The Law of Ellipses (Kepler s First Law): all planets orbit the sun in a

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Dominick Kristian Norman
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Team Number Team Members Present Learning Objectives 1. Practice the Engineering Process a series of steps to follow to design a solution to a problem. 2.

Learn principles of Celestial Motion Having Knowledge Skills & Abilities FIVE DIMENSIONS OF BEING A GOOD TEAM MEMBER Task 1: Orbital Motion and Kepler s Laws The Law of Ellipses (Kepler s First Law):

1 Team Number Team Members Present Learning Objectives 1. Practice the Engineering Process a series of steps to follow to design a solution to a problem. 2. Practice the Five Dimensions of Being a Good Team Member good team players result in strong teams and better designs, and effective team players will have better opportunities for advancement. 3. Learn principles of Celestial Motion Having Knowledge Skills & Abilities FIVE DIMENSIONS OF BEING A GOOD TEAM MEMBER Task 1: Orbital Motion and Kepler s Laws The Law of Ellipses (Kepler s First Law): all planets orbit the sun in a path described by an ellipse, with the sun being located at one of the foci of that ellipse. e=eccentricity The Law of Equal Areas (Kepler s Second Law): During equal time intervals, the radius vector from the sun sweeps out equal areas. These Laws are valid for: Earth s satellites (including the Moon) Objects orbiting the Sun Satellites of other planets.

2 Problems: The figure below shows several positions of a comet traveling in an elliptical orbit around the sun. Four different segments of its orbit (A-D), and the corresponding triangular shaped areas swept out by the comet, have been shaded in gray. Assume that each of the shaded triangular segments have the same area. A. Rank the time it took (from greatest to least) for the comet to move along each of the segments (A- D) of the orbit. 3. The time to travel each segment would be the same. B. Rank the distance (from greatest to least) the comet traveled during each of the segments (A-D) of the orbit. 3. The distance traveled during each segment would be the same. C. Rank the speed (from greatest to least) of the comet during each of the segments (A-D) of the orbit. 3. The speed of the comet during each segment would be the same.

3 Task 2: Use scientific observations to determine a relationship for orbiting bodies Background You are team of graduate students doing research on orbital motion. Using a telescope mounted camera, you record the configuration of Jupiter s largest Moons every 12 hours for 18 consecutive days. You are looking for a relationship between the time it takes a moon to orbit Jupiter (it s period T) and the average radius of a moon s orbit around the Jupiter (the semimajor axis a). You are looking for a relationship where for any of Jupiter s moons T m = constant an Use a computer program to determine the values of m and n. Use trial and error for the values for m and n until you determine the best values. (Hint: m and n are <5). Note that Jupiter s moons Ganymede, Europa, Io, and Callisto have very small orbital eccentricities (0.002,0.009,0.0041,0.0074), thus their orbit is nearly circular. Perform the following: 1. Identify the Problem and constraints 2. Brainstorm Steps and Strategies to solve the problem 3. Determine a Good Solution 4. Test and evaluate the Solution.

4 A. Our Solution is: B. Test your solution. Substitute your values of m and n in the equation, and calculate the result below for each moon (include units). T m a n Io Europa Ganymede Callisto C. Using the data below, determine if the relationship applies for planetary motion around the sun. Planet Average radius ( AU ) Period ( Years ) Venus Earth Mars Jupiter D. The constant you determined is related to the mass of the body being orbited (M) and the Universal Gravitational Constant (G) as shown in the equation below. Estimate the mass of the sun based on the data table above. 2 2 GM = constant E. Summarize your findings.

5 Figure 1. Galileo s drawings of Jupiter and its four largest moons, during Figure 2. Apparent distance

The Revolution of the Moons of Jupiter

The Revolution of the Moons of Jupiter Overview: During this lab session you will make use of a CLEA (Contemporary Laboratory Experiences in Astronomy) computer program generously developed and supplied