Introduction

For the medieval astronomer/astrologers the Universe was a small place, the Earth was the center, and events in the heavens were orderly and designed to benefit humanity. The only change that was deemed appropriate was cyclic change such as the (mostly) orderly motion of the planets on the sky or the daily travel of the sun around the heavens, for cyclic change returns one to the starting point and so is not really change at all. In Europe of the Middle Ages this belief was elevated to the level of religious dogma, and one dared challenge this worldview at considerable personal peril.

However, the Copernican revolution began a long process that changed completely our perception of the heavens and humanity's place in the Universe. Beginning in the 16th and 17th centuries and continuing until today, observations and increased theoretical understanding demonstrated that the Universe is enormous, that it has existed for periods that dwarf human lifetimes, and that we do not occupy the center of the Universe (for there is no center). Probably less appreciated is a change with antecedents in events observed hundreds of years ago, but that has accelerated at breathtaking pace over the last 30 years. As observational astronomy at wavelengths other than visible light (Radio-Frequency, X-Ray, Gamma-Ray, Ultraviolet, ...) has become more commonplace, we have begun to appreciate that the Universe is party to scenes of unimaginable violence. Far from an orderly stage for stately and gentle physical processes, the Universe at various times and various places undergoes violent cataclysms releasing energy on a scale to numb the mind of even the most analytic physical scientist.

The medieval natural philosopher would perhaps have had even greater difficulty accepting this insight than accepting the Copernican hypothesis that the Earth was not the center of the Universe, for it would have destroyed the strongly held belief that the Universe existed as a nurturing cocoon for humanity. However, it is supremely ironic that these violent processes that on the surface seem hostile to the place of humanity in the Universe are in fact essential to the production of the present Universe. In particular, our modern understanding is that there would be no matter as we know it, no life as we know it, and no humanity to contemplate these questions, in the absence of violent processes that would, of themselves, destroy all life within countless light years.

The development of these ideas has been a truly remarkable odyssey in the history of human thought. These lectures represent an introduction to how this modern worldview has come about, and a survey of the often beautiful, sometimes astonishing, but never dull, Universe described by these evolving ideas.

Time and Scale

Our modern perception of the Universe has been drastically reshaped from the corresponding perception of only a few hundred years ago.

Changing Perceptions of the Universe

Our understanding of the Universe with respect to it size, temporal duration, the kinds of events that take place in it, and the kinds of objects that it contains has undergone serious revision in the last few centuries:

• Only in the last 400 years or so have we realized that the earth is not the "center", and that the Universe is immense.
  1. The Sun would hold 1.3 million Earths.
  2. There are 200 billion "Suns" in a galaxy like our own Milky Way Galaxy.
  3. Astronomers can see billions of galaxies.
  4. We don't know whether the Universe has an "end" or not; we are not completely sure even of the full meaning of the question.

• Only in the last 50 years have we realized that the Universe is not static.
  1. The entire Universe is expanding.
  2. Events of fantastic violence take place in the Universe.

• In the last half-century we have come to believe that the Universe contains objects that are truly bizarre as measured in human terms.
  1. Neutron Stars and Pulsars
  2. Black Holes
  3. Quasars
  4. Exploding and Colliding Galaxies

• Only in the last 200 years have we begun to appreciate the age of the Universe.
  1. The Universe is probably 10-20 billion years old.
  2. Our Solar System is probably 4-5 billion years old.

A Sense of Scale

If the solar system were the size of a table, the Andromedae Galaxy would lie at 10 times the distance to the moon and the most distant galaxies would lie at 60 times the distance to the Sun.

A Sense of Time

If we were to compress the time since the Big Bang into one year, and make the time of the Big Bang January 1,

• The Earth was formed in mid-September.
• The mammals appeared on December 26.
• All human prehistory (from the first known stone tools) and history have occurred in the last 1/2 hour of New Year's Eve.

The Celestial Sphere

Much of our initial discussion of Astronomy will concern the motion of objects in the sky. Therefore, we shall introduce some terminology and a coordinate system that allow us to specify succinctly the location of particular objects in the heavens. For a more extensive discussion, see Astronomy without a Telescope.

The Celestial Sphere

It is useful in discussing objects in the sky to imagine them to be attached to a sphere surrounding the earth. This fictitious construction is called the celestial sphere. At any one time we see no more than half of this sphere, but we will refer loosely to the imaginary half-sphere over our heads as just the celestial sphere (see adjacent figure).

The point on the celestial sphere that is directly over our heads at a given time is termed the zenith. The imaginary circle passing through the North and South points on our horizon and through the zenith is termed the celestial meridian. We will introduce additional terminology associated with the celestial sphere later. Motion in the SkyIt is clear after only minimal observation that objects change their position in the sky over a period of time. This motion is conveniently separated into two parts:

1. The entire sky appears to turn around imaginary points in the northern and southern sky once in 24 hours. This is termed the daily or diurnal motion of the celestial sphere, and is in reality a consequence of the daily rotation of the earth on its axis. The diurnal motion affects all objects in the sky and does not change their relative positions: the diurnal motion causes the sky to rotate as a whole once every 24 hours.

2. Superposed on the overall diurnal motion of the sky is "intrinsic" motion that causes certain objects on the celestial sphere to change their positions with respect to the other objects on the celestial sphere. These are the "wanderers" of the ancient astronomers: the planets, the Sun, and the Moon.

Diurnal motion at different latitudes

Celestial Coordinate Systems

We can define a useful coordinate system for locating objects on the celestial sphere by projecting onto the sky the latitude-longitude coordinate system that we use on the surface of the earth. As illustrated in the adjacent figure, this allows us to define "North and South Celestial Poles" (the imaginary points about which the diurnal motion appears to take place) and a "Celestial Equator".

The figure illustrates that these imaginary objects are the exact analogs of the corresponding imaginary objects on the surface of the earth. Thus, we shall be able to specify the precise location of things on the celestial sphere by giving the celestial analog of their latitudes and longtitudes, or something related to those quantities.

The "Road of the Sun" on the Celestial Sphere

Another important imaginary object on the celestial sphere is the "ecliptic" or "Road of the Sun", which is the imaginary path that the Sun follows on the celestial sphere over the course of a year. As the diagram at left indicates, the apparent position of the sun with respect to the background stars (as viewed from Earth) changes continuously as the Earth moves around its orbit, and will return to its starting point when the Earth has made one revolution in its orbit.
Thus, the Sun traces out a closed path on the celestial sphere once each year. This apparent path of the Sun on the celestial sphere is called the ecliptic. Because the rotation axis of the Earth is tilted by 23.5 degrees with respect to the plane of its orbital motion (which is also called the ecliptic), the path of the Sun on the celestial sphere is a circle tilted by 23.5 degrees with respect to the celestial equator (see diagram at right).

The ecliptic is important observationally, because the planets, the Sun (by definition), and the Moon are always found near the ecliptic. As we shall see later, this is because all of these objects have orbits that lie nearly in the same spatial plane.

East and West on the Celestial Sphere

It is useful to define east and west directions on the celestial sphere, as illustrated in the following figure.

Thus, objects to the west of the Sun on the celestial sphere precede the Sun in the diurnal motion of the celestial sphere (they "rise" before the Sun and "set" before the Sun). Likewise, objects to the east of the Sun trail the Sun in the diurnal motion (they "rise" after the Sun and "set" after the Sun). Generally, one object is west of another object if it "rises" before the other object over the eastern horizon as the sky appears to turn, and east of the object if it "rises" after the other object.

Celestial Coordiante System

It is useful to impose on the celestial sphere a coordinate system that is analogous to the latitude-longitude system employed for the surface of the Earth. For a more extensive discussion, see Astronomy without a Telescope.

Right Ascension and Declination

This coordinate system is illustrated in the following figure (for which you should imagine the earth to be a point at the center of the sphere).

The celestial coordinate system

In the celestial coordinate system the North and South Celestial Poles are determined by projecting the rotation axis of the Earth to intersect the celestial sphere, which in turn defines a Celestial Equator. The celestial equivalent of latitude is called declination and is measured in degrees North (positive numbers) or South (negative numbers) of the Celestial Equator. The celestial equivalent of longitude is called right ascension. Right ascension can be measured in degrees, but for historical reasons it is more common to measure it in time (hours, minutes, seconds): the sky turns 360 degrees in 24 hours and therefore it must turn 15 degrees every hour; thus, 1 hour of right ascension is equivalent to 15 degrees of (apparent) sky rotation.

The point on the ecliptic where the Sun is most north of the celestial equator is termed the Summer Solstice and the point where it is most south of the celestial equator is termed the Winter Solstice. In the Northern Hemisphere the hours of daylight are longest when the Sun is near the Summer Solstice (around June 22) and shortest when the Sun is near the Winter Solstice (around December 22). The opposite is true in the Southern Hemisphere. The term solstice derives from a root that means to "stand still"; at the solstices the Sun reaches its most northern or most southern position in the sky and begins to move back toward the celestial equator. Thus, it "stands still" with respect to its apparent North-South drift on the celestial sphere at that time.

Traditionally, Northern Hemisphere Spring and Fall begin at the times of the corresponding equinoxes, while Northern Hemisphere Winter and Summer begin at the corresponding solstices. In the Southern Hemisphere, the seasons are reversed (e.g., Southern Hemisphere Spring begins at the time of the Autumnal Equinox).

Right Ascension and Declination for Sirius

This tells us that when the vernal equinox is on our celestial meridian, it will be 6 hours and 45 minutes before Sirius crosses our celestial meridian, and also that Sirius is a little more than 16 degrees South of the Celestial Equator.

Thus, the directions get reversed: moving to the right from the vernal equinox in the first diagram will look like moving to the left as viewed from its center, which is the perspective of the second diagram (that is, the actual view of the sky from Earth). That direction, by convention, is chosen to be the positive direction for right ascension.

Timekeeping

Historically, the regular motion of objects in the sky served as the basis for timekeeping. The diurnal motion of the sky caused by the rotation of the Earth on its axis defined the day, the year was defined by the motion of the Earth on its orbit about the Sun, and the month was defined in relation to the revolution of the Moon about the Earth. Although precise modern timekeeping is done electronically, many of the details and the terminology of timekeeping remain rooted in its astronomical heritage.

Sidereal Time and Solar Time

In using the sky for timekeeping, we must define a reference point to determine when a cycle of the required motion has been completed. If we choose a reference point afixed to the celestial sphere, the corresponding time is being referenced to the distant stars and is termed sidereal time. If instead we choose the Sun as the reference point, the corresponding time is called solar time (or tropical time).

Technically, the sidereal time is defined as the length of time since the vernal equinox has crossed the local celestial meridian. An equivalent definition of the sidereal time is the right ascension of any star presently located on the local celestial meridian. Thus, if the star Sirius is presently on your celestial meridian, the sidereal time is 6 hours and 45 minutes because we saw earlier that Sirius is located at 6 hr 45 min right ascension on the celestial sphere. Generally our everyday (civil) time is referenced to the (average) motion of the Sun, not the vernal equinox. Thus, sidereal time generally does not coincide with the everyday (wall clock) time. To be precise, the sidereal time agrees with the solar time only at the autumnal equinox; at any other time, they differ (they are exactly 12 hours apart at the time of the vernal equinox).

Sidereal Days and Solar Days

The sidereal day is defined to be the length of time for the vernal equinox to return to your celestial meridian. The solar day is defined to be the length of time for the Sun to return to your celestial meridian. The two are not the same, as illustrated in the following animation.

The sidereal and solar day

Because the Earth is in motion on its orbit around the Sun in the course of a day, the Earth must turn about 4 minutes longer each day (3 minutes and 56 seconds, to be exact) to bring the Sun back to the celestial meridian than to bring the vernal equinox back to the celestial meridian. Thus, the solar day is 3 minutes and 56 seconds longer than the sidereal day. It is this almost 4 minute per day discrepancy that causes the difference in sidereal and solar time, and is responsible for the fact that different constellations are everhead at a given time of day during the Summer than in the Winter.

Time Zones and Universal Time

As a matter of civil convenience, the Earth is divided into various time zones. The time for many astronomical events is given in Universal Time (UT), which is (approximately) the local time for Greenwich, England---the Greenwich Mean Time or GMT. The conversion from UT to local zone time may be made using this map or this set of links. Alternatively, here is a clickable Java applet illustrating the world's timezones.

Calendars

There are two basic sources for calendars presently in use: the monthly motion of the Moon (Lunar calendars) and the yearly motion of the Sun (Solar Calendars). Examples of Lunar calendars still in use are the traditional Jewish and Chinese calendars. The difficulty with Lunar calendars is that the seasons are correlated with the Sun, not the Moon. Thus, Lunar calendars require elaborate adjustments or translations to relate to the seasons. That calendars correlate with seasons is now primarily a matter of convenience, but in more ancient cultures keeping track of the seasons was serious business: it could be a matter of survival to know things like the proper time to plant to ensure a bountiful harvest.

The Roman Lunar Calendar

Our present calendar (called the Gregorian Calendar) is a basically solar calendar that grew from what was originally a Lunar calendar used by the Romans. The original calendar contained 10 months of length 29 or 30 days. This was later modified to a 12 month calendar, but 12 months of average length 29.5 days gives only 354 days in the year, whereas the orbital period of the Earth is 365.242199 days. Thus, at the end of each year this calendar was 11 days out of step with the seasons and at the end of 3 years it was almost a month out of step. This was initially corrected in an arbitrary way by adding 13th months, but this was used for various political purposes and soon threw the calendar into severe confusion.

The Julian Calendar

In 46 B.C., Julius Caesar reformed the calendar by ordering the year to be 365 days in length and to contain 12 months. This forced some days to be added to some of the months to bring the total from 354 up to 365 days, so the months now were out of phase with the cycles of the Moon: although the Julian Calendar retained monthly divisions, it was no longer a Lunar calendar. The Julian Calendar improved things tremendously, but there was still about a quarter day difference between the true length of the year and the 365 days assumed for the Julian Calendar. Thus, February was given an additional day every 4 years (leap years) and the average length of the Julian year with leap years added was 365.25 days.

The Gregorian Calendar

However, the Julian year still differs from the true year of 365.242199 days by 11 minutes and 14 seconds each year, and over a period of 128 years even the Julian Calendar was in error by one day with respect to the seasons. By 1582 this error had accumulated to 10 days and Pope Gregory XIII ordered another reform: 10 days were dropped from the year 1582, so that October 4, 1582, was followed by October 15, 1582. In addition, to guard against further accumulation of error, in the new Gregorian Calendar it was decreed that century years not divisible by 400 were not to be considered leap years. Thus, 1600 was a leap year but 1700 was not. This made the average length of the year sufficiently close to the actual year that it would take 3322 years for the error to accumulate to 1 day.

A further modification to the Gregorian Calendar has been suggested: years evenly divisible by 4000 are not leap years. This would reduce the error between the Gregorian Calendar Year and the true year to 1 day in 20,000 years. However, this last proposed change has not been officially adopted; there is plenty of time to consider it, since it would not have an effect until the year 4000.

Adoption of the Gregorian Calendar

An interesting historical sidelight on the Gregorian Calendar is that not all countries adopted it immediately. In particular, it was adopted uniformly in Catholic countries, but Protestant countries often still used the Julian Calendar. Thus, the date could change by 10 days simply by crossing certain country borders! England and its American colonies did not adopt the Gregorian Calendar until 1752, when 11 days were removed from the calendar, and Russia resisted this change until after the 1917 Revolution. One conseqence of the British adoption of the Gregorian Calendar in 1752 is that George Washington was born on February 11, 1731, according to the calendar in use on his birthday, but we now celebrate his date of birth as February 22, 1731 (actually, even that is no longer true with the advent of Presidents Day).

The Seasons

There is a popular misconception that the seasons on the Earth are caused by varying distances of the Earth from the Sun on its elliptical orbit. This is not correct. One way to see that this reasoning may be in error is to note that the seasons are out of phase in the Northern and Southern hemispheres: when it is Summer in the North it is Winter in the South.

Seasons in the Northern Hemisphere

The primary cause of the seasons is the 23.5 degree of the Earth's rotation axis with respect to the plane of the ecliptic, as illustrated in the adjacent image (Source). This means that as the Earth goes around its orbit the Northern hemisphere is at various times oriented more toward and more away from the Sun, and likewise for the Southern hemisphere, as illustrated in the following figure.

Thus, we experience Summer in the Northern Hemisphere when the Earth is on that part of its orbit where the N. Hemisphere is oriented more toward the Sun and therefore the Sun rises higher in the sky and is above the horizon longer, and the rays of the Sun strike the ground more directly. Likewise, in the N. Hemisphere Winter the hemisphere is oriented away from the Sun, the Sun only rises low in the sky, is above the horizon for a shorter period, and the rays of the Sun strike the ground more obliquely.

In fact, as the diagram indicates, the Earth is actually closer to the Sun in the N. Hemisphere Winter than in the Summer (as usual, we greatly exaggerate the eccentricity of the elliptical orbit in this diagram). The Earth is at its closest approach to the Sun (perihelion) on about January 4 of each year, which is the dead of the N. Hemisphere Winter. (The time for perihelion, aphelion, and the solstices for any year 1992-2000 is available in this compilation.)

For a more extensive introduction to how variations in the amount of solar energy reaching the Earth's surface influence climate, see this discussion of solar databases for global change models.

Another Fallacy to Avoid

Incidentally, one should be precise in terminology. A common student answer for the cause of the seasons is that "the Earth tips toward the Sun in the Summer, . . .". This conveys the impression that the Earth moves around its orbit and at certain times of the year the rotation axis suddenly tips one way or another and thus we have seasons. As the preceding diagram makes clear, the rotation axis of the Earth remains pointed in the same direction (except for small effects from precession) as it moves around its orbit. It is the relative location of the Sun with respect to this constant tilt angle that causes the seasons, not some elaborate square dance of the Earth bowing to its partner as it moves around its orbit!

Southern Hemisphere Seasons

As is clear from the preceding diagram, the seasons in the Southern Hemisphere are determined from the same reasoning, except that they are out of phase with the N. Hemisphere seasons because when the N. Hemisphere is oriented toward the Sun the S. Hemisphere is oriented away, and vice versa:

The Seasons in the Southern Hemisphere

The Lag of the Seasons

The preceding reasoning for the causes of the seasons is idealized. In reality, we know that the seasons "lag": for example, the hottest temperatures in the Summer usually occur a month or so after the time of maximum insolation (the time when maximum solar energy is deposited during a day at a point on the surface of the Earth). This is because the Earth and its atmosphere store heat (the oceans are particularly effective heat sinks). Thus, a detailed description of the seasons is quite complicated since it must take into account complex local variations in the storage of solar energy. However, the basic reason for the seasons is simple, as described above.

Simulating the Apparent Motion of the Sun

One can use the Starry Night program for Windows and the Macintosh to simulate the appearance of the sky at any time, from any chosen vantage point in the Solar System. Thus, by choosing different points on the surface of the Earth at different times of the year, this program can be used to show the motion of the Sun through the sky and illustrate clearly the preceding points about the causes for the seasons. Here is an extreme example:

In the N. Hemisphere Summer at latitudes above the Arctic Circle (23.5 degrees away from the N. Pole) the Sun stays above the horizon for the entire day (midnight sun). The adjacent image illustrates the midnight sun. This GOES-8 weather satellite visible light image is taken from a vantage point high above the western hemisphere, with the North at the top. Even though the local time for the longitude line under the satellite is near midnight, the Northernmost portion of the globe is illuminated by sunlight (the lighted portion actually extends below the arctic circle in this image because of sunlight scattering in the atmosphere).

This simulation of the midnight sun was made using the Starry Night program with a "fisheye lens" perspective to show a wide (180 degree) region of the sky from a vantage point at the North Pole on July 4, 1996. As the movie illustrates, the Sun moves more or less parallel to the horizon and never goes below it during the course of a day at these latitudes at this time of the year. Conversely, in the N. Hemisphere Winter the Sun never comes above the horizon for the entire day at this latitude. This is an extreme example of the difference in insolation in Winter and Summer for the N. Hemisphere that is responsible for the seasons.

Rotation Axis Procession

The Earth's rotation axis is not fixed in space. Like a rotating toy top, the direction of the rotation axis executes a slow precession with a period of 26,000 years (see following figure).

Pole Stars are Transient

Thus, Polaris will not always be the Pole Star or North Star. The Earth's rotation axis happens to be pointing almost exactly at Polaris now, but in 13,000 years the precession of the rotation axis will mean that the bright star Vega in the constellation Lyra will be approximately at the North Celestial Pole, while in 26,000 more years Polaris will once again be the Pole Star.

Precession of the Equinoxes

Since the rotation axis is precessing in space, the orientation of the Celestial Equator also precesses with the same period. This means that the position of the equinoxes is changing slowly with respect to the background stars. This precession of the equinoxes means that the right ascension and declination of objects changes very slowly over a 26,000 year period. This effect is negligibly small for casual observing, but is an important correction for precise observations.

The Dawning of the Age of Aquarius (Almost)

Because of the precession of the equinoxes, the vernal equinox moves through all the constellations of the Zodiac over the 26,000 year precession period. Presently the vernal equinox is in the constellation Pisces and is slowly approaching Aquarius.

The Vernal Equinox

This is the origin of the "Age of Aquarius" celebrated in the musical Hair: a period when according to astrological mysticism and related hokum there will be unusual harmony and understanding in the world. We could certainly use a dose of harmony and understanding in this old world; unfortunately, it is unlikely to come because of something as irrelevant as the position of the vernal equinox with respect to the constellations of the Zodiac.