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ECCENTRIC ORBITS Johannes Kepler determined that the planets did not revolve around the sun in circular orbits as previously thought. The purpose of this activity is to understand the nature of these non-circular orbits. Procedure – Part 1 You have been provided diagrams with planetary orbit information. Included on each diagram is the maximum diameter of the planet’s orbit (major axis) and the location of the foci; with the sun at one focus. 1. Place the planet diagram supplied by your instructor on the board provided. Place pins at the center of each foci and a third pin at one end of the major axis. Wrap string around the “sun” pin and the outermost pin. Tighten and knot the string to this distance. 2. Remove the outer pin and replace it with the tip of a pencil. While holding the string taught with the pencil, trace the orbit of the planet around the paper (see diagram below). Your partner may have to hold the pins in place as you complete your trace. major axis sun 3. Label the aphelion and perihelion points on your diagram. Measure the distance from the sun to each of these points in centimeters and convert your measurement to AU. (Note the scale factor given in the lower right hand corner of your diagram.) Record the answers in your data sheet. Look up the accepted values for these distances and record them in your data table. Calculate the percent error for each. Procedure – Part 2 4. Determine the eccentricity of your planet’s orbit using the steps outlined below. a. Measure the distance between the center of the orbit and the center of the sun. Record this distance as ‘c’ on your worksheet (see diagram below). b. Measure the distance along the major axis between the center point and the edge of the orbit. Record this semi-major axis distance, ‘a’, in your data sheet. c a major axis sun c. Calculate the eccentricity of your planet’s orbit using the equation, e = c / a. Record your value in your data sheet. Look up the accepted value and record it in our data table. Calculate your percent error. 5. To determine how different your planet’s orbit is from a true circle, place a single pin at the center of the ellipse in your diagram and a second pin at the orbits edge. Tie a new string around the two pins. Remove both pins. Place a pin at the center of the sun and stretch your string around this pin and the other end around a pencil. Trace this circular orbit. How does this orbit compare to the actual orbit of the planet? 6. Repeat steps 1-5 for other planets assigned by your instructor. Obtain results for the planets you did not analyze from your classmates and fill in your data table. Analysis 1. As you view the data for all the planets, what general statements can you make about the orbits of the planets? 2. What sources of error might account for your calculated percent errors? 3. Which planet has the most eccentric orbit? Which as the least? Data Table – Part 1 Planet Mercury Venus Earth Mars Jupiter Saturn Uranus Neptune (Pluto) Calculated Accepted Aphelion Distance Aphelion Distance (AU) (AU) Percent Error Calculated Perihelion Distance (AU) Accepted Perihelion Distance (AU) Percent Error Data Table – Part 2 Planet Sun-Center Distance, ‘c’ Semi-major Axis Distance, ‘a’ Calculated Eccentricity Mercury Venus Earth Mars Jupiter Saturn Uranus Neptune (Pluto) Possible resource for orbital information: http://www.enchantedlearning.com/subjects/astronomy/glossary/Eccentricity.shtml Accepted Eccentricity Percent Error
