Lab 2: The Earth-Moon System and the Sun and Seasons

Transcription

1 Lab 2: The Earth-Moon System and the Sun and Seasons Moon Phases We heard lectures about the moon yesterday, so here we will go through some interactive questions for lunar phases. Go to Background Material on the Moon Answer the following questions after reviewing the background pages for the simulator. Background Page 1 Introduction to Moon Phases Is there a dark side of the moon? (Note: this question can be effectively answered either yes or no, so it is important to explain your reasoning.) How long does it take the moon to complete one cycle of phases, in days? If the moon is full today, what phase do you expect it to be at in a week? How about one month later? Many words in astronomy also non-astronomical uses as well. Using your knowledge of how the terms on the left are used in astronomy match them with the non-astronomical uses on the right. waning convex, rounded -- also hunch-backed, having a hump gibbous waxing to increase in size, quantity, volume, intensity, etc. decrease in magnitude, importance, brilliancy, intensity, etc. Lab 2:The Moon and Seasons 1/15

2 The following sketches of the moon's appearance were made over about four weeks. Identify the phases and put them in the correct numerical order. One is labeled for you. Picture Order Phase Picture Order Phase A D B 1 waning gibbous E C F Background Page 2 Introduction to Moon Phases From the perspective of an observer above the North Pole, the moon moves clockwise / counter-clockwise (circle) in its orbit around the earth. In the diagram below the sun's light is coming in from the right. The moon's location is marked at several points on its orbit. These are the points the moon was at when the sketches above were drawn. Identify each position with the letter of the corresponding sketch. Lab 2:The Moon and Seasons 2/15

3 Background Page 3 The Time of Day Use the interactive diagram at the bottom of the page to determine the direction of the earth s rotation when viewed from above the North Pole. (Hint: rotate the observer the stickfigure to the noontime position, then sunset position, then midnight position, and finally back to sunrise position. The earth has made one complete rotation and the observer has experience one daily (diurnal) cycle of day and night.) Background Page 4 Rising and Setting When viewed from above the North Pole, does the earth rotate clockwise or counterclockwise? When the moon crosses the western side of the horizon plane it is rising / setting (circle). When it crosses the eastern side of the horizon plane it is rising / setting (circle). Background Page 5 The Horizon Diagram Describe the location of the moon in the sky of the horizon diagram at bottom. Use direction words (like north, west, etc.) and estimate its altitude in degrees. Background Page 6 The Witness and Detective If we know the moon's position in the sky and its phase, we can estimate the. In general, knowing any two of the following three things allows us to estimate the third: 1. moon's position in the sky Visualizing Moon Phases Question 1: We can determine the appearance of the moon based on the orientation of the moon and sun with a simple heuristic. In the figure below, bisect the moon twice. a) Draw a line (perpendicular to the direction of sunlight) that shows the half of the entire moon that is illuminated and shade the shadowed region. Lab 2:The Moon and Seasons 3/15

4 b) Draw a line (perpendicular to the Earth-moon line) that shows the half of the moon visible for an observer on earth. c) Mark the region that is both visible from earth and illuminated by the sun. That region will be the phase of the moon we on earth see. sunlight Moon Earth We normally draw the phases of the moon with the terminator (the dividing line between light and shadow) from the north pole to the south pole of the moon. This is how the moon would be seen if it were on the observer s meridian. We can use the drawing above to determine the amount of illumination and whether it is on the left or right hand side of the moon. Use the drawing above to draw the appearance of the moon in the box to the right. Open the Moon Bisector Demo and use the simulator to check your answer to the above problem. The Lunar Phase Simulator The items below will help familiarize yourself with the controls and usability features of the simulator. If you have not already done so, launch the NAAP Lunar Phase Simulator The main panel has sunlight, the earth, and moon. The earth and moon can be dragged with the mouse. Below the main panel, there are animation controls. The moon and earth can be dragged. The increment buttons move both the moon and earth by the specified time. The Moon Phase panel shows the current moon phase. Drop down menus will jump to a predefined position. Note that the phases, such as crescent and gibbous, are more broad than the particular point chosen by the presets. The Horizon Diagram panel displays the point of view of the observer (and you are a second observer looking down on that observer). Lab 2:The Moon and Seasons 4/15

5 The observer s horizon diagram can be dragged to allow for the most convenient viewing orientation. The sun and moon on the globe can be dragged around. In the Diagram Options panel, the show angle option shows the earth-moon-sun angle. The phases are technically defined in terms of this angle. In the Diagram Options panel, the show lunar landmark option draws a point of reference to more easily observer lunar rotation and revolution. In the Diagram Options panel, the show time tickmarks option displays the time of day of the observer. Earth Moon Sun Geometry (optional) Question 2: Click on the option labeled show angle which graphically displays the angle between the direction of the sun and moon. Now drag the moon around the sun to a variety of different locations and note the appearance of the Moon Phase. Describe how the value of the angle correlates with the appearance of the moon. Question 3: Each row on the following table shows diagram of the earth-moon system. For each diagram, find the age of the moon at that position (that is, the time passed since new moon), its phase, and its percent illumination. Finally, make a sketch of its general appearance. You will need to take into account the orientation of the sunlight it is different in each diagram from the orientation in the applet. The first row is completed for you. You may need to rotate your paper and hold it up to the screen to check your answers. Lab 2:The Moon and Seasons 5/15

6 Moon Geometry Age Phase Percent Illumination Sketch 11 days, 9 hours Waxing Gibbous 88% Lab 2:The Moon and Seasons 6/15

7 Stop at this point and wait for others to catch up (or for instructions from the instructor). Motion of the Sun 1. Stellarium many observational phenomena require you to observe the sky for many days, weeks, or months. We can simulate predictable patterns of change with the planetarium program Stellarium. Start up Stellarium on your computer. a. Click on F6 to open the Location Window. Set your location to Amherst. b. Click on F5 to open the Time Window. Set the time to about noon today. c. Practice re- orienting the view to different azimuths and elevations. 2. Azimuths and elevations of astronomical objects. By clicking on objects in Stellarium, you can get a lot of information about them. What are the azimuth and elevation of a. the Sun? b. the Moon? c. Jupiter? Now advance the time by an hour, how do the azimuths and elevations change? 3. The noontime position of the Sun in Amherst. a. Set up Stellarium so that you can see both the Sun and the horizon at noon today from Amherst. Where in the sky is the Sun? b. Adjust the time until the Sun is precisely due south (azimuth '). What time is it? Why do you suppose it is not 12:00 noon? c. Plot the altitude of the Sun at noon over the course of the year below. Be careful to adjust for daylight saving time. Altitude of Sun at Noon /1 2/1 3/1 4/1 5/1 6/1 7/1 8/1 9/1 10/1 11/1 12/1 1/1 Lab 2:The Moon and Seasons 7/15

8 a. On what date is the Sun highest, and what is its angle from the zenith (the point straight overhead)? On what date is it lowest, and what is its angle from the zenith? b. On the dates when the Sun is highest and lowest in the sky at noon which are called the summer and winter solstices watch the path of the Sun over the course of a day and describe its motion. Turn on the Alt- Az grid (press z) to help you examine the path. c. On March 20 or September 22 (called the equinoxes), watch the Sun s motion through a day. How is it similar and how is it different from the solstices? The Zodiac Throughout the year, the sun moves through a set of 12 constellations called the Zodiac. This lab will show you how this works! 1. The Sun, the Moon, and the Zodiac. Make sure Stellarium has been adjusted back to today at 4:30pm this evening in Amherst. a. What constellation are the Sun and Moon each in today? (Turn on constellation figures and titles to help you decide.) b. Turn off the atmosphere (A) and center and lock (spacebar) on the Sun around noon today. Now step forward day by day by holding down the = key. What constellations does the Sun move through? c. What is causing the Sun to move through the stars? What other things happen as you watch the Sun move through the stars? 2. The Pole Star. Change Stellarium back to today s date (8), turn on the equatorial grid (E), and look to the north to find the star Polaris. a. Shift the date forward and backward a few hundred years. How far is Polaris from the celestial pole? Lab 2:The Moon and Seasons 8/15

9 b. The ancient Egyptians used the star Thuban ( The Star ) when they built the great pyramids. About when in the past was Thuban the north star? c. Move forward to the year What will the north star be then? Stop at this point and wait for others to catch up (or for instructions from the instructor). Seasonal Motion As astronomers, we are always obsessed with the motion of the sun. It gets in the way of our night observations, so it is best to understand it! Start at Work through the explanatory material on Sidereal vs. Synodic and Seasons and the Zodiac. All of the concepts that are covered in these pages are used in the Paths of the Sun Simulator. Question 1: For each of the following statements respond shorter, the same, or longer. (A) If the Earth revolved more rapidly, its sidereal day would be. (B) If the Earth revolved more rapidly, it solar day would be. (C) If the Earth rotated more rapidly, its sidereal day would be. (D) If the Earth rotated more rapidly, it solar day would be. Question 2: Use the Zodiac Explorer to answer the following questions. (A) On May 25 th, the sun is in the constellation of. (B) What would be a good time of year to observer the constellation Aries? (C) On July 4 th at midnight, the constellation is on the observer s meridian. (D) At sunrise on Christmas Day, the constellation on the observer s meridian is. Paths of the Sun Simulator This simulator allows you to simulate the path of the sun for any date during the year for any latitude on the Earth. Spend some time familiarizing yourself with the simulator most of the controls are fairly intuitive and similar to those in the preceding modules. Practice using the yearly slider to move to different dates during the year. Lab 2:The Moon and Seasons 9/15

10 Practice using the map to move to different latitudes during the year. Note that the simulation lists the right ascension, declination, azimuth, and altitude for the sun at all times. Note that some advanced features such as the sidereal time, hour angle, equation of time, and the analemma are available in a box in the lower left in this simulation, but will not be covered in this guide. Note that there are three different animation modes. o If you select continuous, time will move forward in a natural fashion. You may adjust the rate at which time passes using the animation speed slider. You may modify this mode with the loop day check box which will cause the sun s motion for the current day to continually repeat. o If you select step by day, time will leap forward in 24 hour increments and the time of day will not change. Special care should be taken to make sure that you understand what is being simulated at all times. This is especially true in regard to discriminating between the yearly and daily motion of the sun. o Move to a middle United States Latitude like 35 N. Click show ecliptic and show month labels. This is the sun s yearly path on the celestial sphere and is denoted by a white circle in the simulator. Note that it crosses the blue celestial equator on the equinoxes. o Change your time to noon (12 pm) and animate the simulator in the step by day mode. You can watch the changing meridinal altitude (highest position in the sky) of the sun throughout the year. o Stop the simulation near the summer solstice. The simulator readout should state The horizon diagram is shown for an observer at latitude 35 on 21 June at 12:00 (12:00 pm). Think about what the sun s path should look like in the sky on that day. o Now check show the sun s declination circle which is a yellow circle in the simulator. This is what the sun s path in the sky would be on the summer solstice. Note that this circle has the proper meridinal altitude (78.8 ) and is a coaxial circle with the celestial equator (picture the slinky). Question 3: Set up the simulator for Lincoln, NE which has a latitude of 41 N. Complete the following chart for the meridional altitude and the rising and setting azimuths for the 3 major paths of the sun. Note that the rising azimuth can be determined by dragging the sun (dragging in time of day mode) and reading off the azimuth when the altitude is zero. Try adjusting the minute hand of the clock for more precise control over the Sun s altitude. Lab 2:The Moon and Seasons 10/15

11 Date Meridional Altitude Rising Azimuth Setting Azimuth Summer Solstice Autumnal Equinox Winter Solstice Now use the results from the table above to help you draw the 3 paths in the horizon diagram below. Label each path. Question 4: Suppose that you are visiting Lincoln, NE and on July 10 you wake up early and note the rising azimuth of the sun. In which direction would the value change if you measured it two weeks later? Question 5: Note that the sun can never be at the zenith for Lincoln (lat = 41ºN)? How far would you need to move on the Earth to find a latitude where the sun can be at the zenith? Lab 2:The Moon and Seasons 11/15

12 Question 6: Set up the simulator for Nordkapp, Norway which has a latitude of 71 N. Complete the following chart for the meridional altitude and the rising and setting azimuths for the 3 major paths of the sun. Date Meridional Altitude Rising Azimuth Setting Azimuth Summer Solstice Autumnal Equinox Winter Solstice Now use the results from the table above to help you draw the 3 paths in the horizon diagram below. Label each path. Question 7: Note that the sun doesn t rise every day from Nordkaap. How far would you need to move on the Earth to find a latitude where the sun does rise every day? Lab 2:The Moon and Seasons 12/15

13 Measuring Angles in the Sky 1. Stellarium Set Stellarium back to today at 4:30pm this evening in Amherst. 2. Angular sizes One way that angles are used in astronomy is to measure positions and separations of objects in the sky. Another way is to measure the apparent sizes of objects. A convenient way to measure angular size is to compare objects to your hand held stretched out in front of you. The following activities will help you gauge how to measure different angular sizes with your own hand. a. To get a rough idea of how wide your fingers are, pick two points 90 apart in the room, then starting from one of them, put your 4 fingers side by side till you cover the whole right angle. How many fingers did that take? How many fingers would be 10 for you? 90 Next, we re going to put a grid up on the monitor screen, and we ll give instructions for how far to stand back from it so that the squares on the grid are 1 in size. (There are also heavy lines every 5 to help you keep count.) Figure out what you could use on your outstretched hand to measure 1, 2, 5, 10, 20. (You might also use something like a pencil or coin that you always have with you.) Sketch these on the grid below: Some possible angle scales: Simulating the Sky: We will adjust the field of view of Stellarium so that the projection will show the sky at the same size as you would see standing outside. Estimate the angular size of the following objects in the sky: a. The Sun Lab 2:The Moon and Seasons 13/15

14 b. The Moon c. The bowl of the Big Dipper d. The belt of Orion e. The Pleiades f. The Little Dipper Now on your individual computer press z to add an Alt/Az grid to your screen. Look at the objects above again and compare the angular size you measure using the grid with your earlier estimates. 4. Angular size vs. Distance: From where you re sitting, estimate the angular height of the wall that s closest to you. Estimate the angular height of the wall that s farthest from you. Why are they different? We re going to compare the angular width of one of the walls of the room that you measured to your distance from it to see what this relationship looks like. a. On the worksheet, write down the location of your measurement and the width in degrees that you found. b. Find the distance of your observing position. Add that information to the worksheet. c. Plot your data on the graph and add your points to the class graph on the board. 5. Interpreting the Graph: Look over the points plotted by the class. a. Do the plots exhibit a pattern? How would you describe that pattern in words? b. How might you describe the relationship mathematically? c. Do all the points agree with each other? What factors might explain the differences we see? 6. The Sun s Angular Size: Start up Stellarium. Focus in on the Sun, and zoom in so that it fills about half your screen. The Sun s angular size is about half a degree. Angles smaller than a degree are broken up into arc minutes, which are 1/60 th of a degree. Angles smaller than an arc minute are broken up into arc seconds, which are 1/60 th of an arc minute. If you click on the Sun, you will see its size reported as a little over 30 arc minutes and some number of arc seconds. Lab 2:The Moon and Seasons 14/15

15 a. Did you know that the Sun s angular size to change during the year? When do you expect it to be smallest? b. In the graph below, plot the Sun s angular size over the course of a year at least one point for each month. Note that in Stellarium it may be easiest to open up the time window (F5) and shift the month field by one each time. You can keep the Sun centered in the field of view by hitting the space bar when the Sun is centered. Angular size of the Sun /1 2/1 3/1 4/1 5/1 6/1 7/1 8/1 9/1 10/1 11/1 12/1 1/1 Day of the Year Lab 2:The Moon and Seasons 15/15