Chapter 1 -- Scale of the Cosmos, Powers of Ten

This is a good overview chapter, and from it you should take away some sense of the scales of the Universe. In particular, it would be a good idea to know, or at least have a sense of, the following scale lengths:

Earth's diameter	104 km
Sun's diameter	106 km
Earth's orbit	108 km	This is one Astronomical Unit (1 A.U.=1.5x108 km)
Pluto's orbit	1010 km
Nearest Stars	1013 km	One light-year is 9x1012 km. Nearest star = 4.2 ly
Open Cluster Diameter	1015 km
Distance to Galactic Center	1017 km
Nearest Galaxies	1019 km
Clusters of Galaxies	1021 km
Size of Universe	1023 km

Chapter 2: Constellations, the Celestial Sphere, Magnitude Scale

There are 88 official constellations, and about half of these are traditional constellations such as Pisces and Orion. The newer constellations often have fainter stars, or are located in the Southern hemisphere. They also tend to have more "modern" names such as Telescopium , the Telescope.

The brighter stars also have traditional names, such as Sirius , "The Scorched One" in Arabic, and Aldebaran, "The Follower of the Pleiades." While beautiful and historic, the traditional names are not very useful in that they tell us little or nothing about either the location or the brightness of the star. Modern astronomers therefore use a more rational labelling system, in which Sirius is Canis Majoris, "a " meaning that it is the brightest (next would be b) star in the constellation Canis Major. You should know the first few letters in the Greek alphabet: .

Magnitude scale : The Greek astronomer Hipparcos (or Hipparchus), who lived around 160 - 127 BC, developed a method for classifying the apparent brightness of stars. He divided all the stars visible to the naked eye into six classes, which he called magnitudes. The brightest stars were 1st magnitude, the next brightest 2nd, and so on. The faintest naked-eye were 6th magnitude.

An important concept to keep in mind when considering the magnitude scale is that it is logarithmic rather than linear. This means that a first magnitude star is not 50% brighter than a second magnitude star, or even twice as bright: it is about 2.5 times as bright. When modern astronomers adopted the magnitude scale, they modernized it in two ways:

1) A difference of 1 magnitude corresponds to a difference in brightness of 2.512 . This odd number was chosen so that a difference of 5 magnitudes corresponds to a difference in brightness of 100 times .

2) The scale was extended to very bright stars (e.g. Sirius, m = -1.4 ) and very faint stars (visible in telescopes but not to the naked eye)

Mathematically, the magnitude scale can be described as follows:

where IA is the intensity (apparent brightness at Earth) of star A and IB of star B. This can also be written as: Note the change in position of the various I's and m's!

Celestial Sphere : Ancient (and some not-so-ancient) astronomers believed that the earth was surrounded by a crystalline sphere, and the stars were attached to this sphere. The sphere rotated once a day (this kind of motion is called diurnal ), carrying the stars around the earth. We know that this model for the universe is not actually true, but since it appears to be true, it is still a useful model for setting up a reference system for finding objects, which we call the celestial sphere .

From a fixed point on Earth's surface, the sky appears to rotate around an axis that goes through the north and south celestial poles, which are located above the earth's north and south poles. The celestial equator is the projection into the sky of the earth's equator.

The location of the celestial poles and equator in the sky depends on the observer's latitude. For an observer at the north pole of the earth, the north celestial pole is always directly overhead, and the celestial equator lies on the horizon. As the observer moves southward on the earth's surface, the apparent elevation of the north celestial pole drops, and that of the equator rises. (See the figure on page 25 of the text.) For any latitude (except 0 ), some stars will never rise and set, but will always remain above the horizon: the constellations containing these stars are called circumpolar .

Observers in the Northern hemisphere of the earth happen to have a star, Polaris, located quite close to the north celestial pole. Polaris is thus known as the North Star, and its altitude above the horizon is equal to the observer's latitude.

Astronomical Angles: Angles are measured in degrees, minutes (of arc), and seconds (of arc). There are 360 degrees in a circle, 60 minutes in a degree, and 60 seconds in a minute. Don't confuse minutes of arc with minutes of time!

Precession: Hipparcos (the magnitude guy) also compared his observations with those made by a more ancient culture, the Babylonians, and established that the earth's axis doesn't point in a constant direction but slowly circles with time. This phenomenon is similar to what you would observe with a spinning gyroscope: the axis wobbles in a conical motion, known as precession . Because the earth is not a perfect sphere but bulges out at the equator, the Moon's gravity tends to make the earth wobble just like a gyroscope. Since the earth is very massive, the period for it to complete one wobble is very long: about 26,000 years . This means that, several thousand years ago, the earth's axis did not point at Polaris, and no star marked the north celestial pole.

The "Motion" of the Sun: The Sun has two main apparent motions in the sky. The first is its diurnal rising and setting which are, as we know, simply reflections of the rotation of the earth. The second motion is a bit more subtle...

As the earth revolves around the Sun, a process which takes one year , we see the Sun against different background stars and constellations (or we would, if the Sun were not so bright!). For example, in January the Sun lies in the same direction as the constellation Sagittarius (shorthand: the Sun is in the constellation Sagittarius), while by February the motion of the earth around the Sun has changed things enough so that the Sun is in the constellation Capricornus.

This apparent path that the Sun sweeps out in the sky over the course of a year is called the ecliptic. A band 9 on either side of the ecliptic is called the zodiac, and the constellations that the Sun passes through during the year are called the zodiacal constellations. These are the ones that astrologers use to cast horoscopes.

Another way of thinking of the ecliptic is that it is the plane of the earth's orbit around the Sun . Most of the other planets (except Pluto) lie in nearly the same plane, and so they are always found close to the ecliptic, and within the zodiac.



















The Seasons : The earth's axis is not perpendicular to the ecliptic, but is tilted at an angle of about 23.5 degrees . This tilt is responsible for our seasons. Look at Figure 2-14 on page 31 in the text and consider an observer in the Northern hemisphere. In the summer, from his point of view, the Sun rises early, reaches a point very high in the sky, and sets late, while in the winter the Sun rises late (or not at all), doesn't get very far over the horizon, and sets early. The amount of heat delivered to the northern hemisphere is thus much less in the winter than in the summer for two reasons:

1) The sun spends much less time above the horizon in the winter than in the summer.

2) The angle with which the Sun's rays hit the surface is much less steep in the winter than in the summer, so the incoming energy is spread out over a much larger area. See Figure 2-15 on page 32.

There are four locations along the ecliptic that are associated with the seasons. The vernal equinox is where the Sun crosses the celestial equator heading north, and is thus the first day of spring, while the autumnal equinox is where the Sun crosses the celestial equator heading south, and is thus the first day of fall. Note that both equinoxes occur where the celestial equator crosses the ecliptic. Midway between the equinoxes are the solstices (summer and winter), which define the beginning of summer and winter. Note that all of this is from the point of view of someone in the northern hemisphere: a person living in Australia, for example, has all of his seasons reversed with respect to ours.

Remember that seasons are NOT due to variations in the earth-Sun distance! (If they were, how would you explain the reversal of seasons in the southern hemisphere??) In fact, the Sun is at perihelion (closest approach to the Sun) on about January 2, and at aphelion (farthest distance from the Sun) in the first week of July. Since the earth's orbit is nearly circular, these distances only vary by about 2% anyway.

Motion of the Planets: Planet comes from the Greek work meaningwanderer . As noted above, all of the planets but Pluto can always be found near the ecliptic. Remember, "Mother Very Easily Made Jam Sandwiches, Using No Peanutbutter" for the order of the planets, outward from the Sun: Mercury, Venus, Earth, Mars, Jupiter Saturn, Uranus, Neptune, Pluto.
Just be sure you remember that Mercury is hot -- close to the Sun. Also, at the moment, Pluto is closer to the Sun than Neptune, but things will go back to normal near the end of this century.

As seen from Earth, Mercury and Venus can never move far away from the Sun.This is because their orbits are smaller than the Earth's. Draw it and see! These two planets, known as inferior planets because their orbits lie inside the earth's orbit, can therefore be seen only around sunrise and sunset, when they are traditionally known as morning stars or evening stars. They don't both have to be "morning stars" at the same time, though, since their orbits have different periods.

F.Y.I. Only (not on test): Climate and Ice Ages: In the past, the earth has experienced many periods of glaciation, when the average temperature drops and sheets of ice engulf much of both hemispheres. The process seems to be periodic, in the following way:

1) There are Ice Age periods occurring about every 250 million years. The latest started only about 3-5 million years ago. However, just because we are in an Ice Age does not mean that there are always sheets of ice covering the earth. Within an Ice Age, there are

2) periods of glaciation , occurring about every 40,000 years and lasting about 20,000 years. Between these periods, there is an interglacial period , when the ice sheets melt back. We are living in such a period.

There are many possible explanations for the Ice Age/glaciation phenomenon. The most plausible are:

1) The changing shape of the earth's orbit. The ellipticity of the earth's orbit varies with a period of about 93,000 years.

2) Precession of the earth's rotational axis, with a period of about 26,000 years

3) The changing inclination of the earth's axis. The inclination (now 23.5 degrees) varies from 22 to 28 degrees with a period of about 41,000 years.

4) Passage of the earth and Sun through giant molecular clouds located around our Galaxy, causing apparent dimming of the Sun. It is an interesting conincidence that the period of our Sun's revolution around the galactic center is about 250 million years.

Probably the true cause is a combination of all of the above.=====end of FYI section =====

Chapter 3: Lunar Phases, Tides, and Eclipses

Chapter 4: History of Astronomy: Greeks and Others

Archaeoastronomy is the study of astronomy as practiced by ancient peoples for whom there is no surviving written record of observations. The Caracol at Chichen Itza, Stonehenge, the Bighorn Medicine Wheel, the Moose Mountain Wheel, and the Sun Dagger in Chaco Canyon are all good examples of archaeoastronomy sites. The stone-age sites in the New World are not older than written records of observations in the Old World (including China), so the term really refers to astronomy carried out at a primitive level of technological advancement in the local society, as opposed to a specific number of years ago. Thales of Miletus was making observations and predictions centuries before the Moose Mountain Wheel was built.

In the old world, Thales was followed by several other mathematicians and philosophers.Aristotle was noteworthy among these for his model of the Universe (actually, the solar system, although they didn't know the difference at the time) -- with Earth at the center -- called the geocentric model (wrong) and his observation that the curved shadow in a lunar eclipse meant the Earth had to be round (right). A very clever fellow named Eratosthenes used a stick and the well at Syene to determine the Earth's circumference , about 100 years after Aristotle's death.

The geocentric model failed to explain many subsequent observations of planetary motions and had to be more and more complicated to get the theoretical positions of planets at any given time to agree with the observations. The kludge-meister of the geocentric model was Ptolemy (a.k.a. Ptolemaeus), who had a fabulously complex geocentric model with epicycles, deferents and equants . The Ptolemaic system ruled astronomy for more than 1300 years! Copernicus finally came out with his revolutionary book (de Revolutionibus Orbium Coelestium ) placing the Sun at the center. This heliocentric view, because the fundamental assumption was correct, finally overthrew the geocentric system. But not without a fight!

Galileo took up the banner where dead Copernicus had dropped it, and used a new Dutch invention -- the telescope -- to look at heavenly objects. He discovered the four large inner moons of Jupiter (called the Galilean moons in his honor), and observed the phases of Venus. This observation really got him into hot water with the Holy Roman Empire, because they were sticking with the geocentric theory, and you can't have phases such as a gibbous Venus and a crescent Venus unless Venus goes around the Sun (work it out with a ball and a light source). He also had the cheek to observe sunspots on the Sun and craters on the Moon, evidences of imperfection from the point of view of that time (when many many people had terrible skin due to smallpox; they had a real smooth-skin fixation and considered smoothness evidence of perfection. Heavenly bodies were supposed to be perfect).

Tycho Brahe , in Denmark, had been naked-eye observing for many years before Galileo was born, and his work (moved to Prague by a change in patrons) was turned over to his assistant, Johannes Kepler , on his death. Shortly after that, the telescope was invented, and so Kepler really went into high gear. He observed the motions of the planets even more accurately than Tycho had been able to, but he had all of Tycho's data giving him a long timeline to work with. He came up with Kepler's three laws of planetary motion :

1. Orbits are ellipses , with the central body at one focus of the ellipse.
   
2. When the orbiting body is closer to the central body it moves faster. At the far end of its orbit it moves slower. A line from the central body to the orbiting body would sweep out equal pie-slice-shaped areas in equal times.
   
3. P²=a³