Understanding Coordinates and Seasons in ASTR 110L Lab 04

ASTR 110L Lab 04 Lab 04 Basic Coordinates and Seasons In this Lab, we will first explore how we use coordinate systems to locate objects and places on the Earth’s surface and on the sky. Our focus in the first 5 Exercises will be to understand the working of Longitude and Latitude, the coordinates used on the Earth’s surface. In the next 3 Exercises, we will apply this understanding to the locations of stars and planets in the sky. We will learn about Right Ascension and declination, the analogues on the sky of Longitude and Latitude. In the final 2 Exercises, we will study about orbits, particularly the orbit of the Earth about the Sun. Because Earth is tilted and because its axis of rotation is constrained to point at one particular point in the sky, the amount of light delivered daily to any one point on the globe varies cyclically through the year. This gives rise to the seasons, which we will understand as phenomena with mechanical roots in the basic motions of the Solar System. In the Exercises below, please give comprehensive and well-reasoned answers to the questions posed. The spaces provided for your answers will expand as you add more text. There are no constraints to the amount of space you may wish to use, since the space will expand to accommodate all your expressed thoughts.

ASTR 110L Lab 04 ******************************************************************* Terrestrial Coordinates Exercise #1 – Units of Longitude and Latitude Please read the information provided for this Exercise. Complete the following questions: 1. Use the calculation tool to convert the following angles from the decimal system to the sexagesimal system: (3 points) Decimal Angle Sexagesimal Angle 12.587 o 12’35’13 86.2 o 1’26’12 159.45 o 2’39’27 2. Use the calculation tool to convert the following angles from the sexagesimal system to the decimal system: (3 points) Sexagesima l Angle Decimal Angle 6 o 4’50” 6.0806 75 o 12’46” 75.2128 141 o 42’58” 141.7161 ********** Exercise #2 – Finding Longitude and Latitude (0 points) Please read the information provided for this Exercise. Absorb it and integrate it into your Discussion & Conclusion section. ********** Exercise #3 – A Bit of History (0 points) Please read the information provided for this Exercise. Absorb it and integrate it into your Discussion & Conclusion section. ********** Exercise #4 – Flat Map Explorer Click on the Map to launch the simulator in a new window.

ASTR 110L Lab 04 The horizontal red line is the line for longitude; it will run from 180 o E to 0 o to 180 o W. The vertical blue line is the line for latitude; it will run from 90 o N to 0 o to 90 o S. By clicking around on the Map, the Longitude and Latitude of any point may be displayed. The tip of the blue line is the point whose Longitude and Latitude are displayed. The Latitude and Longitude are displayed alongside the blue and red lines, respectively; they are also displayed in the Point Location area in the lower left of the screen. The Point Location area also permits one to switch between decimal and sexagesimal display modes. The Show Cities checkbox displays about 19 cities around the Earth. (Is McMurdo Station a city?) Clicking on a city gives its Longitude and Latitude. The Show Map Features checkbox displays important Meridians of Longitude and Parallels of Latitude. Google Maps may opened for any point selected on the Map. By using the arrows at the top, the Map may be shifted left and right.

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ASTR 110L Lab 04 Complete the following questions: 1. Which cities lie between the Tropic of Cancer and the Tropic of Capricorn? (2 points) Cuba, Havana, Sao Paulo, Brazil 2. Which cities lie north of the Arctic Circle? (2 points) Barrow & Alaska 3. Which cities lie south of the Antarctic Circle? (2 points)v Reykjavik & Iceland 4. Which cities are closest to the Equator? (2 points) Singapore, Monrovia & Liberia 5. Find the Longitudes and Latitudes of the following cities: (10 points) City Longitude Latitude Barrow, Alaska 157.7W 71.0N Havana, Cuba 82.6W 23.1N Monrovia, Liberia 11.1W 6.2N Beijing, China 115.9E 40.1N McMurdo Station 166.3E 77.7S ********** Exercise #5 – Globe Explorer Click on the Map to launch the simulator in a new window.

ASTR 110L Lab 04 The horizontal red line is the line for longitude; it will run from 180 o E to 0 o to 180 o W. The vertical blue line is the line for latitude; it will run from 90 o N to 0 o to 90 o S. By clicking around on the Map, the Longitude and Latitude of any point may be displayed. To rotate the Earth in any direction, hold down the shift key and use the left mouse button to orient the Earth into any desired position. As with the Flat Map, the tip of the blue line is the point whose Longitude and Latitude are displayed. The Latitude and Longitude are displayed alongside the blue and red lines, respectively; they are also displayed in the Point Location area in the upper right of the screen. The Point Location area also permits one to switch between decimal and sexagesimal display modes. The Show Cities checkbox displays about 19 cities around the Earth. Clicking on a city gives its Longitude and Latitude. The Show Map Features checkbox displays important Meridians of Longitude and Parallels of Latitude. Google Maps may be opened for any point selected on the Map. Complete the following questions: 1. Find the Longitudes and Latitudes of the following cities: (10 points) City Longitude Latitude Canberra, Australia 149.0E 35.5S Baghdad, Iraq 44.6E 33.4N Calcutta, India 88.3E 22.6N Moscow, Russia 37.4E 56.1N Washington, DC 76.5W 39.1N ********** ******************************************************************* Celestial Equatorial Coordinates Exercise #6 – Celestial Equatorial Coordinate System Complete the following questions:

ASTR 110L Lab 04 1. Compare and contrast Latitude and Declination. (2 points) Both measured in degrees N or S of equator since declination is measured from equator and latitude measures how far from equator. 2. Compare and contrast Longitude and Right Ascension. (2 points) E & W degrees measured for longitude and the right ascension is measured in the duration the earth rotates. Both measuring east while right ascension only measures out east. 3. In the Celestial Equatorial Coordinate System, what plays (somewhat) the role of the Prime Meridian on Earth? (1 point) N & S Poles **********

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ASTR 110L Lab 04 Exercise #7 – Flat Sky Map Explorer (15 points) Click on the Map to launch the simulator in a new window. The horizontal line is the line for Right Ascension; the standard symbol for Right Ascension is a ; we will refer to it as RA. Measured in hours, it runs here from the left at about 16.5 hours to the right to 0 hours, which becomes 24 hours, and on to about 16.5 hours. The vertical line is the line for Declination; the standard symbol for Declination is d ; we will refer to it as DEC. it runs from +90 o to 0 o to -90 o . This rectangular map is a wrap-around panoramic view horizontally and a top- to-bottom view vertically. You can see that the stars are not evenly distributed around the sky. By clicking around on the star field, the RA and DEC of any point may be displayed. The tip of the vertical line is the point whose RA and DEC are displayed. The RA and DEC are displayed alongside the horizontal and vertical lines, respectively; they are also displayed in the Point Location area in the lower left of the screen. The Point Location area also permits one to switch between decimal and sexagesimal display modes. There are 5 checkboxes we will be using here. These are used to show the Celestial Equator, the Ecliptic, the Equinoxes and Solstices, the Galactic Equator (the Equator of the Milky Way galaxy), and the Zodiac Constellations. By using the arrows at the top, the Map may be shifted left and right. Familiarize yourself now with the Flat Sky Map and the checkboxes. Check only the boxes for the Celestial Equator and the Ecliptic. Then answer the following questions:

ASTR 110L Lab 04 1. What is the ecliptic? Why does it go up and down? (2 points) It is the plane of earth’s orbit around the sun 2. Describe differences between the Celestial Equator and the Ecliptic. (2 points) Ecliptic is not coplanar with celestial equator 3. Select the leftmost point where the Ecliptic crosses the Celestial Equator. What is the RA/DEC of this point? (2 points) 11.9 h/0.0 4. Select the rightmost point where the Ecliptic crosses the Celestial Equator. What is the RA/DEC of this point? (2 points) 0.1 h//0/0 Check only the boxes for the Celestial Equator, the Ecliptic, and the Equinoxes and Solstices. Then, remembering that these points represent a Northern Hemisphere point of view, answer the following questions:

ASTR 110L Lab 04 5. What are the Celestial Coordinates of the Autumnal Equinox point (about 21 September)? (2 points) 21.1h/0.0 6. What are the Celestial Coordinates of the Summer Solstice point (about 21 June)? (2 points) 6.0h/23.7 7. What are the Celestial Coordinates of the Vernal Equinox point (about 21 March)? (2 points) 0.0h/0.0 8. What are the Celestial Coordinates of the Winter Solstice point (about 21 December)? (2 points) 18.0h/-23.1 9. What does it mean that the dates go from right to left along the horizontal axis? (2 points) Check only the boxes for the Galactic Equator, the Celestial Equator, and the Ecliptic. Then answer the following questions: 10. Describe the Galactic Equator. (2 points) Imaginary planes that splits the galaxy into a top and a bottom

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ASTR 110L Lab 04 11. Is there any visible significance for the Galactic Equator? (2 points) Positive towards the N Galactic Pole 12. What might it mean that the Galactic Equator doesn’t line up very well with the Ecliptic? (2 points) The earth is tilted at an angle aligning with the plane of it’s orbit Check only the boxes for the Ecliptic and the Zodiac Constellations. Then answer the following question: 13. Why do the Zodiac Constellations line up with the Ecliptic? (2 points) Because they are season ********** Exercise #8 – Sky Map Explorer (15 points) Click on the Map to launch the simulator in a new window. The “horizontal” line is the line for RA; it runs from 0 hours to 24 hours, where it becomes 0 hours again. The “vertical” line is the line for DEC; it runs from +90 o down to -90 o . By clicking around on the Map, the RA and DEC of any point may be displayed. To rotate the Celestial Sphere in any direction, hold down the shift key and use the left mouse button to orient the Celestial Sphere into any desired position.

ASTR 110L Lab 04 As with the Flat Map, the tip of the “vertical” line is the point whose RA and DEC are displayed. The RA and DEC are displayed alongside the “horizontal” and “vertical” lines, respectively; they are also displayed in the Point Location area in the upper right of the screen. The Point Location area also permits one to switch between decimal and sexagesimal display modes. There are 6 checkboxes we will be using here. These are used to show the Celestial Equator, the Ecliptic, the Equinoxes and Solstices, the Galactic Equator, the Celestial Poles, and the Zodiac Constellations.

ASTR 110L Lab 04 Check only the boxes for the Celestial Equator, the Celestial Poles, and the Ecliptic. Then answer the following questions: On the Celestial Sphere, find: 1. the largest DEC of the Ecliptic north of the Celestial Equator. (2 points) 90.0 2. the largest DEC of the Ecliptic south of the Celestial Equator. (2 points) -60.0 3. Find the Celestial Coordinates of the two points where the Ecliptic intersects the Celestial Equator. (2 points) 6.0h/23.3

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ASTR 110L Lab 04 Check only the boxes for the Celestial Equator, the Celestial Poles, the Ecliptic, and the Equinoxes and Solstices. Then, remembering that these points represent a Northern Hemisphere point of view, answer the following questions: 4. Relate the inclusion of the Equinoxes and Solstices to the answers to the questions directly above. (2 points) Check only the boxes for the Celestial Poles, the Ecliptic, and the Zodiac Constellations Then, answer the following questions: 5. How are the Zodiac Constellations aligned on the Celestial Sphere? Does the Sky Map Explorer provide any other insights that the Flat Sky Map Explorer did not? (2 points) The sky map explorer showed the different constellations that appeared during certain equionoxes. Check only the boxes for the Galactic Equator, the Equinoxes and Solstices, and the Ecliptic. Then answer the following questions: 6. Are there any interesting observations to be made in this image of the sky? (2 points) The galactic equator acts as a right angle as is crosses the ecliptic

ASTR 110L Lab 04 ******************************************************************* Seasons and the Ecliptic Exercise #9 – Orbits and Light (15 points) Read the information provided and digest it well. Click Animate on the Sun at Noon animation. Then answer the following questions: 1. The Sun is on the meridian at Noon. Why is the arc of the Sun moving? (2 points) Because the tilting of the earth towards and away from the sun changes. 2. What is this animation telling us? (2 points) The tilting axis moves towards and away from the sun in a one year period. Examine the Light Rays and Angle of Incidence animation. Then answer the following questions: 3. What is the range of the Sun’s Angle from the Zenith in this animation? (2 points) 50.0 The angle of the Sun’s rays is here equal to the Latitude of the location on Earth. 4. What is the angle of the Sun’s rays at the Equator? (2 points)

ASTR 110L Lab 04 90.0 5. What is the angle of the Sun’s rays at the North Pole? (2 points) 66.2

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ASTR 110L Lab 04 6. At the Equator, the 1 sq.m. shaft of sunlight is most concentrated. So, the ground has the maximum heating. At different latitudes, the shaft would be more spread out and the ground would be less heated. Use the animation to complete the Table to determine how the shaft’s energy is spread out. (20 points) Angle of Sun’s Rays (degrees) Area of Spot (sq.m.) Relative Intensity 0.6 1.000 1.000 10.0 1.015 0.986 20.0 1.064 0.940 30.0 1.156 0.865 40.0 1.311 0.763 50.0 1.575 0.635 60.0 2.050 0.488 70.0 2.910 0.344 80.0 5.816 0.172 88.8 81.853 0.012 7. At approximately what latitude is the relative intensity of the light reduced to 50% (0.500)? -59.8

ASTR 110L Lab 04 Exercise #10 – Seasons and Ecliptic Simulator (15 points) The 3 frames in this screen are all interrelated. In the left frame, the scene opens in the orbit view. The Earth can be dragged to different positions on its orbit; its tilt, though, cannot be changed. Besides shifting the Earth in its orbit, the orbit can be tilted so as to be seen as edge-on or as face-on. As it is moved, the red arrow on the Calendar Bar moves, indicating the month. The day side and the night side of the Earth are evident. The Earth has visible Parallels of Latitude. From north to south, these, in green, are the Arctic Circle, the Tropic of Cancer, the Equator, the Tropic of Capricorn, and the Antarctic Circle. The red Parallel of Latitude corresponds to the location of the stick-figure in the upper right frame. The daylight side of the Earth has a Subsolar Spot; this is the spot on the earth where the Sun shines vertically downward. In the lower left, the Sun’s RA and DEC are displayed. In the upper right frame, we see the observer, the Earth, and the incoming Sun’s rays. The observer can be dragged to different positions on the Earth; he/she cannot be dragged past the poles; the red Parallel of Latitude moves along with the observer. The observer’s Latitude is given in the lower left corner of the frame. The checkbox in the lower right corner turns on the labels identifying the Parallels and the Poles. In this frame, Earth’s axis remains vertical while the Sun’s rays swing up and down as the Earth orbits the Sun through the year.

ASTR 110L Lab 04 Clicking on the button for View From the Sun shows the full Earth with the subsolar point at the center of the image. The Earth’s tilt is evident, but it appears to precess as the Earth orbits the Sun. In the lower right frame, we see the incoming Sun’s rays tilted at an angle to the ground. The observer can be dragged to different positions on the Earth; he/she cannot be dragged past the poles; the red Parallel of Latitude moves along with the observer. The observer’s Latitude is given in the lower left corner of the frame. The checkbox in the lower right corner turns on the labels identifying the Parallels and the Poles. In the information box, the Sun’s Altitude and the observer’s Latitude is given. Across the bottom, we have a timeline of 1 year, measured in months. Its red indicator can be moved to any position. The calendar date is given on the far right. The start animation button is located there. On the far left, there is a checkbox for displaying or hiding the subsolar point. Above that is a choice box for the left frame permitting a selection between the orbit (heliocentric) view and the celestial sphere (geocentric) view. In the celestial sphere view, the Sun is a flat disk moving on the Ecliptic; Earth stands with its axis perpendicular to the horizontal line. Set the Orbit View; the horizontal line is the Orbital Path, the Ecliptic. Set Subsolar Point On. Select Sunlight Angle and View from Side. 1. For the following observer Latitudes and dates, measure the Sun’s Altitude: (84 points)

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ASTR 110L Lab 04 Observer Latitude (degrees N) 1 st Day 0 15 30 45 60 75 90 D A T E Jan 7.2 -7.9 -22.9 Feb 13.0 -2.0 -17.0 Mar 22.3 7.3 -7.7 Apr 34.3 19.2 4.3 May 45.0 14.9 Jun 52.1 22.1 Jul 53.0 23.0 Aug 47.4 17.4 Sep 37.2 7.1 Oct 25.6 -4.5 Nov 14.7 -15.4 Dec 7.9 -22.1 Answer the following questions: 2. Which Latitude shows the largest range in the Sun’s Altitude? What is that range? (2 points)

ASTR 110L Lab 04 3. Which Latitude shows the smallest range in the Sun’s Altitude? What is that range? (2 points) 4. Set the left frame to Celestial Sphere. How do we describe what the Sun is doing?(2 points)

Lab 04 - NAAP Worksheet _2

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