Astro 105: The Milky Way

Lecture II: Childhood
The Sky
The Early Greeks

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World Views are just social constructions and they channel the search for facts. But facts are found and knowledge progresses however fitfully.
steven jay gould
 
 

Do you agree with this?
(What is a fact?)
(Are facts independent of theories?)

 

Our first goal today is to understand the raw material that astronomical world views begin with. That is, we are going to spend a little time thinking about what's in the sky and how it behaves (facts).

We then are going to look at the early attempts of western culture (the Greeks) to make a ``model'' of these ``facts''.

The Greeks did not have the first astronomical world view but they were the first to try and construct mathematical (geometry) representations of what was in their heads that could be tested against what was seen.
 

 


The Sky

  • In the modern world we don't often see all that is in the sky. (Light Pollution).
  • Imagine a world without artificial light.

 




  • Until a few hundred years ago that is what people knew. The sky and its inhabitants was far more present for them than for us.


 

  • They watched and noticed how things changed.
    • Individual stars didn't move but the whole tapestry did.
    • The saw that there were basic daily, monthly, seasonal, and yearly changes in the patterns of stars including the sun.
    • There were also things that wandered across the sky in regular patterns (the planets).
  • Somethings appeared out of nowhere either often (meteors) or rarely (comets).
  • If you don't have TV the whole pageant is pretty startling.

Every culture tried to make sense of it.

There are just 3 motions we will focus on.

1. Daily Rotation of the Stars/Sun  



 

Explanation : As the Earth spins on its axis, the sky seems to rotate around us. This motion produces The concentric arcs traced out by the stars in this time exposure of the night sky. In the middle of the picture is the North Celestial Pole (NCP), easily identified as the point in the sky at the center of all the star trail arcs. The very short bright trail near the NCP was made by the star Polaris, commonly known as the North Star.
 

 

Above is one way of representing the sky as a "celestial sphere" with a north and a south pole. We are standing at mid-latitude in the northern hemisphere. With this picture it should be easy to see how the rotation of the Earth produces the star tracks seen in the photo above.

 


2. The Yearly Motion of the Sun

 

The sun traces a yearly path through the sky. You notice this if you were to go out and check where the sun was at the same time each day: say noon.
 

  • Summer - sun is high
  • Winter - sun is low
  • At summer and winter solstice the sun is at its highest (lowest) point.
  • At the autumn and spring equinox the sun is at the mid-points in its up and down oscillation


 

 

The point where the Sun rises on the horizon moves North and South as the year progresses also moves.  This is another aspect of the Sun's yearly motion.

A point on the horizon also makes a good marker for this.
 

 


 

 

Why does this happen? Its because the Earth's rotation axis is tilted compared to the plane of its orbit (The axis currently points to the North Star).

As the Earth swings around the Sun the Northern Hemisphere (us) is either tilted more towards, or more away from, the sun. This makes the sun appear to move up and down in the sky.
 
 

This is also the reason why we have Seasons!

Q. What is the causal relation between the Earth's tilt and the Seasons?

?

3. Retrograde Motion of Planets

From watching the sky people noticed that certain bright objects moved against the fixed background of stars. These objects were called wanderers or planets. This motion was regular, repeating itself (different planets had different periods for repeating their motions).

One aspect of planetary paths was very strange: a start-stop loop called retrograde motion.
 

 

Mars Retrograde Motion

·     Planets change directions

·     Planets appear to brighten

·     Planets change speed

As we will see the retrograde motion of planets presented one of the most difficult issues for early "model-building" astronomers to solve.
 
 

Angles and Size and Distance

Angles are the basic unit of measure in astronomy. Everything appears on the "bowl" of the sky.

How "big" something is, how far two things are apart - these are measured as angles.

Remember there are 360 degrees (360o ) in a circle.

The moon, for instance, is about .5o across (that's its angular diameter). Your little finger at arms length covers about 1o.

But your finger is a lot smaller than the moon so there is a basic problem with only knowing angles.

The "little kid squish" effect

So how do we get useful physical information from angles?

 

 

Distance, size and angles

SMALL ANGLE FORMULA
a = angle in arc seconds
(1 degree = 3600 arc seconds)

a = 206,265 (linear diameter) / (distance)

If I know somethings distance from me, and I measure it's angular size on the sky I can rearrange the formula above and solve for its real size.

Example:

Car Headlights sperated by .5 meter  (L = .5 m)
Car is 1 kilometer away (d = 1 km = 1000 m)

a = 206,265 (.5 m)/(1000 m) =  103 arc seconds.

Greek Astronomy

"One thing only I know and that is that I know nothing"
"For man, the unexamined life is not worth living"
socrates

The Greeks were not the first to watch the sky. Every culture did so and many built astronomical observatories to both watch and MEASURE the Celestial changes.
 
 


Stonehenge, an observatory in pre-historic Britain

 

The Babylonians (1600 BCE) compiled star catalogues and began making long term records of planetary motion.

Long-Term  Project: Saturn repeats its motion every 29.46 years. That was about as long as the average lifespan at the time.

This required State support .

You have to pay priests year after year to keep the effort up. The state supported this kind of astronomy because of the need for accurate calendars and astrology. The calendars were for farming and commerce. The astrology was part of the State supported religion.

The angular size and duration of retrograde loops were recorded and found to vary from cycle to cycle.

With years of observations on clay tablets PREDICTIONS concerning planetary motion could be made.
 

"Every X years Planet Y will experience Retrograde Motion"

 

What Babylonians didn't do was explain the cycles with a physical model.

"It was as it was"  - cosmic order was arranged by divinity.


 

Greek philosopher/scientists believed the world was rationally ordered.

They constructed MODELS of the world.

What is a model?

  • Something you built with sticks and paper?
  •  
  • Architect's Model of a Building (Shapes)?

Something you build out of mathematical equations!

Geometry = representations of shapes

  • The Greeks believed there was a harmony and unity inherent in the world which was expressed in geometry.
  • It was an object of beauty .

 

 

Geometry <-> Beauty <-> Truth



 

"Let know one without Geometry enter here"

inscription over entrance to Plato's academy

"All things are numbers"

Pythagoras

 

 

The first Greek models of the heavens were GEOCENTRIC . (centered on Earth)

They incorporated spheres and spherical motions into their models of the heavens because these were held to be the most harmonious, the most beautiful ( Pythagorus 6th cent. BCE)

Plato (427-347 BCE) gave the Greeks philosopher/scientists a homework problem.

"Save the appearances" - using only spheres and uniform spherical motions produce a model which reproduces all the patterns seen on the sky.
 

Aristotle (384-322 BCE): The changeable Earth (4 elements) was at the center of an unchanging crystalline starry sphere (the empyrean). The sun, moon, and planets moved around the Earth.

Aristotle's universe had a physics that went along with it: Natural Motion

  • The elements earth and water always fell towards Earth
  • The elements fire and air always rose to the sky


 

Aristotle's Physics lasted for 1500 years! In medieval Europe he was
known simply as THE Philosopher.

Why?

"A model gains credibility when it explains observations in a natural way"

Aristotle's model explained two important FACTS

  • The spherical shape of the Earth
  • The lack of stellar PARALLAX

PARALLAX = the apparent shift in position of a body because of motion of the observer.

 

 

In a HELIOCENTRIC (sun centered) model, the movement of the Earth around the sun would naturally produce a shift in nearby stars relative to distant ones.

 

 
(It is, actually, a little different if the stars are all confined to spherical shell as in Aristotle's model but the basic idea is the same).

Since no Parallax was observed most astronomers concluded that Aristotle was right.

Why was no parallax observed?

WARNING! Don't Laugh at Other Peoples Physics (World views)

A few centuries from now people are going to think we were pretty dumb too!

There were some Greeks who were so far ahead of their time its astonishing! Below is a woefully inadequate list of their accomplishments.

Democritus: taught that atoms and empty space make up all existing matter, that worlds such as the earth evolved and decayed, that there were many other worlds, some inhabited, some not and that the milky way was composed of millions of unresolved stars.

Aristarchus : developed a fully heliocentric model!

Eratosthenes: used to length of shadows falling at different latitudes to calculate the radius of the Earth. This was an amazing piece of observation and math.

Hipparchus: performed careful measurements of positions and brightness of stars (the magnitude system). He developing excellent catalogues which would be used and added to for centuries.
 

 

Question: Where are the Women?
Answer: They are there. They just don't "appear" in the record (Hypatia).

Ptolemy - The Almagest

In the beginning of the first millennium an astronomer, Claudius Ptolemy, developed a geocentric geometrical model of the sky that was to last for more than 1000 years.

("Almagest" is arabic for the Greatest. That is what Islamic astronomers called Ptolemy's book. It was muslim world which kept astronomy alive during Europe's dark ages)
 
 


 

We don't know when he was born but from his observations we can deduce that he worked sometime around 125 ACE.

Ptolemy's model was built on earlier work by Hipparchus. He used a number of geometrical "devices" to accomplish Plato's task of saving the appearances.

The most difficult observations to recover were:

  • the retrograde motion of the planets
  • their variable speed of the planets in their orbits

To get things to work Ptolemy began with planets moving on circular orbits around the Earth but he included:

Epicycles : a small circle whose center lies on a larger one (the deferent ). The planet swings around on the epicycle while the center of the epicycle is carried around the deferent. In this way the retrograde motion could be explained.

 

Eccentrics: a point offset from the center of circular motion. By offsetting the Earth from the center of the circular motion it would appear that planets moved faster at some times of the year than others.

Equant: A point displaced from the center of the circular orbit around which the motion of the planet really was uniform. This helped get the varying speed of the planets better than just using eccentrics.
 

 

 


 
 
 

Epicycle Movie

By varying the size of the epicycles and the speed of the motions, Ptolemy was able to build a complete model for the motion of the planets that did a very respectable job of predicting observations.

Note that Ptolemy never worried about forces: all the spheres (circles) in his model were real and their rotation was a natural state.

The Size of Ptolemy's Universe

Ptolemy measured the distance to the sun and moon in units of Earth radii. (the Earth's radius = 6,378 km = 3,986 miles)

By nesting his spheres (the deferents) he got the following numbers:

  • Earth-moon distance 59 Earth radii = 376,302 km (very close to real value)
  • Earth-stars distance 20,000 Earth radii = 1.8x108 km (way way off! real value ~ 1015 km)

This is a tiny universe!