The Constellations and Coordinate Systems

Tracking the Motions of the Sun and Planets

• Introduction
• Daily and Annual Motions
• Practice with Concepts
• Discussion Questions
• Optional Website Reading

Introduction

Daily and Annual motions

There are four types of permanent objects that we can see easily without a telescope: the sun, the moon, the planets (Mercury, Venus, Mars, Jupiter, and Saturn), and the brighter stars, about 3000 of them easily visible in clear weather. Each of these appears to move about in the sky. Figuring out how the objects actually move is complicated because the earth itself has two movements, one the daily rotation on its axis and the other its annual revolution around the sun. There are other movements, like the slight wobble called nutation that causes the north celestial pole to move slowly away from Polaris. An observer on earth sees the motion of the sun, moon, planets, and stars from a moving platform.

The sun's daily motion

Each day we see the sun, moon, planets, and stars rise in the east and set in the west. While we realize now that this daily motion is the result of the earth's rotation on its axis, for the purposes of simplicity in plotting positions in the sky, we still talk as though the sun moves east and the planets occasionally go backwards.

The simplest motions are those of the sun and the background stars. While these both rise and set daily, they don't keep exactly the same pace. Let's see why there is a difference between a solar day and a sidereal (star) day, where a day is the time between two appearances of the star or sun directly overhead.

At noon one day, both the sun and a very distant star are directly overhead. As the earth turns on its axis counterclockwise (as seen from above the north pole), it also revolves around the sun in a counterclockwise circle. The earth makes one complete turn on its axis. The very distant star is overhead again, but the sun isn't overhead again! Because the earth has moved a bit around the sun, it has to turn a little more to get the sun directly overhead. The time to reach solar noon is 4 minutes more than the time it takes to reach stellar noon (see the diagram below).

So a sidereal day is 23 hours, 56 minutes long, while a solar day is 24 hours long.

The sun's annual motion

Because of the earth's annual revolution around the sun, the sun appears to move eastward or left each day from its previous position, as seen against the background stars. Stars that were "behind" the sun move out into visibility to the right or west of the sun, becoming morning stars (rising before the sun does into a dark sky). The first time they appear in the morning before the sun after being lost for several months in the sun's glare is called the heliacal rising of the star (rising after Helos, the sun).

Over the course of the year, the sun appears to move once all the way around the sky. The constellations through which it appears to pass were important markers in the sky to the ancient observers; there are twelve of them and because many of them are animals, they were called the Zodiac constellations (from the Greek zoe, life).

The path of the sun through the middle of the Zodiac band is called the ecliptic. As the Earth moves around the Sun, the Sun appears to move against the background stars on this path. To see how this works, use the animation below and observe which constellations are overhead at midnight and which constellation the sun appears in at different points of the year (March 21, the first day of spring, June 21, the first day of summer, and September 21, the first day of fall). By tracking the sun's location in the sky (or which constellation is above our south point at midnight), we can tell what season of the year it is and prediction when we can observe constellations and the stars or planets located in them.

Earth's Seasons

Because earth is spherical, sunlight reaching the equatorial region strikes the ground at a perpendicular angle, but strikes the ground near the poles at a slant. This means that the same amount of light leaving the sun covers a smaller ground area at the equator than it does at the poles, concentrating more energy there. So the equatorial regions receive more energy and have more heat and light to work with.

Because the earth is tilted on its axis in a constant direction, the angle of the poles with respect to the position of the sun changes over the course of a year. In the northern hemisphere summer, the north pole is pointed toward the sun, and because of the earth's tilt, the sun never sets -- although it still reaches the ground with slanted rays, so it isn't very warm. In the northern hemisphere winter, the sun doesn't rise at all at the poles for nearly three months. The diagrams show the difference in daylight in September, December and June for the globe.

At the fall and spring equinoxes, the north and south poles and the equator receive the same amount of daylight, but at the winter solstice, the north poles receives no light, and at the summer solstice, the south poles receives no light.

Daylight pattern on autumnal equinox

Daylight pattern on first day of winter

Daylight pattern on first day of summer

We can now start putting together solar motion and the celestial coordinate system. The sun at 0 ° declination at the two points where its path (the ec liptic) crosses the celestial equator. We start counting around the celestial equator in hours of Right Ascension where the sun moves from the southern to northern hemisphere, at the vernal equinox. The sun is thus at 0hrs RA, 0 ° declination. It blocks all the constellations behind it, so we can't see those constellations that are near 0 hr RA. At midnight, the sky will have turned 12 hours, and the stars near 12hr RA will be overhead -- so that's a good time to look for those stars.

On the first day of summer, it is as far north of the celestial equator as it can get, 23.5°; since it has gone 1/4 of the way around the equator, it is at 1/4 of 24 hours or 6 hours of Right Ascension. At this point it blocks with its own light any stars and constellations that are at 6 hours RA, so the first day of summer is a good time to observe constellations half-way round the sky, at 6+12 hours RA, or 18 hrs RA.

Date	Event	Sun's position (RA:dec)	RA (sidereal time) at midnight	Constellations Overhead
March 21	Vernal Equinox	0 hrs/0°	12 hours	Leo
June 20	Summer Solstice	6 hrs/23.5° N	18 hrs	Libra ahd Hercules
September 21	Autumnal Equinox	12 hrs/0°	0 hours	Pegasus
December 21	Winter Solstice	18 hrs/23.5° S	6 hours	Orion
November 1	Extrapolation example!	9 days(Sept 21-30) + 31 days(October 1-31) = 40 days Total days = 9 + 31 + 30 + 21 = 91. So the sun has moved 40/91 ~ 4/9 of the way autumnal equinox and winter solstice 4/9 * 6 hours = 4/9 * 360 minutes = 160 min = 2hrs 40 min. The sun's RA will be 12 + 2:40 = 14:40. The sun's declination will be 4/9 * 23.5° = 10.4° S	14:40 + 12 = 4:40	Taurus and the Pleiades

Using this information, can you determine where the sun should be on the first day of fall and the first day of winter?

Practice with the Concepts

Where is the sun in the around February 22 of any year?

Discussion Questions

• How is the calendar related to astronomical observations? Why are corrections to the calendar required?

Optional Readings

• There is some interesting information on the history of our modern Western calendar at the Calendar Origins site.

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