Grade Level/Subject 11th/12th Grade Astronomy Unit Models of the Universe Enduring Understanding The physical and orbital properties of the Earth and all of the objects that orbit the Sun are regulated by their mass and proximity to the Sun. SOL Objectives N/A Title Heliocentric Model Lab Lesson Objective Visualization of different orbits from the earth’s perspective. The reason why Venus and Mercury always appear close to the Sun, while others maybe possibly be visible at any time during the night. Inquiry Level Level 2 – Questions and methods given, solution open Materials Required Computer with Internet access Name ____________________________________ Date _________________ Pd ____________ Heliocentric Model Lab Use the following website: http://astro.unl.edu/naap/ssm/ Go to the page titled Elongation. 1. What is elongation? Explain in words and make a diagram. Copernicanum The Harmonia Macrocosmica of Andreas Cellarius From http://www.staff.science.uu.nl/~gent0113/cellarius/c ellarius_plates.htm 2. Which planets have “greatest elongations?” Inferior or Superior 3. How can planets have a ‘greatest’ elongation? Explain with a diagram that includes earth (where we are), Venus, and the sun. Show the angle that is made by using the Greek letter θ (pronounced ‘theta’). 4. What are superior and inferior conjunctions? Draw diagrams to help explain your answer. Name ____________________________________ Date _________________ Pd ____________ Now check out the page titled “Elongations and Configurations” 5. Which planets can be in quadrature? Inferior or Superior 6. Place the planet at locations A-D according to the information in the boxes, or fill the boxes accordingly. Be sure to draw elongation angles in the diagram. Location Elongation A Term 180° B Earth Western Quadrature Sun C D East 120° No term for this configuration C 7. Complete the table below, place the planet at the indicated positions, and draw elongation angles. Location Elongation A Term Earth Superior Conjunction Sun B Inferior Conjunction C C D West 20° No term for this configuration Name ____________________________________ Date _________________ Pd ____________ 8. What is a synodic period? Open the Planetary Configurations Simulator. Select the “Show Elongation Angle” option. 9. Find the synodic period for the Earth and Mercury. Use a configuration, such as superior conjunction as your reference point to tell whether a whole period has passed. You can drag the planets around and be sure to reset your counter for the new configuration. Synodic period of Earth/Mercury: ______________________ 10. Why is superior conjunction not the best reference for measuring synodic period? Hint: look at the zodiac view. Compare this to other configurations. Which would be the best configuration for measuring synodic periods? 11. Use greatest elongation as the reference configuration to calculate the synodic period of Venus. Be sure to stick with either East or West. Synodic period of Earth/Venus: _____________________ Greatest elongation of Venus: __________________ 12. What trend do you notice between an interior planet’s distance from the Earth and its synodic period? Name ____________________________________ Date _________________ Pd ____________ 13. Now use the simulator to find the value of Mercury’s greatest elongation. Greatest elongation: ______________________ What relationship do you notice between the value of greatest elongation of a planet and its distance from the Sun? 14. Measure the synodic period of Mars. Set up a preferred configuration between the two planets, reset the counter, and animate. How long does it take to for Mars and the Earth to return to the same configuration? Synodic Period of Mars __________________________________ 15. Just as with superior conjunction in Problem #10, why is conjunction not the best configuration to observe a superior planet in the sky? What would be a better configuration? 16. Measure the synodic periods of Jupiter and Saturn. Synodic Period of Jupiter _________________________________ Synodic Period of Saturn _________________________________ Name ____________________________________ Date _________________ Pd ____________ 17. Look over the synodic periods of the superior planets. Is there a trend? What value does the synodic period of a superior planet approach as we consider planets farther and farther away from Earth? Explain the trend. 18. Fill in the table below based on the data from your past runs. Planet Synodic Period (Yr) Distance from Earth (AU) Looking at your data table, what’s a relationship between a planet’s synodic period and its distance from the Earth? Name ____________________________________ Date _________________ Pd ____________ Supplementary Lab The following lab is a supplementary lab if more time is given on the Ptolemaic Model (geocentric). Name ____________________________________ Date _________________ Pd ____________ Ptolemaic Model Lab Use the following website for this lab: http://astro.unl.edu/naap/ssm/animations/ptolemaic.html 1. Draw a basic Ptolemaic System. Include the earth, an equant, deferent (with center), a planet with an epicycle, the sun, and background stars/constellations/zodiac. 2. When the sun goes around once in the animation, how long of a period of time is it? 3. Choose Venus and “start animation.” Epicycles were invented to account for apparent retrograde motion. Describe in complete sentences how epicycles account for this motion as seen from the earth. Note the planet’s perceived movement relative to the zodiac. 4. Describe what each of the settings do: a. Epicycle size: b. Eccentricity: c. Motion rate: d. Apogee angle: Name ____________________________________ Date _________________ Pd ____________ 5. Epicycles were invented to account for apparent retrograde motion. What do you think equants were invented for? 6. What do the inferior/superior options refer to? 7. Using the planet presents, what happens to the epicycle size as you get to outer planets? 8. What happens to “motion rate” as you go from inner to outer planets? What do you think this corresponds to in our modern model of our solar system? 9. Rank the planets in terms of how quickly they go through the background stars/zodiac. 10. An “inferior planet” is one in which the planet at apogee (closest approach to earth) is collinear with the earth and the moon. Draw a sketch of what you see at apogee. Which planet did you choose? 11. Venus has been called both the “morning star” and the “evening star.” Why do you think that is? Use the simulation to support your assertion. Name ____________________________________ Date _________________ Pd ____________ 12. Make a data table of the number of orbits the sun completes for each complete orbit of the planets. Planet Number of orbits of the sun (years) What trend do you notice? 13. What does “apparent retrograde motion” look like according to the fixed zodiac? 14. If Mercury were on this simulation, what would you expect its orbit to be like? Go to the following page: http://astro.unl.edu/naap/ssm/ssm.html Use the pages under Geocentric Model to answer the following questions and prompts. 15. Describe elongation, opposition, superior and inferior conjunction, and quadrature. Draw a diagram for each. Name ____________________________________ Date _________________ Pd ____________ 16. Generally, which direction to the planets move with respect to the stars? 17. Draw a diagram of what apparent retrograde motion looks like. Include arrows, directions (east, west, etc.).