Lab 4 – 2024 – Basic Coordinates and Seasons

Astronomy 020 —Lab 4 Basic Coordinates & Seasons There are three main sections to this lab: 1. terrestrial coordinates, 2. celestial equatorial coordinates 3. understanding how the ecliptic is related to seasons on the Earth Each of these sections has its own simulator(s). The background material necessary to utilize these tools is contained in each section. All of this content is organized on the following webpage: https://astro.unl.edu/naap/motion1/motion1.html Terrestrial Coordinates Work through the explanatory material on units of longitude and latitude , finding longitude and latitude , and a bit of history (optional). • Open the flat map explorer . • Familiarize yourself with the cursor and how it prints out the longitude and latitude of the active map location. • Note that you can vary the central meridian of the map (i.e. change its longitude) by using the shift- click feature of the cursor for control. • Note what information is accessible through the show cities and show map features check boxes. • Center the cursor on your present location. Click the open Google Maps button to launch the Google Map tool focused on this location. Question 1: Use the flat map explorer to complete the following table. You are encouraged to try and predict the answers and then use the map’s cursor and other features to check the accuracy of your estimates. Location Longitude Latitude The center of the island of Sri Lanka. 18.4° W 33.9º S International Date Line 16.8° S 150.5° W Tropic of Capricorn Reykjavík, Iceland 91° 04’ E 29° 37’ N 23° 43’ E 37° 55’ N Pigeon Forge, Tennessee 25.7° E Arctic Circle 66.1° W 18.4° N

106° 45’ E 6° 09’ S Question 2: Using show cities , which city shown in the flat map explorer is the closest to the Tropic of Cancer? Question 3: The exact coordinates of the Great Pyramid of Giza (tomb of pharaoh Khufu) are 31.134° E and 29.979° N. What are these exact coordinates in sexagesimal notation? Show your calculations below. • Open the globe explorer. You are encouraged to use the Terrestrial Coordinate Explorers link which opens both simulators at the same time for the following two questions. Familiarize yourself with the features noting that they are very similar to those in the flat map explorer. Question 4: A) Where is the north pole on the flat map explorer ? What is its shape? B) Where is the north pole on the globe explorer ? What is its shape? C) Why does the north pole not have the same shape in the two different map explorers?

Question 7: The image below, from the Sky Map Explorer, shows the celestial sphere including labeled representations of the celestial equator, the ecliptic, and the galactic equator. What does it mean that the galactic equator is angled relative to the ecliptic? Consider describing the ecliptic plane as a disk in your answer, or discussing what the galactic plane might appear to an observer on Earth. Question 8: Complete the following table of positions on the ecliptic. Ecliptic Location Approximate Date Right Ascension Declination Vernal Equinox March 21 Summer Solstice June 21 Autumnal Equinox December 21 Question 9: Complete the descriptive criteria for the following items from the Flat Sky Map Explorer : Shape of the ecliptic : Total range of declination angle of ecliptic : Shape of the galactic equator : Total range of declination angle of galactic equator :

Seasons and the Ecliptic Work through the introductory material on the page entitled Orbits and Light . • Open the Seasons and Ecliptic Simulator . • Note that there are three main panels (left, upper right, and lower right) each of which have two different views. Controls run along the bottom of the simulation that affect more than one panel. Click animate and then move through the six views to get an overview this simulator’s capabilities. We will address each of these six views separately. • Experiment with the various methods to advance time in the simulator. You may click the start animate/stop animation button, drag the yearly time slider, or drag either the sun or the earth in the left panel to advance time. • Note that this animation does not illustrate the rotation of the earth. Because the timescales of rotation and revolution are so different, it isn’t possible to effectively show both simultaneously. Left Panel – Orbit View • Practice clicking and dragging in this panel to change the perspective. Change the perspective so that you are looking directly down onto the plane of the Earth’s orbit • Click labels. Note that you can see how the direct rays of the sun hit at different latitudes throughout the year. • Experiment with this view until you can quickly create the two views shown below. Note that these images explain the shape of the elliptic on the celestial sphere. In the image on the left (summer solstice) an observer on the Earth sees the sun above the celestial equator. In the image on the right (winter solstice) an observer on the Earth sees the sun below the celestial equator. Left Panel – Celestial Sphere • This view shows the earth at the center of the celestial sphere. The celestial equator and the ecliptic with the sun’s location are shown. Note that you may click on the sun and drag it and read out its coordinates. • Experiment with this view until you can quickly create the image to the right – the direct rays of the sun hitting the earth on the summer solstice. Upper Right Panel – View from Sun • This view shows the earth as seen from the sun. It gives the best view of the subsolar point – the location on the earth where the direct rays of the sun are hitting. The noon observer’s location on the Earth is indicated by a red parallel of latitude which can be dragged to new latitudes (this affects the appearance of the lower right panel). It is possible for the red parallel to be Tip: Note that if you click and drag the Earth, you will change the date and location rather than the perspective.

Question 10: The table below contains entries for the coordinates for the sun on the ecliptic as well as the latitude on Earth where are found the most direct and least direct sunlight rays (just before no light rays). Use the simulation to complete the table. Question 11: Using the data in the table above, formulate general rules relating the declination of the sun to the latitude where the most direct and least direct rays of the sun are hitting. Describe your general rule in the language of a mathematical equation. Date RA DEC Latitude of Most Direct Sun Rays Latitude of Least Direct Sun Rays January 29 th February 27 th 22.7 h − 8.4 ° 8.3 ° S 81.4 ° N March 13 th May 18 th June 24 th August 31 st October 8 th November 15 th December 22 nd