Unit 1: The Sky vs. Space, Lunar Motions, Solar Motions, and Celestial Coordinates

Babylonian Universe: How the sky looks

When you go out and look on a clear night, the Earth seems flat (well, hilly, but not like a big ball) with a dome of the sky overhead. The recorded history of Western astronomy begins in Mesopotamia (in modern-day Iraq), specifically in Babylon, so we start with the Babylonians' take on the sky. They thought the universe was just what it looks like, flat, with a dome called the firmament.

Certainly the Babylonians weren't the only or the first culture to believe in a sky dome--we just have their written record. 
 

The concept is completely wrong in 3-d space, yet astronomers have retained the idea of the dome overhead as the "celestial sphere," a useful tool for describing the appearance of the sky.
 

We will return to the celestial sphere later. For now it is worth noting that over the course of a night, the whole sky seems to be revolving around the north celestial pole. From our view from the center of the celestial sphere (and you are always in the center!) the stars, moon, planets and sun turn counterclockwise together around the pole, rising in the east and setting in the west (except for the stars up north that just spin around the pole). The moderately bright star Polaris is very close to the north celestial pole, and is always hanging within 1 degree of true north.

There are a lot of ways to draw the celestial sphere.  I like to use it to describe the appearance of the sky at night with the horizon shown horizontal.  The textbook Schoolcraft uses currently (2004) uses the celestial sphere to illustrate other concepts, and you may notice that it places the celestial equator horizontally.  These are both correct, but you should be aware of the difference.

Ancient Greeks: Figuring Out Space in 3-D

Our earliest record of humans decyphering the sky in three dimensions are the writings of ancient Greek scholars. In this unit we we look at what they got right. In unit 2 we look at what they got wrong.

Aristarchus (ca. 300 BC), Greek

Aristarchus applied geometry, light and shadow to understand the relation of Moon and Earth in three dimensions.

Most ancient people were much more aware of the moon's phases than modern inhabitants of technological societies.  Moonlight was an important source of illumination before the excessive street lighting of the 20th century rendered night a mere natural curiosity.  Any ancient person knew the moon's phases intimately, but since most modern American students don't, here's a summary:

New
.....0 days
.....Up all day, not visible (rises sunrise, sets sunset)
Waxing Crescent
.....1-6 days
.....Visible early evening
First Quarter
.....7-8 days
.....Visible afternoon and evening (rises ~noon, sets ~midnight)
Waxing Gibbous
.....9-14 days
.....Visible late afternoon and evening
Full Moon
.....15 days
.....up all night (rises sunset, sets sunrise)
.....Some full moons have clever names--like the Harvest Moon in the fall, and a "blue Moon" when two full moons fall in the same month.
Waning Gibbous
.....16-22 days
.....Visible late night and morning
Last Quarter
.....22-23 days
.....Visible mornings (rises ~midnight, sets ~noon)
Waning Cresent
.....24-29 days
.....Visible just before dawn
New
.....30 days
.....Up all day, not visible (rises sunrise, sets sunset)

Aristarchus knew that these phases represented the play of sunlight on the spherical moon as it traveled around Earth.

 

Notice that the full moon happens when the sun is at your back.  Looking at this diagram, you'd think that the Earth would block the sunlight from reaching the Moon on a full moon.  This doesn't really happen often because the scale of the diagram is off, and because all this stuff happens in three dimensions.  Usually the Moon misses the Earth's shadow, but roughly twice a year, the Moon does pass into the Earth's shadow, and we see a lunar eclipse.

Lunar eclipses reveal relative Moon/Earth size

--Aristarchus saw that the shape of Earth's shadow is a uniform curve for all eclipse geometries--Earth must be spherical

--He also saw that the inner part of the shadow (called the umbra) was about three times the size of the Moon.  Taking into account some fuzziness in the Earth's shadow, it is really about 4 times the size of the moon.  This means that the moon is about 1/4 size of Earth
 

Here is a collection of five photographs of three lunar eclipses.  They have been placed on a black background so that they are in the correct positions relative to the Earth's shadow.  The circular shape of the umbra, or deep shadow is obvious.  Because these shots were taken with different exposures, the fuzzy outer shadow, or penumbra, is obvious in some photos and not in others.  The photo in the middle was exposed for 30 seconds to show the dim red light that refracts around the Earth to illuminate the shadowed moon during a total lunar eclipse.

Lunar Phases indicate that the Sun is much farther than the Moon

Because the angular distance (angle between lines of sight) between the sun and moon is just about exactly 90 degrees at first quarter and last quarter, we can tell that the direction to the sun is the same for the moon and earth, meaning the Sun is much farther away than the moon.

 

Aristarchus underestimated the distance.

 

But at least he came up with some sort of sensible 3-d concept of the nearest part of the Solar System, using nothing more than the eye and the brain.

 

Eratosthenes (ca. 200 BC), Greek living in Alexandria Egypt:

Eratosthenes used shadows to calculate the size of the Earth.  He heard of a well in the town of Syene, up the Nile River in Egypt, where one could see the reflection of the sun at nune on June 21, meaning that the sun was directly overhead.  This never happened at Alexandria.  Eratosthenes realized he could use this fact to measure the size of the Earth.

 

The Sun was vertically overhead in Syene, Egypt on June 21
The Sun 1/50 of a circle (7 degrees) from vertical at Alexandria
Eratosthenes concluded that Syene is 1/50 of Earth's circumference from Alexandria
 

Eratosthenes hired a runner to pace off the distance to Syene. He reports a distance of 5000 stadia
(1 stadium is length of stadium track--but which stadium? Experts on ancient Greece know of two possible standards. Either 10 stadia = 1mile or 8 stadia = 1 mile)
1/50 of a circle = 5000 stadia.
full circle = 250,000 stadia
Depending on the definition of stadium, he was right on or 20% too big.
The correct value for Earth's circumference is about 25,000 miles
The Earth's diameter is circumference/pi = 25,000 / 3.14 = about 8000 miles
From Aristarchus, Moon's diameter = Earth's Diameter / 4 = about 2000 miles

Angular Size, Actual Size, and Distance

To complete our Earth-Moon system understanding, we need relationship of angular size, actual size, and distance

Definition of anglular size

"Angle between lines of sight to opposite sides of object"

 

Informally, angular size measures how large something appears, measures in degrees. You can use a protractor in a diagram, but it's useless under the real sky. A cross staff can get you better measurements, but for this class, you can use nature's cross staff.
 

You can use a fist at arm's length to measure angular size and angular distance--1 fist is about 10 degrees, one finger about 2 degrees.
 

Definition of actual size

Size of the object you are looking at, measured in meters, feet, kilometers, miles

Definition of distance

Distance from observer to object, measured in meters, feet, kilometers, miles

The general relationship is summed up by

Angular size = 57.3 degrees x Actual size / distance

This equation (aside from the 57.5 degrees part, which you don't need to remember) is just a summary of relationships you've known since you were two.

For a given distance:
Larger actual size gives you larger angular size
Smaller actual size gives you smaller angular size
(you know that bigger things look bigger!)

For a given actual size:
Greater distance gives you smaller angular size
Shorter distance gives you larger angular size
(you know things look smaller when they are farther away!)

For a given angular size
Greater distance implies larger actual size
Shorter distance implies Smaller actual size
(think about this one for a minute. hold a toy close enough to your eye, and it fills as much of your vision as the real thing)

To find distance to moon, rearrange formula:

Angular size (in degrees) =(actual size x 57.3) / distance

Distance = (actual size x 57.3) / angular size

Eratosthenes and Aristarchus give us 2000 miles for the moon's diameter. We can measure an angular size of the moon of about 1/2 degree.

Distance = (2000 miles x 57.3) / 0.5 degrees

Distance = about 230,000 miles

More precise values for actual angular size give a distance to the moon of 240,000 miles.

Find a globe (or a ball) to represent the Earth , and find a ball (or fruit) to represent the Moon, about a quarter the size of the Earth. Set up your moon about 30 Earth diameters away. Is this the relationship you expected? You now have all the knowledge of space available to the ancient Greeks.

Part 1 A of the course covers the ancient greek discoveries of sky and space--You Are Here
Part 1 B of the course is a craft project--we build a scale model of the Solar System!
Part 1 C of the course covers celestial coordinates and motions
Part 1 D of the course is Arts and Crafts again--we make a planisphere (star finder)

More to come!