Astronomy 100 Name(s):

Exercise 3: Seasons in the sun The following exercise illustrates some basic ideas about time, and how our position in the solar system uniquely configures the measurement of time. The hours 1. a. How many degrees in a circle (such as the ecliptic around the Earth)? The ecliptic is broken up into the twelve Zodiacal constellations (e.g., Aries, Taurus, Gemini, etc.); assuming each constellation is equally large, how many degrees does each Zodiacal constellation subtend? b. How many degrees of the sky does one hour represent? Another way to look at this question: how many degrees of the sky disappear over the western horizon every hour? 2. a. When you get the chance, go check out the sundial in the south courtyard on campus. Local noon is obviously when the Sun is directly overhead (also called “Sun transit”). When there is no shadow on the sundial, the time should be noon. Is the time accurate? If not, estimate how many minutes the sundial is “off”. b. Assuming that the sundial is set up correctly, explain this observation. The lunar cycle 3. a. In the figure below, indicate the direction of the Sun with an arrow.

b. Telling time using the Moon: At what time of day would you expect to observe a full Moon rising? Over which (eastern or western) horizon would it rise?

c. At what time of day would you expect to observe a first quarter Moon setting? d. At what time of day would you expect to observe a new Moon overhead? A guide for naming the phases of the Moon: If only a minimal crescent of the Moon is illuminated, it is a new Moon. If less than half of the Moon is lit, it is a crescent Moon. A half-illuminated Moon is a quarter (not half) Moon (first quarter occurs before full Moon, third quarter occurs after). If more than half is illuminated, but the Moon is not full, it is gibbous. If it is fully illuminated, it is a full Moon. When the lighted side’s apparent area increases from night to night, the Moon is said to be waxing; when the apparent area decreases, the Moon is waning.

4. In the upper portion of the figure above (which represents looking down from the celestial north pole), eight positions of the Moon (labeled 1 through 8) are given in its orbit around the Earth. The lower part of the figure shows what an Earth observer would see of the Moon at each of the eight positions. a. For each position on both parts of the figure, shade the dark and illuminated portions of the Moon.

b. For the lower part of the figure, label each Moon's phase. c. For the upper part of the figure, is the Earth rotating clockwise (CW) or counterclockwise (CCW)? Indicate this with an arrow. 5. a. If you observe a quarter moon, how can you tell if it is the first or third quarter moon? b. Night after night, in what compass direction does the moon appear to move, relative to the fixed stars? 6. a. Why isn’t every new moon coincident with a solar eclipse? In other words, why isn’t the sun eclipsed every 28 or so days? b. If your answer to the previous part is true, then, how do we ever see a fully lit, full Moon? Shouldn’t some of its face toward us always be dark? 7. a. Does the Moon rotate on its own axis? Note: Rotate, not revolve. Equivalent question: Does the Moon always present the same face to us on Earth? b. So what percent of the whole Moon’s surface should we be able to see and map from telescopes on the surface of the Earth? c. In fact, we have been able to map 59% of the Moon’s surface from Earth-based telescopes (the rest was done by sending satellites around the “back”). How are we able to see that much? Hint: look up “libration”.

Modeling the Earth-Sun System You will need a piece of pipe cleaner, a large styrofoam ball, a small wooden dowel, an index card and a light source. Turn the light bulb on and fix it so that you can move the styrofoam ball around it easily. Take a small wooden dowel and push it through the center of the styrofoam ball, so that the ball will rotate about this axis. The ball will represent Earth; place it so that the bulb (which represents the Sun) evenly illuminates both hemispheres and poles. The Earth should be about three feet from the Sun. On the index card, write “N”, “E”, “S” and “W” at the cardinal points of the card. This card will represent the horizon for an observer; notice that the horizon appears flat when you are standing in the middle of a large plain on Earth, though you know very well that the Earth is spherical. So the index card is a good approximation of the horizon. The piece of pipe cleaner is a “person” who will be standing and casting a shadow on the styrofoam Earth. Punch the pipe cleaner through the middle of the index card, then place the person at approximately 45° N latitude on the ball. Align the index card so that “N” is in the direction of the north rotational pole. The days (diurnal cycle) Rotate the Earth so that, from the perspective of the pipe cleaner person, the Sun rises in the east and sets in the west. This is tricky so have someone watch the person as you spin the ball. 8. When viewing the Earth from above the North Pole, which direction does the planet rotate, clockwise (CW) or counterclockwise (CCW)? With respect to the cardinal points on the horizon, is the Earth’s rotation in an easterly or westerly direction? The seasonal cycle If the Earth’s axis of rotation was oriented so that each pole received equal illumination from the Sun, we could not explain why the poles receive no sunlight six months of the year. In June, the North Pole must be tilted toward the Sun to produce daylight over an entire day in the Arctic and darkness over an entire day at the South Pole. In December, the North Pole must be tilted away from the Sun to produce daylight over an entire day in the Antarctic and darkness over an entire day at the North Pole. Tilt the North Pole of your ball so that points towards the north wall of the room. As you rotate the ball around its axis, note which pole is in complete darkness and which pole is in complete light during a full rotation. Now, revolve the Earth around the Sun until the Earth reaches the opposite side of its orbit from where you started. Remember to keep the North Pole pointed toward

the north wall. Again, note which pole is in complete darkness and which pole is in complete light during a full rotation. 9. a. If “summer” is the term used to describe the season when daylight is longer than night for a given hemisphere, should “summer” occur when that hemisphere’s pole is tilted toward or away from the Sun? Keep moving the Earth around the Sun, rotating the Earth continuously. b. Look at the shadow of your stick figure during the course of a “day” at four different positions around the Sun (the different seasons of the “year”). Orient the stick figure at each of these positions so that the Sun is overhead. What is the orientation of the North Pole (toward or away from the Sun) when is the shadow of the stick figure is the shortest? Which season does this correspond to? c. Are the changes in the seasons due to the North Pole is oscillating in space, alternately toward and away from the Sun over the course of one year? We know from experience that the Sun is lower in the sky at noon during the winter months than during the summer. The annual variations in the Sun’s altitude and the length of the day, resulting from the tilt of the Earth’s axis, cause the seasons. In the summer, long days and the high altitude of the Sun give us more daylight hours and more direct sunlight than in the winter, which means we receive a higher concentration of sunlight on the surface of the Earth in the summer than in the winter. 10. a. Consider a planet with no tilt at all (in other words, its rotational axis is exactly perpendicular to the planet-Sun plane). Will this planet have seasons? b. Consider a planet that has its rotational axis parallel to the plane on which it orbits. Will this planet have seasons? c. Using a list of planetary data, which planet in the solar system will very nearly not have any seasons? Remember, a planet does not need an atmosphere to have seasonal changes (for instance, uneven heating of the rocks due to seasons may lead to different amounts of gases being released from the rocks). d. Which planet in the solar system will have extreme seasons?