©1998 - 2004 by RCBrill. All rights reserved.
1. Describe the different kinds of heavenly objects visible to us with the naked eye.
2. Define the celestial sphere and describe its motion.
3. Describe the nature of heavenly objects and their motions as observed with the naked eye.
4. Demonstrate understanding of the problems with distance and scale in studying the heavens.
5. Demonstrate understanding of how the relationship between the tilt of earth's axis and seasonal changes
6. Demonstrate understanding of the motion of the planets as seen from Earth, especially retrograde motion.
7. Demonstrate understanding of the phases and motions of the moon and their relationship to the sun.
8. Distinguish between the appearance and nature of meteors, comets, and novas.
1. Describe the celestial sphere and its movement.
2. What kinds of objects and motions would one observe in the sky?
3. Why does the sun rise and set in a different place each day?
4. Explain why days are short in the winter and long in the summer.
5. How does the location of sunrise and sunset vary throughout the year
6. If you had never seen a calendar and did not know the number of days in a year, how might you find out?
7. Draw a diagram that shows how the phases of the moon arise from the position of Earth, moon and sun.
8. Why does the moon rise fifty minutes later each day?
9. The word planet means "wanderer". Why were the planets given that name?
10. What is retrograde motion and in what objects is it observed?
11. Discuss the relationship between counting, numbers, and record keeping.
12. What is different about the retrograde motion of inferior planets and superior planets?
13. What is the difference in the appearance of meteors, comets and novae?
1.1.1. heliocentric and geocentric are both used by astronomers
1.1.2. calculations and true motion are heliocentric
1.1.3. observed locations and movements are geocentric
2.1.1. rotates once every 23 hours 56 minutes
2.1.2. Circular centered roughly on Polaris
2.1.3. East To West motion
2.1.4. Contains Sun, Moon, Stars, Planets, and other heavenly objects
3.1.1. What is the sky?
3.1.2. What kind of things do we see in the sky?
3.1.3. How big and how far away are things in the sky?
3.1.4. What is beyond the sky?
3.2.1. attached to the celestial sphere
The stars are attached to the celestial sphere and rotate with it. Because the stars all move together with the celestial sphere we often refer to it as the fixed star background.
3.2.2. about 3000 visible to naked eye
Although the sky seems to contain many stars, there are only about 3000 visible to the naked eye under the best viewing conditions, and many fewer than that on a typical night. On a haze, full moon night in the city the stars may not be visible at all, or only a few of the brightest may be visible.
3.2.3. in recognizable patterns called constellations
From earliest times, people worldwide have recognized and named patterns in the stars and built myths around them. Different cultures see different patterns, our modern astronomical paradigm recognizes specific regions of the sky by the name of some ancient constellation which dominates the sky in that region.
3.2.4. vary in brightness and color
Stars vary in brightness and color. In addition to white stars, there are blue, red, yellow, and green stars.
The brightest stars in the sky other than the sun and the moon are really the planets, five of them. Their motions are a little complex, so we'll consider them later in the lesson.
The brightest stars and planets can be seen even in the early dawn or twilight. The dimmest stars are far dimmer than we can see with the eye alone even under ideal viewing conditions. Telescopes and cameras allow us to see stars that we cannot see.
The full moon obliterates all but a hundred or so stars. Of course the sun lights up the sky so no stars are visible at all in full daylight.
3.2.5. brightest is Sirius
The brightest star of all is the dog star, Sirius which lights up the low southern horizon in November, December and January. As it twinkles, flashes of light of different color radiate from it so that it looks alive and pulsating. No wonder the Egyptians worshiped Sirius ! Sirius is the ever-faithful companion to Orion the hunter, the most recognizable constellation.
3.3.1. Motion of the Moon
The motion of the moon around the earth takes one month to complete a cycle. During this cycle the earth is also moving around the sun in its yearly orbit. The combination of motions causes several effects on the apparent motion of the moon against the fixed stars and in its presentation of phases.
The most notable feature of the moon on a daily basis is the changing phases. We will study these and the reason for them later in this lesson. Along with the changing phases, the moon's position relative to the changes in a regular and related way. Sometimes the moon is ahead (to the west) of the sun on the celestial sphere, and sometime it lags behind the sun to the east.
18.104.22.168. full moon rises at or near sunset
The full moon is always twelve hours behind the sun and will be on the meridian (t line which points north-south and passes directly overhead) at midnight. The reason for this is simple once we understand the cause of the phases. We will get to that shortly.
22.214.171.124. daily motion against celestial sphere
The moon moves daily against the star background. Although its imperceptible, the moon moves its own diameter every hour. This is something you can check on. Find a group of stars near the moon and estimate their distance from the moon. Use a mark on a ruler held at arm's length, or use the size of a thumbnail at arm's length.
One hour later, go out and compare the location of the moon with that group of stars. You'll be amazed that you can actually see the moon moving like the small hand on the clock, but much much slower.
Each day the moon is about fifty minutes behind (to the east of) the sun and so it rises fifty minutes later each day.
How many fifty minutes periods are there in twenty-four hours? A month is about 29 days long.
126.96.36.199.1. moves its own diameter every hour
188.8.131.52.2. completes a complete cycle on celestial sphere every month
184.108.40.206. about 50 minutes later (eastward) each day
220.127.116.11.1. Moon Moves Relative To Sun About Twelve Degrees Per Day, Equivalent To About Fifty Minutes Of Time
In these figures we can easily see why the angle between the moon and sun changes as the moon against the star background thirteen times faster that the sun does. The angle between the two represents the time that it will take a point on earth's surface to rotate that far.
The earth rotates one complete turn in 24 hours, or 360 degrees/24 degrees per hour. That's 15 degrees per hour. At that rate it will take 12/15 of an hour, or 48 minutes to "catch up" to the moon.
The moon revolves 1/30 of a complete revolution in one day, or 360 degrees/30 days which equals 12 degrees per day. Because it revolves in the same direction as earth rotates, a point on earth's surface must rotate that extra 12 degrees in order to be under the moon.
The moon "gains" about 50 minutes per day on the earth as it orbits around it once a month.
3.3.2. FOCUS: Distance and Scale
Distances in space are vast compared to the size of the objects. In our heliocentric model of the solar system we can't show the orbits and the sizes of the planets on the same map.
18.104.22.168. Distances in space are vast
Objects even in our solar system are very far away. It is a quarter of a million miles to the moon. If you started walking now, assuming you walk three miles per hour and walk for twenty-four hours a day, you could walk to the moon in ten years, if there was a sidewalk. At that same rate you could reach the sun in only 3,500 years.
22.214.171.124. objects are very small compared to their distance apart
The distance to the moon is 250,000 miles, yet its diameter is only about 3000 miles. The sun is almost one hundred million miles away, yet its diameter is only a little less than a million miles. That's really big, but it is only about one one-hundredth of is distance away.
Try to picture the relative sizes when you look at the outline below.
126.96.36.199.1. moon is 30 earth diameters away from Earth
188.8.131.52.1.1. about 120 moon diameters
184.108.40.206.1.2. if earth is a basketball, the moon is asoftball 25 feet away
220.127.116.11.2. sun is about 400 times further away than the moon
18.104.22.168.2.1. about 116 sun diameters
22.214.171.124.2.2. about 16,000 earth diameters
126.96.36.199.2.3. a sphere the size of a large arena two miles away
188.8.131.52.2.4. 180 feet diameter
184.108.40.206. cannot represent both distance and size at true scale at the same time
Can't you see that it is impossible to visualize both the distance and size at the same time. If the scale is small enough to see the size of the orbit, it is impossible to see the tiny planet. On the other hand, if the scale is big enough to see the planet, then its orbit is too far away.
220.127.116.11.1. sun is basketball, earth is a grape nut 100 feet away, moon is a sesame seed one quarter inch away
3.5.1. relationship between moon phase and sun
We have already seen how the changing relationship between the sun and moon causes the moon to lose fifty minutes per day. Now we can see how the changing angle between the earth, sun and moon causes the phases and why the full moon rises at sunset, twelve hours behind the sun.
18.104.22.168. timing changes daily
22.214.171.124. angle between sun, earth, and moon
126.96.36.199. full moon rises at sunset
3.5.2. The Phases
188.8.131.52. waxing: new, crescent, quarter, gibbous
184.108.40.206. waning: full, gibbous, quarter, crescent
220.127.116.11. one full cycle of phases is one month, 29.5 days
18.104.22.168. How Old is a Quarter Moon?
3.5.3. Food for thought
Why do we call it a new moon? It is difficult to know where to call the start of a cycle, so why is the new moon new? What's new about it?
And why is it a called a quarter moon when it is exactly one half of a full moon?
3.5.4. Earth, Sun, Moon positions
It is easy to understand the phases if we know just a couple of facts.
1. The moon, like the earth, is only lighted brightly by the sun. All of the planets, earth and moon included, shine only by reflected sunlight.
2. The moon is roughly spherical in shape which makes the boundary between the dark and the light lie on a meridian, like the sections of an orange.
The phases result from the amount of the lighted portion of the moon that we can see. In the series of eight pictures above, imagine that they represent a spherical globe in a black room illuminated by a harsh light which circles behind your head and behind the moon globe. If you can't visualize it, try it in a dark room with a golf ball, a flashlight, and a friend.
22.214.171.124. full moon
126.96.36.199.1. The full moon results when the earth, sun and moon are nearly aligned so that the sun and the moon are on exactly opposite sides of the earth. They're not really lined up perfectly most of the time, but occasionally they do line up and there is an eclipse of the moon as it passes into earth's shadow. Note that it would take a point on earth exactly twelve hours to go from sun overhead to moon overhead (plus the amount the moon will move in that time, which is about 25 minutes.
188.8.131.52. new moon
184.108.40.206.1. The new moon results when the moon is directly between the earth and the sun. The lighted half of the moon is completely hidden from view. Unless the earth, moon and sun are perfectly lined up, the moon will be invisible. If they line up some locations on earth would witness a solar eclipse.
220.127.116.11. quarter moon
18.104.22.168.1. There are actually two quarter moons. They occur when the earth, moon and sun meet a a right angle (90 degrees). Any point on earth will see exactly half of the moon lighted and half dark. At these phases the moon will be exactly three hours ahead of or behind the sun. It is quite a sight to see the waning quarter moon high in the sky as the sun disappears on the western horizon.
3.6. The Sun
The sun is the source of all light, most energy, and it is the energy source for most life. The day night cycle is so ingrained into each of us that it is hard to imagine what it might be like to live in twenty-four hour darkness or daylight. Imagine how difficult timekeeping might be without such cycles.
The sun's position in the noon sky and on the horizon at sunrise and sunset provided the earliest measure of the length of the year. If you had no watches, calendar and had no concept of the number of days in a year, how would you know when exactly one year had passed? Days are easy to keep track of because of the distinct boundary between day and night. Years are not so easy.
3.6.1. Seasonal Oscillation Of Sunrise and Sunset
If you could watch the sunrise every morning from the same location, what would you see happening over the course of the changing seasons? Would the sun rise in the same place every day, would it jump around from place to place, or would it change in some systematic way? With our scientific paradigm, we could pose it as a hypothesis and establish a way to check it out, but it is unlikely that our ancestors 40,000 or so years ago were sophisticated enough to do so.
We don't know when people noticed for the first time that the sun oscillated back and forth across the horizon, but there are artifacts in both the old and new worlds dating back three or four thousand years which indicates it happened fairly early after the glaciers disappeared.
22.214.171.124. Daily Drift through the Star Background
The sun drifts slowly through the fixed star background, a little less than one degree (1 degrees) per day, or about four minutes.. That's not much, but it is about twice the diameter of the sun, so it's fairly noticeable, even over a couple of days. The path of the sun along the celestial sphere is called the ecliptic.
Now you should understand why the celestial sphere completes one cycle in twenty-three hours and fifty-six minutes (four minutes less than twenty-four hours).
126.96.36.199.1. travels along the ecliptic
188.8.131.52.2. Drifts about 4 Minutes Eastward Each Day
184.108.40.206. sunrise and sunset move back and forth between solstices
Along with the slow eastward drift through the star background, the sun also oscillates back and forth along the horizon. In the pictures above the stars move upward relative to the sunrise while the sun moves along the horizon.
This is not really as complicated as it seems, but it would certainly be hard to figure it out on your own.
220.127.116.11.1. solstice: sol (sun) stice (from Latin: stand still, as in static, stationary, stasis)
18.104.22.168. December Sunrise
Here's a representation of a December sunrise looking due east.
Because the light from the sun obscures the nearby stars, it is easier to illustrate with a less complicated graphic.
Here we see the sun rising far to the southeast near a particular group of stars.
22.214.171.124. June Sunrise
But in June the sunrise is in the northeast, and the stars near the sun are different than they were in December.
126.96.36.199. Analema Movie
The video program shows an animation of the sun moving back and forth across the eastern horizon. When you watch it, note how the stars move as compared to the sun's movement.
188.8.131.52. Seasonal Variation in Height of Sun
We also observe that the sun not only rises further to the north in summer, but it also gets much higher in the sky. At the same time, summer days are longer than winter days, as shown in the illustration below that shows the sun's path through the sky at different times of the year.
184.108.40.206.1. noon sun is high in summer low in winter The path of the sun on the celestial sphere at different times of the year causing the day length to vary with the season.
220.127.116.11.2. terminator crosses longitudes
On this model of the illuminated earth, which represents the situation at the December solstice, we see the islands of Hawaii about ready to reach the terminator (that's the what the boundary between night and day is called). At the same clock time (on the same longitude line), the Aleutian Islands, north of Hawaii. are already in complete darkness. If you look carefully you will see that there is a small region right at the top which will get no sunlight at all. Meanwhile, to the southern hemisphere, it is summer time. New Zealand, which is almost due south of Hawaii still has many hours before they reach the terminator. This diagram also show the direction of the sunset. A line drawn through the Hawaiian Islands perpendicular to the terminator represents the direction to the sun, and it is definitely aimed southwest. Where would you expect the sun to rise in June?
3.6.2. Tilt of earth's axis
All of these effects are easily explained once we realize that the earth's axis of rotation is tilted a little (about 23.5 degrees) so that sometimes the north pole leans towards the sun and sometimes the south pole points toward the sun.
18.104.22.168. causes all of those seasonal effects
22.214.171.124. sun does not rise directly upward except at the equator
3.7.1. word means nomads or wanderers
3.7.2. move generally east to west relative to fixed star background
3.7.3. exhibit occasional retrograde motion in loops or zigzags
3.8.1. sporadic and short lived
3.8.2. meteors streak across the sky like 'falling stars'
126.96.36.199. nightly streaks from very bright to barely perceptible
188.8.131.52. certain times of the year meteor showers originate from specific locations in the sky
3.8.3. comets appear from time to time
184.108.40.206. move faster near the sun
220.127.116.11. look like fuzzy cotton balls
18.104.22.168. often have tails which point away from the sun
3.8.4. nova means 'new star', is actually an exploding star
22.214.171.124. suddenly appear, remain stationary
126.96.36.199. brighter than other stars and some planets
188.8.131.52. shine brightly for brief period then disappear
184.108.40.206 Remains may be visible as nebulae indefinitely
Four Supernova Nebulae