10. Orbit, Group Learning Exercises

In this indoor lab we'll try to reconstruct the observations and reasoning needed to understand some properties of the Earth and Mars' orbits. We'll divide the class into small groups that will each prepare a discussion of each of the problems below. Four hundred years ago observers were going through the same deductive process you are using, they just had to wait longer to see what the real observations were like. The Starry Night planetarium program will be set up for you to obtain the necessary "observations." As you decide on the data you'd like to see the TA or instructor will help you obtain them with the software.
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Background Reading: Your A110 textbook discussion of Kepler's laws

A. The Earth's Orbit and Keplers Laws

Is the orbit of the Earth around the Sun circular? You should know the answer to this question because of what you learned in your Astro 110 class, but how can we prove that the orbit isn't a perfect circle with the Sun at the center of the circle?A good hint here is that using the software we can measure the angular diameter of the Sun very accurately. Come up with a set of observations that we can obtain using the software that will prove that the Earth doesn't orbit the Sun in a perfect circle.

If the orbit isn't circular then how is it shaped? Collect some data (at least 4 or 5 measurements) that you can use to find what time of year the Earth is closest to the Sun and when its most distant.

You know what the period of the Earth's orbit is from everything you've learned in astronomy. How could you prove that it takes the Earth one year to go around the Sun? How accurately could you measure this time interval using our software tools -- what observations would you make? Hint: think about observing the zenith at midnight each night (when the Sun is exactly on the
other side of the Earth).

If the Earth spins at a constant rate (an assumption your predecessors also made 400 years ago) how can we prove part ofKeplers 3rd law, that the motion of the Earth in its orbit is faster when it is closer to the Sun? Hint: think about watching what time the Sun rises (or just begins to appear above the horizon line). Since the Earth is spinning in about the same direction as the Earth is orbiting the Sun, how should the exact time the Sun goes above the horizon be affected? When does the Earth move fastest in its orbit? How much faster is it then?

B. Mars' Orbit

Mars orbit is more difficult to understand because its apparent motion depends both on its orbit and our orbital motion around the Sun. Kepler depended on many years of observations that Tycho Brahe obtained over several Mars orbits. To understand the Mars orbit you may want to first watch a "movie" (day-day) of how Mars appears to move in the sky.

Does Mars move exactly along the ecliptic (the path the Sun makes against the stars)? How far is the plane of Mars orbit inclined away from the plane of the Earth's orbit?

As you observe Mars during several years time, notice how it moves along the ecliptic. Does it move in the same direction as the Sun appears to move (compared to background stars)?

A conjunction occurs when Mars and the Sun appear to cross on the ecliptic. Consider these conjunctions. Can you think of a way to measure the period of Mars' orbit as seen from space, not just the apparent period of its orbit due to the motion of the Earth?

You should notice that Mars sometimes moves in the opposite direction of the Sun on the ecliptic. When is the next period of such retrograde motion? Between successive conjunctions, how many retrograde episodes are there? Are there ever more? What is going on to cause these apparent backwards periods?

Lab Writeup Ingredients

Everyone in your group needs to turn in a complete set of solutions, but you will be working together to generate the data you need and to figure out how to use this data. Each writeup should include these ingredients:

Include sketches whenever you can.
Clearly show the question you're answering
Include the data/observations you obtained from the simulation software
Briefly describe your deductive process to reach the answer
When giving numerical results you should accurately describe your numerical uncertainties with error bars or proper significant figures
Designate your spokesperson for giving a 5 min presentation (total) of your answers at the end. The most understandable presentation will gain extra credit (each group has a vote along with the instructor and TA).

Jeff Kuhn (kuhn@ifa.hawaii.edu)

Last modified: Oct. 8, 2006
http://www.ifa.hawaii.edu/users/kuhn/a110L/orbitslab.html