Unit 3: The Sky and the Calendar
 
 

OVERVIEW

In this unit of study the basic motions of celestial objects in the sky and what causes them are discussed. The method that astronomers use to find objects in the sky is outlined. Time and the nature of the modern calendar is also reviewed.

LEARNING OBJECTIVES

At the end of this unit you should be able to:

1. Discuss the differences between the motions of the stars, Sun, Moon, and planets in the sky.

2. Discuss the underlying causes of the (apparent) motions of celestial objects in the sky.

3. Describe the celestial coordinate system.

4. Discuss time zones and the nature of the modern calendar.

 KEY WORDS rotation

revolution

constellation

latitude

longitude

celestial equator

ecliptic

meridian

celestial pole

pole star

celestial coordinates

right ascension

declination

local sidereal time

time zones

mean solar day

precession

sidereal year

tropical year

Gregorian calendar

 WRITTEN NOTES

The Motion of Celestial Bodies in the Sky

An observer of the sky will find qualitative differences between the motions of: (i) stars outside our Solar System, (ii) the Sun, (iii) the Moon, and (iv) any one of the planets.

The motions of these celestial bodies as observed from hour-to-hour, night-to-night, and year-to-year are primarily governed by four types of movement in the Solar System (there are more subtle effects which we will discuss as needed):

1. The Earth rotates about its axis approximately once each day. On a daily time scale, this causes celestial bodies to appear to rise and set approximately once each day when observed from moderate latitudes.

2. The Earth revolves around the Sun approximately once each year (365 days). Since a circle has 360 degrees, this means that each day the Sun moves about 1 degree east with respect to the background stars.

3. At the same time, the Moon revolves around the Earth approximately once each month. This means that each day the Moon moves about 12 degrees east with respect to the background stars.

4. Since the planets (which are some of the brightest objects in the night sky) also revolve around the Sun, their motions are more complex. However, their positions with respect to the background stars don't change more than a few degrees from night-to-night, and usually the change is much less.

 [As an example of angular scale in the sky, note that the angular diameter of the Sun and Moon are both approximately ½ degree.]

The plane of the Earth's revolution about the Sun, the plane of the Earth's rotation, and the plane of the Moon's revolution about the Earth are all tilted with respect to one another. This causes seasons on Earth, and solar and lunar eclipse cycles.

 The Stars as Viewed from Earth Ancient astronomers grouped the stars seen in the sky into constellations (e.g., names we still use are associated with Greek mythology). However, we now know that the stars which make up constellations are in no way related to one another, because their distances from our Solar System vary greatly from star to star.

The locations of stars in the sky are specified in terms of their celestial coordinates.

· An astronomical object's celestial longitude is called right ascension (RA).  RA is measured in hours, minutes, and seconds, increasing to the east from a line running through the Spring Equinox.  Since the Sun and Moon move to the East through the sky from one night to the next, they increase their right ascension as they move.

· An astronomical object's celestial latitude is called declination (Dec).  Dec is measured in angular degrees north of the Celestial Equator.  The Celestial Equator is 0 deg., the North Celestial Pole is +90 deg., and the South Celestial Pole is -90 deg.

· The local sidereal time (a time-keeping system used by astronomers which is based on the apparent motion of the stars) tells you when a star of a particular right ascension will be at its highest point in the sky.

 Time and the Calendar There are 24 standard time zones on Earth, each approximately 15 degrees wide in longitude.  (360 degrees divided by 24 hours)  The standard time in these time zones is adjusted so that the Sun will be at its highest point in the sky within about one-half hour of noon each day. Standard time is based on the average length of the solar day, which is called the mean solar day.

If we observe the Sun, we find that the Sun takes about 365.2564 mean solar days to come back to the same point in the sky with respect to the background stars. This is called a sidereal year.

The Earth's axis of rotation changes the direction it's pointed with a cyclic period of 26,000 years. This is called precession of the equinox. Because of this, we do not base our year on the sidereal year but rather on the tropical year which lasts 365.2422 mean solar days. By using the tropical year, we can always be assured that winter in the northern hemisphere will begin in December, etc.

The Gregorian calendar, invented in 1582 and based on the tropical year, uses leap years to make time-keeping sensible.

 READING ASSIGNMENT

Chapter S1;

Chapter 3 (sections 3.1 & 3.2 only).

HOMEWORK

Chapter S1, Problem 8.