29:52 Characteristics and Origins of the Solar System

            January 23, 2004     

           The Solar System in the Night Sky

 

The purpose of the next few lectures will be to make the link between the structure of the solar system, and what we see in the sky. I will not give a formal development of the history of astronomy. 

 

Most of the material is taken from Chapters 1 and 2 of the textbook, and I will refer to figures there.

 

(1)  "Horizon" Coordinate system and the "Celestial Sphere"

We have to have some frame of reference in which to describe celestial events. "Horizon System"

is the most basic, and is what we see. Look at Figure 1.14 for definition.

            >Diagram drawn on blackboard. 

 

When we look up at the sky, it looks like a big bowl over our heads.  We refer to this bowl as the Celestial Sphere.

The basic definitions to note are:

·                     zenith

·                     nadir

·                     horizon

·                     azimuth angle

·                     altitude angle

            In this system we see the following things happen.

·                     The Sun rises in the east, reaches a highest elevation angle due south, and sets in the west.

·                     Ditto with the stars

·                     Some stars (the circumpolar stars) move in big circles around the pole star and never set.

·                     (More subtle) As you go further south, the pole stars slumps toward the northern horizon, stars (and the Sun) transit at a higher elevation angle, and you see "new" stars peeking above the southern horizon.

            What is happening here?

The Answer is that this is all a consequence of the rotation of the Earth.  It looks as if the celestial sphere is rotating with respect to us, on an axis pointing toward the north star. 

            >See diagram 1.19, also globe.

(2) Seasonal Variations

            There are important astronomical seasonal variations (in addition to temperature changes)

which you might not have noticed previously. You will notice them in the course of this semester. It might also interest you to know that these were very well known to people before the Old Kingdom of Egypt, and before the Pre-Classical period of the Maya Indians.

·                     Different constellations are visible at different times of year.

·                     As we go into winter, the Sun rises further to the south, and is lower at its maximum altitude angle or elevation angle.

·                     It gets colder.

            What is happening here?

The Explanation, is that the Earth is orbiting the Sun, and that its axis is tilted 23.5 degrees with respect to the plane of its orbit. The fancy term for this angle is the obliquity of the ecliptic and it has a value of 23 degrees 27 arcminutes (23.45 degrees).

            >diagram on blackboard showing show obliquity of Earth's axis can affect sky positions of Sun.  

 

·                     The varying angle between Sun-Observer at Noon-Pole Star is also responsible for temperature changes associated with seasons, as well as fact that northern hemisphere and southern hemisphere winter and summer are interchanged.

·                     Seasonal changes in constellations are due to orbital motion of Earth around Sun. We see the Sun "projected against" different stars at different times of year.  Look at Figure 2.10 of the book. 

            >Look at SC1 constellation chart showing dates of Sun's position.

            >Look at SOHO web page showing Sun moving against background stars. 

http://sohowww.nascom.nasa.gov/

 

(3) How Long is the Day?

            Would seem to be a stupid question. 24 hours=86400 seconds. But what do we mean by a day?

What is 24 hours is actually more precisely known as the mean solar day. It is the average  time during the year between successive transits of the Sun.

            We could also define the day by the time between successive transits of a star, say   Sirius,  which  transits around 11 PM  these evenings. This is called the sidereal day. Strangely enough, it is almost the same as the mean solar day, but not quite. (Nota Bene: this material is discussed on p 26ff of your book).

The sidereal day is 23hours, 56minutes, 4seconds long.

            >Question for the august assembly: Why are the two days different?

(4) The Year

            The year is the length of time it takes the Earth to complete its orbit around the Sun. The official term for this is the sidereal year, and could be measured by the time it took for the Sun to start out at

one place in the sky (defined relative to the background stars), move completely around the sky, and return to the same place. The value of the sidereal year is 3.1558 X 10**7 seconds.

(5) The Year and the Day are not commensurate numbers.

            Two entirely different physical periods lie behind the astronomical definitions of the day and the year. The day (precisely the sidereal day) is the time it takes the planet Earth to turn on its axis like a spinning top. The year is the time it takes to complete its circuit around the Sun, like a racecar running around a track.

            There is no physical reason for the year to be an integral number of days, and it isn't. In fact, one year = 365.2564 solar days. The little extra 0.2564 days is responsible for annoyances such as leap years, intercalcary days, the discrepancy between the Julian and Gregorian calendars, etc.  Read p28 of your textbook. 

            Every high civilization, from Old Kingdom Egypt to Classical Mayan, was aware of this discrepancy, although they naturally did not have the correct physical explanation for it.