Understanding Solar System Models: Heliocentric vs Geocentric

Ahmad Turner Lesson 3 Lab - Solar System Models Background Material Review the Geocentric Model background material. The simulation of Ptolemy’s model demonstrates the dominate model when Copernicus presented his heliocentric model. Thoroughly review the Heliocentric Model background material. Locatio n Elongatio n Term A 180° opposition B 90 degrees Western Quadrature C 0 degrees conjuction D East 120° XXX Question 1: (1 point) Look at the Animation of the Copernican Solar System on the “Heliocentricism” page. What relationship do you notice between how fast a planet moves in its orbit and its distance from the Sun? It moves faster when it is closer to the sun. Question 2: (1 point) The table below concerns various elongation configurations for a hypothetical superior planet. Complete any missing elongations, terminology, or lettered labels on the drawing where the Sun and Earth are shown. C Sun Earth

Question 3: (1 point) C Sun Earth The table below concerns various elongation configurations for a hypothetical inferior planet. Complete any missing elongations, terminology, or lettered labels on the drawing where the Sun and Earth are shown. Locatio n Elongatio n Term A 0 degrees Superior Conjunction B 0 degrees Inferior Conjunction C 46 degrees elongation D West 20° XXX Simulator Exercises Open up the Planetary Configurations Simulator and complete the following exercises. Question 4: (1 point) In this exercise we will measure the synodic period of Mercury. Set the observer’s planet to Earth and the target planet to Mercury. The synodic period of a planet is the time it takes to go from one elongation configuration to the next occurrence of that same configuration. However, it makes sense to use an easily recognized configuration like superior conjunction. Drag a planet (or the timeline) until Mercury is at superior conjunction. Now zero the counter, click start animation, and observe the counter. A synodic period is that time until Mercury is once again at superior conjunction.

What is the synodic period of Mercury? .322 years Question 5:

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(1 point) In the previous exercise superior conjunction was used as the reference configuration, but in practice it is not the best elongation configuration to use. Explain why. What is the best elongation configuration to use? (Hint: when is an inferior planet easiest to observe in the sky?) Do you get the same result for the synodic period you got in Question 4? The sun is in front of the planet making it difficult to see also great elongation is the best to use because it takes the same amount of time. Question 6: (1 point) Use greatest elongation as the reference configuration to calculate the synodic period of Venus. (Be careful. There are two different occurrences of greatest elongation for an inferior planet: eastern and western.) Also, record the value of the greatest elongation of Venus Synodic period of Venus: 1.570 years Greatest elongation of Venus: 46 degrees What general trend do you notice between an inferior planet's distance from the Earth and its synodic period? Closer to the Earth the longer the synodic period of a planet. Question 7: (1 point) Now use the simulator to find the value of Mercury's greatest elongation. Greatest elongation of Mercury: 23 degrees Compare the values of greatest elongation for Mercury and Venus. What relationship do you notice between the value of greatest elongation of a planet

and its distance from the Sun? Can you create a hypothetical 3 rd inferior planet in the simulator to check your reasoning? Closer to the sun the smaller the elongation angle. Also yes i can Question 8: (1 point) Now we will measure the synodic period of Mars. As before, set Mars up in a particular elongation configuration, zero the counter, and then animate the simulator again to see how long it takes Mars to return to the same configuration. Synodic period of Mars: 2.144 years Question 9: (2 point) Just as with superior conjunction in Question 2, conjunction is not the best configuration to observe a superior planet in the sky. Explain why this is and explain which configuration is best for observing a superior planet. because the planet is behind the Sun, obstructing it from view. A superior planet, though, is typically the brightest point in the sky, and the Earth is positioned between the planet and the Sun, this makes an ideal platform for the observation of a Superior planet. Measure the synodic periods of Jupiter and Saturn . Synodic period of Jupiter: 1.092 years Synodic period of Saturn: 1.035 years Question 10: (2 point) 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 this trend.

The farther away the superior planet the shorter the synodic periods. The value slowly starts to approach 1 year. The farther out the planet the slower it will be. This means that the planet would barely move a few degrees by the time the Earth has made a full year cycle around. Question 11: (2 point) Compare your answer above and your answer to the last part of Question 5, and then state a relationship between a planet’s synodic period and its distance from Earth that is valid for both inferior and superior planets. Superior or inferior planets both have an increase of synodic periods if they are relatively closer to Earth. Question 12: (2 point) So far we have only considered elongations of planets as viewed from Earth. Suppose you were standing on Mars, watching the planets go through their motions. Could you use the same terminology as before to explain the configurations of other planets? Yes, you could – the only difference would be that there is an additional inferior planet: the Earth. As an observer on Mars, you would see the Earth go through the same configurations as any other inferior planet. For example, when the Earth appears on the opposite side of the Sun as viewed from Mars, it is at superior conjunction. When the Earth appears at superior conjunction from Mars, at what configuration does Mars have as seen from Earth? No because Mercury is closer to the sun and so therefore it

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has a shorter year than the Earth. Set up the simulator so that the Earth appears at superior conjunction from Mars and time how long it takes the Earth to return to this same elongation configuration – that is, the synodic period of Earth as observed from Mars. Record the synodic period of Earth as viewed from Mars: 2.144 years How does this answer compare with the synodic period of Mars as found in Question 8? Explain why they are related. They are the same. They are related because whether you’re on Mars or the Earth the distance between them, the sun, and how fast they go won’t change. Question 13: (2 point) Copernicus was interested in measuring the synodic periods of the planets so that he could calculate their sidereal periods. In this exercise we will calculate the sidereal periods of the planets using the data you have already collected. You may use a handheld calculator or make use the “Synodic Period Caclulator” on the Elongations and Configurations background page. Recall that the sidereal and synodic periods of a planet are related by planets superior for , 1 1 1 planets inferior for , 1 1 1 P E S E P S    

where P stands for the planet's sidereal period, S stands for the planet's synodic period, and E stands for the Earth's sidereal period. We will now work an example to see how these formulas are used to find a planet’s sidereal period. The synodic period of Jupiter is 1.09 yr. Since E is 1 year, we have 1 1 1 1 1 , so 0.0826 , therefore 12 yr. 1.09yr 1yr yr P P P     Now calculate the sidereal periods of the rest of the planets to complete the table below. (Be sure to use the same units of time for each of the variables. If you measured S in days then you should convert it to years by dividing by 365.25 days/year.) Planet Synodic Period (from exercises above) Sidereal Period (calculated) Mercury 322 yr .244 yr Venus 1.57 yr .611 yr Earth Not Applicable 1 yr Mars 2.144 yr 1.87 yr Jupiter 1.09 yr 12 yr Saturn 1.035 yr 29.57 yr Is there a relationship between the sidereal period of a planet and its distance from the Sun? How does this relate to your observations in Question 1? Further from the sun planets move or longer their periods are. Question 14: (2 point) Put yourself on the planet Mars and carefully note the location of the sun on the Zodiac Strip. Now zero the counter, animate, and time how long it takes for the apparent position of the sun relative to the background to return to the same position. How does this value for the Sidereal Period of Mars agree with your value in the table from Question 12? It is very close to the sidereal period of Mars.

Question 15:

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(2 point) Make Earth the Observer’s Planet and Mars the target planet. Zero the Counter and note the location of Mars in the Zodiac Strip. Animate the planets until Mars (the target planet) comes back to the same place in the Zodiac Strip. How long did it take? It this number related to either the sidereal or synodic period? Why or why not? 1.930 years. It is somewhere in between because we measuring the period of Mars with respect to the fixed stars but from a moving Earth. Question 16: (2 point) Let’s use the simulator to observe the retrograde loops of a superior planet. Set up the simulator for being located on the Earth and viewing Mars at conjunction. Zero the counter and start the animation. How long after conjunction does retrograde motion start and how long does it last? Starts at .957 years and lasts until 1.172 years. Duration 0.215 years or 78.5 days.

Turner lesson3_lab_solar_system

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