Lecture Notes

Arny Chapter 1, Section 2

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Chapter One: History of Astronomy

A model is an explanation of how or why something happens.
The celestial sphere idea is a model of how the cosmos works (in particular, it explains why the stars move the way they do in our sky).
Other models are needed to explain the more complex motions of the Sun, moon, and planets.
We now study the history of such cosmological models, models of the cosmos.


Sec. 1.2: Classical Astronomy

Most of the cosmological models which were to shape the history of astronomy were developed by the ancient Greeks.
[I'm covering the people in chronological order rather than grouped by topic as is done in our textbook.]

Pythagoras (560-480 BC) (another text said 582-507 BC) (you do not have to memorize exact dates)
Geometry (Pythagorean theorem).
Proposed that the Earth is round (for aesthetic reasons the sphere was considered the most perfect shape).
Previously, the favored view was that the Earth was a flat disk, maybe floating in some giant sea.

Geocentric model. Geocentric = "Earth-Centered", Earth at the center of the universe.
Crystal spheres, stars on one sphere, Sun and planets each on their own sphere. Rotation of the spheres explain the motions we see in our sky. [His model had 8 spheres.]

 

Eudoxus (400-347 BC) (another source said 408-356 BC)
Created a geocentric model to explain motions of stars and planets including retrogrades.
[His model had 27 spheres.]


The basic geocentric model works like this: [Full Page Diagram]

The Earth is at the center of everything, see figure 1.26 on page 46.
The stars are affixed to a giant crystal sphere that surrounds the Earth.
This sphere rotates once a day (once every 23h 56m actually) and explains the motion of the stars.

The Sun is on its own crystal sphere, attached to the sphere of stars so that the Sun whirls around us once a day.
But the Sun's sphere is tilted 23.5 degrees and rotates once a year causing the Sun to move slightly slower than the stars across the sky and to move north and south in the sky in the course of a year.

The Sun is like a bug slowly crawling over the spinning celestial sphere, following the path we call the ecliptic.
After a year, the Sun returns to the same place relative to the stars, back to the same constellation.

The Moon is on its own sphere, again attached to the sphere of stars giving the Moon its daily motion.
The Moon's sphere has its own rotation and tilt (27 days, about 5 degrees from Sun).
The Moon is also crawling over the sphere of stars, faster than the Sun does and along a different path.

But how does one explain planets and their retrogrades?
We'll discuss this later.



Aristotle (384-322 BC)
Aristotle did an incredible amount of stuff, far more than mentioned in our text.

Agreed with Pythagoras that Earth was round.
Evidence for this included:
1. The shadow of the Earth as seen on the Moon during a lunar eclipse, the shadow is curved because Earth is round.
2. People living further north or south could see different stars in the north and south part of the sky even when viewing at the same time.

He even explained why the Earth is round.
Aristotle had developed laws of motion.
One law was that "earth"-type materials (rock, dirt, etc.) naturally move towards the center of the universe.
This natural downward motion of earthly material caused that material to accumulate into a ball - the Earth.
This explained why the Earth was at the center and why it didn't move.
Aristotle had other physics laws to explain motions of clouds, planets, etc.

Aristotle made numerous other calculations and measurements.
Aristotle may be the most brilliant man in history!
Certainly he was one of the most influential ever.
Aristotle's ideas were revered for 2000 years past his death.
Unfortunately, many of his ideas were wrong and blind obedience to the teachings of Aristotle hindered scientific progress more than it helped it.

You all know far more about how the universe actually works than did Aristotle.
Still, Aristotle's influence remains today.
For example, when you try to memorize something you try to "learn it by heart", that's because Aristotle taught that memory (all mind activity) takes place in the heart organ.

Aristotle also expanded the geocentric model to improve its accuracy [up to 55 crystal spheres].


Aristarchus (310-230 BC)
Estimated distances and sizes for the Sun and Moon.
Pretty good results, not widely believed.
Because he found that the Sun was so large, he proposed that the Sun was at the center of the solar system (heliocentric model).
His model had Earth moving around the Sun while spinning.
This model also explains the observed motions of things in our sky, this is the model we know to be correct today.

We don't know for sure all the objections and arguments Aristarchus faced, but we know the major arguments against a heliocentric model:

(1) Lack of "stellar parallax"
If, as Aristarchus claimed, Earth is moving, then the phenomenon of stellar parallax should be observed.
As I move around this room, alignments of students change.
As I move closer and further from pairs of students, the apparent angle separating them changes.
"Parallax" is the shifting of angles as an observer moves.

Careful observation of stars revealed no stellar parallax!
This doesn't completely rule out the heliocentric model, if we add an additional assumption that the stars are extremely distant, the lack of stellar parallax can be explained.
This weakened the heliocentric argument - preference is generally and rightly given to models that are simpler and require fewer special assumptions to work. [Occam's Razor]
[Today, with telescopes, stellar parallax has been observed, but it cannot be detected with the naked-eye.]

(2) Not needed
If it ain't broke, why fix it?
Aristarchus was not presenting a better model, just a different one.
His sole inspiration for the heliocentric model was the discovery that the Sun was much larger than the Earth, not everyone believed that result.

(3) Moon left behind?
In Aristarchus's model, Earth was moving around the Sun while the Moon moved around Earth at the same time.
Some argued that a moving Earth would leave the Moon behind.
Since it was unknown then what holds the Moon in orbit, it was impossible to reject this criticism.

(4) People on spinning Earth
If the Earth is a moving, spinning ball, shouldn't people be "thrown off"?
With our modern understanding of physics and gravity, we know Earth is spinning much too slowly to throw people off.
But back then, it was a valid argument.
Earth doesn't feel like its moving, and there was no clear evidence that it was.

(5) Contradicts Aristotle's physics
Aristotle had explained why the Earth must lie at the center of the universe.
If Aristarchus is right, then the revered Aristotle must be wrong.

[Usual end of second lecture.]


Eratosthenes (276-195 BC)
He ran the legendary Library at Alexandria.
Eratosthenes made many astronomical measurements.

[Not discussed in textbook:] [May skip]
He measured the 23 1/2 degrees difference between the ecliptic and celestial equator.
That is, how far north and south the Sun moves relative to the celestial equator.
The ecliptic is the Sun's path against the stars.
The celestial equator is the Earth's equator extended out into space.
That the two are different is why the Sun appears to move further north and south in our sky during the year.
He actually measured the tilt of the Earth!

 

[This is in text, section 1.2, pages 41 and 42.]
Eratosthenes made an ingenious
measurement of Earth's size:
On the summer solstice, sunlight
would shine directly down a well in
Syene (in southern Egypt near the
modern city of Aswan).
See figure 1.22 on page 42.

In Alexandria (800 km north in northern Egypt), the Sun was not directly overhead because of the curvature of the earth.

There a vertical object cast a 7 degree shadow.

Now apply some geometry.
By alternate interior angles,
the angle at the center of the
Earth between the cities will
be 7 degrees.

A complete circle is 360 degrees.
Equate ratios, 7·/360· = 800 km/c
where c = circumference of Earth
Cross-multiply, (7·) (c) = (360·) (800 km).
Divide both sides by (7·),
c = (360·) (800 km)/(7·) = 41,143 km
Circumference of a circle c = 2 (pi) r = (pi) d
r = radius d = diameter pi = 3.14
d = 41,143 km/(pi) = 13,096 km
r = 6548 km
Modern result: d = 12,750 km
This is an extremely good result.
We don't know Eratosthenes true result, he used strange units.
The distance between cities was measured by pacers, people hired to walk from city to city and count steps.


Common Misconception
Christopher Columbus, as it should be clear by now, was not the person to prove Earth is round.
At the time of Columbus, it was common knowledge that Earth was round, everyone knew it!

The debate during Columbus's time was on just how big the Earth was.
Columbus believed Earth was very small, so that the Atlantic Ocean would be a shortcut to India.
Columbus was very wrong, he did not find a shortcut to India but he did discover America (Columbus died still insanely insisting that America was India).

The misconception that Columbus was trying to prove Earth was round can be traced back to the American author Washington Irving in the early 1800s.


Hipparchus (160-127 BC)
[Mentioned only in a footnote on page 47, and later on page 360 of text.]
Star Charts.
Made detailed measurements and records of the positions of the planets, stars, Sun, and Moon.
Comparing to more ancient measurements, Hipparchus made a discovery.
The position of the celestial poles shifts with time.
This effect is called precession.

Today, Polaris is the North Star.
In Hipparchus's time, it was not!
In the future, it will not be!
In terms of Aristotle's geocentric model, Hipparchus had found that the crystal sphere of stars changes how it rotates.
It wobbles!
This is also the reason for the shifting dates of astrological signs.
[Today, we know the true source of precession, it is Earth that wobbles, not the stars.]

Hipparchus improved the geocentric model of Eudoxus.
He added new elements, most notably epicycles. [Or were they developed earlier?]

Claudius Ptolemaeus (Ptolemy) (127-151 AD) [Another source: 73-151 AD]
Extended Hipparchus's studies of the sky.
Refined the Geocentric Model.
Published the model in a famous work, the Almagest.

A thirteen-volume compendium of all astronomical and astrological theories and data.
Ptolemy called it "Megale Syntaxis", meaning "Mathematical Compilation".
Arabic translators called it the "Almagest" meaning "The Greatest" in honor of the stunning wealth of information it contained.

The Geocentric Model as worked out by Hipparchus was not good enough for Ptolemy.
It did not predict planetary motions accurately enough.

Ptolemy tinkered with the model in a controversial way that did make it much more accurate.
We aren't going into the details, we haven't even finished explaining the basic theory, particularly planet motion using epicycles.


Geocentric Model continued: [Full Page Diagram]
[See figures 1.26 and 1.27.]
The stars completely surround the Earth, on a distant crystal sphere.
That sphere rotates about the Earth once every 23h 56m.
The Sun is on a separate, but attached, sphere which has its own additional rotation.
Thus the Sun drifts relative to the background stars.

Okay, this works fine for the Sun and Moon.
It is definitely insufficient to explain the motion of planets.
Most importantly, how can we explain the retrograde motions of planets?

To explain retrograde motions, the geocentric model adds a feature called an epicycle.
Literally, a circle on a circle.

The planet moves along a small circle while that circle moves along a bigger circle (the idea of crystal spheres, particularly for the planets, mostly disappears here??).
Think of it as a long arm moving around with a smaller hand swinging around at the end of the long arm.
This combination of motions looks like this:
See figure 1.27 on page 47.

This is motion relative to the stars.
That is, this determines the rate at which
the planet crawls over the sphere of stars,
that sphere of stars causes the planet to
rotate about the Earth daily.
The planet normally moves this way
(counter-clockwise in figure 1.27, eastward)
relative to the stars but occasionally moves
faster (clockwise, westward) relative to the stars.
The planets always move east to west across our
sky relative to the horizon.

Different planets require epicycles of different sizes.
This idea can explain the various motions of planets!
In the geocentric model, when planets have their epicycles must be correlated to the Sun.

Mercury and Venus appear to swing from side-to-side of the Sun, never very far away.
Hence in the geocentric model, the centers of the epicycles of Mercury and Venus are assumed to stay aligned with the Sun.
Note that this model is starting to become more cumbersome, we keep having to add additional rules.



Ptolemy's model predicted planetary motions pretty well for the next 1400 years.
Pretty well, but never perfectly.
Was the theory wrong or did it just need some new detail?

Now the Dark Ages moved in and astronomy stagnated.
There was some progress in Arabic and Asian lands, but 14 centuries with virtually no new ideas.

End Chapter 1, Section 2 Lecture

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