1110AST-lab3

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Feb 20, 2024

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AST 1110: Planetary Astronomy Lab 3 (30 points) Name: Jenna McCarthy Geocentric vs. Heliocentric Models Learning Goals  Describe the motion of objects in Geocentric solar system models  Describe Kepler’s laws of orbital motion for the Heliocentric solar system model  Explain some of the evidence for the Heliocentric model Use any of the Chapter 2 and Chapter 3 resources to help with this lab but remember, your answers need to be written in your own words. Part 1 - Geocentric Models 1. The diagram below is based on a geocentric model . (You can see an animated version of this model from Khan Academy) On the diagram below, label the following things: a. Earth b.Sun c. Mars d.Mars' main orbit e.Mars' epicycle 2. Describe how geocentric models of the solar system explained the prograde and retrograde motion of outer planets on the sky (such as Mars). 1

Retrograde motion occurs when planets appear to move backward in their orbit or east to west due to their relative positions in space. This phenomenon was once explained by the ancient Greeks as the motion of planets on two sets of circles, a deferent, and an epicycle. In the geometric model, prograde refers to the movement of a planet from west to east relative to the stars. 3. The diagram below is also based on a geocentric model , in this case showing the motion of inner planet Venus. On the diagram below, label the following things: a. Earth b.Sun c. Venus d.Venus' main orbit e.Venus' epicycle 4. Check out this animation of phases of Venus in the Ptolemaic model. What phases can Venus show in this model? Waxing and waning crescent phases. 5. Now take a look at the phases of Venus in the Copernican model. Do this by clicking and dragging on Venus while leaving Earth’s position alone. What phases does Venus show in the Copernican model? The full set of phases. 6. Why does the angular diameter of Venus change in the Copernican model? The diameter of Venus varies due to its retrograde orbit, causing it to appear larger or smaller from Earth. 2

7. Describe some of the observations that Galileo made with his telescope that proved that the geocentric model was not correct. Galileo discovered four moons orbiting around Jupiter, with orbital periods ranging from just under 2 days to about 17 days. This discovery was significant because it proved that not everything in the universe had to revolve around the Earth. Moreover, it demonstrated that there could be centers of motion that were themselves in motion. Part 2 - Heliocentric Models Planets normally move from West to East compared to the fixed stars ( prograde motion). Occasionally the planets will stop their prograde motion and move from East to West through the stars. This is called retrograde motion. The image above is a time lapse showing the planet Venus making a retrograde loop over a period of several months (and here’s a video showing Mars moving prograde and retrograde). 8. In the image above, what is the date range when Venus is moving retrograde? May 10 - June 10 9. In the image above, what are the date ranges when Venus is moving prograde? April 1 - May 1 10. In which direction will planets move most of the time, relative to the fixed stars? 3

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West to East. 11. Use the data in Table 1 (scroll down) to plot the motion of Mars on the graph provided (scroll down). You should measure the points in Azimuth and Altitude as precisely as you can! Use a ruler or the edge of a book. Label the date for each point. 12. Connect your data points, in order of date, to show the path of Mars through the sky. 13. According to the data points on the handout, on what date was Mars located farthest to the west? Date: _ February 15 __ What was the azimuth value of Mars on that date? __ 245º __ 14. According to the data points on the handout, on what date was Mars located farthest to the east? Date: __ June 1 _ What was the azimuth value of Mars on that date? ____ 125º __ 15. On what dates was Mars moving from east toward west? Is this prograde or retrograde? Feb 15-March 15 and April 15-June 1. This is retrograde. 16. On what dates was Mars moving from west toward east? Is this prograde or retrograde? March 15-April 15. This is prograde. Table 1: Position of Mars Date of Observation Azimuth (degrees) Altitude (degrees) 4

February 15 245 ° 40 ° March 1 235 ° 35 ° March 15 175 ° 30 ° April 1 155 ° 25 ° April 15 175 ° 30 ° May 1 185 ° 35 ° May 15 145 ° 35 ° June 1 125 ° 30 ° Don’t forget to finish the rest of the questions on page 3-4 after completing your diagram above! I know the next part is a little confusing. Check out this video where they show a really similar diagram explaining orbital motion and how it produces retrograde loops. The way that they connect the points is the way that you should do it as well. 5

17. On the diagram below, use a ruler to connect the same-numbered points along the two orbits. Then run this straight line all the way across to the background stars. Place a dot where the line intersects the background lines. Then connect the dots for 1 - 9. 18. Why does Mars appear to move, but the background stars do not appear to move? Think about where Mars is vs. where the stars are. Mars appears to move because of its proximity to Earth and its orbit around the Sun. This causes its position relative to the background stars to change over time. However, the background stars are so far away that their movement is not noticeable within the timescale of observing Mars. As a result, they appear to be fixed in the sky. 19. Which points on the figure correspond to prograde motion? ___ 1-4 and 6-9 ______ 20. Which points on the figure correspond to retrograde motion? ____ 4-5 _____ 21. Explain what Earth and Mars were doing in their respective orbits that caused Mars to appear to move retrograde. 6

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Part 3 - Kepler’s Laws and Elliptical Orbits 22. On the diagram above, clearly label the following parts of the orbit. a. Sun b. Empty Focus c. Perihelion d. Aphelion e. Semimajor axis f. Semiminor axis 23. On the diagram above, use a ruler to measure the length of the major axis (long axis) in millimeters : 74mm 24. On the diagram above, measure the distance between the two foci in millimeters : 35mm 25. Determine the eccentricity, e, of the ellipse using: e = 35 74 e = ___ 0.473 _______________ 26. Is the ellipse closer to a circle (e = 0) or closer to a parabola (e = 1)? ___ Closer to a parabola ____ 7

27. In your own words, summarize what each of Kepler’s Three Laws tells us about planetary orbits in our solar system. Kepler's First Law states that the orbit of each planet is an ellipse with the Sun at one of its foci. This means that the shape of the orbit is not a perfect circle but a stretched circular shape that forms an ellipse. Kepler's Second Law states that a line segment connecting a planet and the Sun will sweep out equal areas in equal periods of time. This means that the speed of a planet changes depending on its distance from the Sun. When a planet is closer to the Sun (at perihelion), it moves faster, while it moves slower when it is farther away (at aphelion). Kepler's Third Law states that the time it takes for a planet to complete one orbit around the Sun is directly related to its distance from the Sun. 8

1110AST-lab3

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