarchus failed to convince his contemporaries about the heliocentric model because

a) He reduced the earth to a lowly status

b) His model went against common sense - the earth does not appear to move

c) They could observe no parallax effects due to earth’s motion around the sun

d) His approach demanded a radically new perspective on the universe

e) All of the above

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Earth

A

B

Sun

Paradox:Why is there no parallax?

If earth revolves around the sunangle between same stars

will be different between summer and winter

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Earth

Planet

Apollonius introduced a new idea that reduced the number of required circles from 54 to 14.

The planets do not move on large circles centered around the earth, but on smaller circles,

called epicycles

whose centers move around the earth on larger circles called deferents.

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This type of motion would more simply account for the retrograde motion of the planets.

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Apollonius the Mathematician