ࡱ>  qbjbjss GB ))8%\,tUULHHH$B9eIDHeIeI))(NNNeI$)NeINN1p5J>s0,߁ڊKڊ|ڊ hH"HNHHHHHL`HHH,eIeIeIeIڊHHHHHHHHH : Planetary Orbit Simulator Student Guide Background Material Answer the following questions after reviewing the Kepler's Laws and Planetary Motion and Newton and Planetary Motion background pages.  Draw a line connecting each law on the left with a description of it on the right.     When written as P2 = a3 Kepler's 3rd Law (with P in years and a in AU) is applicable to any object orbiting our sun. any object orbiting any star. any object orbiting any other object. The ellipse to the right has an eccentricity of about 0.25 0.5 0.75 0.9 For a planet in an elliptical orbit to sweep out equal areas in equal amounts of time it must move slowest when near the sun. move fastest when near the sun. move at the same speed at all times. have a perfectly circular orbit. If a planet is twice as far from the sun at aphelion than at perihelion, then the strength of the gravitational force at aphelion will be ____________ as it is at perihelion. four times as much twice as much the same one half as much one quarter as much Keplers 1st Law If you have not already done so, launch the NAAP Planetary Orbit Simulator. Open the Keplers 1st Law tab if it is not already (its open by default). Enable all 5 check boxes. The white dot is the simulated planet. One can click on it and drag it around. Change the size of the orbit with the semimajor axis slider. Note how the background grid indicates change in scale while the displayed orbit size remains the same. Change the eccentricity and note how it affects the shape of the orbit. Be aware that the ranges of several parameters are limited by practical issues that occur when creating a simulator rather than any true physical limitations. We have limited the semi-major axis to 50 AU since that covers most of the objects in which we are interested in our solar system and have limited eccentricity to 0.7 since the ellipses would be hard to fit on the screen for larger values. Note that the semi-major axis is aligned horizontally for all elliptical orbits created in this simulator, where they are randomly aligned in our solar system. Animate the simulated planet. You may need to increase the animation rate for very large orbits or decrease it for small ones. The planetary presets set the simulated planets parameters to those like our solar systems planets. Explore these options. For what eccentricity is the secondary focus (which is usually empty) located at the sun? What is the shape of this orbit? Create an orbit with a = 20 AU and e = 0. Drag the planet first to the far left of the ellipse and then to the far right. What are the values of r1 and r2 at these locations? r1 (AU)r2 (AU)Far LeftFar Right Create an orbit with a = 20 AU and e = 0.5. Drag the planet first to the far left of the ellipse and then to the far right. What are the values of r1 and r2 at these locations? r1 (AU)r2 (AU)Far LeftFar Right For the ellipse with a = 20 AU and e = 0.5, can you find a point in the orbit where r1 and r2 are equal? Sketch the ellipse, the location of this point, and r1 and r2 in the space below. What is the value of the sum of r1 and r2 and how does it relate to the ellipse properties? Is this true for all ellipses? It is easy to create an ellipse using a loop of string and two thumbtacks. The string is first stretched over the thumbtacks which act as foci. The string is then pulled tight using the pencil which can then trace out the ellipse. Assume that you wish to draw an ellipse with a semi-major axis of a = 20 cm and e = 0.5. Using what you have learned earlier in this lab, what would be the appropriate distances for a) the separation of the thumbtacks and b) the length of the string? Please fully explain how you determine these values. Keplers 2nd Law Use the clear optional features button to remove the 1st Law features. Open the Kepler's 2nd Law tab. Press the start sweeping button. Adjust the semimajor axis and animation rate so that the planet moves at a reasonable speed. Adjust the size of the sweep using the adjust size slider. Click and drag the sweep segment around. Note how the shape of the sweep segment changes, but the area does not. Add more sweeps. Erase all sweeps with the erase sweeps button. The sweep continuously check box will cause sweeps to be created continuously when sweeping. Test this option. Erase all sweeps and create an ellipse with a = 1 AU and e = 0. Set the fractional sweep size to one-twelfth of the period. Drag the sweep segment around. Does its size or shape change? Leave the semi-major axis at a = 1 AU and change the eccentricity to e = 0.5. Drag the sweep segment around and note that its size and shape change. Where is the sweep segment the skinniest? Where is it the fattest? Where is the planet when it is sweeping out each of these segments? (What names do astronomers use for these positions?) What eccentricity in the simulator gives the greatest variation of sweep segment shape? Halleys comet has a semimajor axis of about 18.5 AU, a period of 76 years, and an eccentricity of about 0.97 (so Halleys orbit cannot be shown in this simulator.) The orbit of Halleys Comet, the Earths Orbit, and the Sun are shown in the diagram below (not exactly to scale). Based upon what you know about Keplers 2nd Law, explain why we can only see the comet for about 6 months every orbit (76 years)?  Keplers 3rd Law Use the clear optional features button to remove the 2nd Law features. Open the Kepler's 3rd Law tab. Use the simulator to complete the table below. ObjectP (years)a (AU)eP2a3Earth1.00Mars1.52Ceres2.770.08Chiron50.70.38 As the size of a planets orbit increases, what happens to its period? Start with the Earths orbit and change the eccentricity to 0.6. Does changing the eccentricity change the period of the planet? Newtonian Features Important: Use the clear optional features button to remove other features. Open the Newtonian features tab. Click both show vector boxes to show both the velocity and the acceleration of the planet. Observe the direction and length of the arrows. The length is proportional to the values of the vector in the plot. The acceleration vector is always pointing towards what object in the simulator? Create an ellipse with a = 5 AU and e = 0.5. For each marked location on the plot below indicate a) whether the velocity is increasing or decreasing at the point in the orbit (by circling the appropriate arrow) and b) the angle  between the velocity and acceleration vectors. Note that one is completed for you.          Where do the maximum and minimum values of velocity occur in the orbit? Can you describe a general rule which identifies where in the orbit velocity is increasing and where it is decreasing? What is the angle between the velocity and acceleration vectors at these times? Astronomers refer to planets in their orbits as forever falling into the sun. There is an attractive gravitational force between the sun and a planet. By Newtons 3rd law it is equal in magnitude for both objects. However, because the planet is so much less massive than the sun, the resulting acceleration (from Newtons 2nd law) is much larger. Acceleration is defined as the change in velocity both of which are vector quantities. Thus, acceleration continually changes the magnitude and direction of velocity. As long as the angle between acceleration and velocity is less than 90, the magnitude of velocity will increase. While Keplers laws are largely descriptive of what planets do, Newtons laws allow us to describe the nature of an orbit in fundamental physical laws!     NAAP Planetary Orbit Simulator  PAGE 8/ NUMPAGES 8 Name: NAAP Planetary Orbit Simulator  PAGE 1/ NUMPAGES 8 Tip: You can change the value of a slider by clicking on the slider bar or by entering a number in the value box. Keplers 1st Law Keplers 2nd Law Keplers 3rd Law Newtons 1st Law planets orbit the sun in elliptical paths planets with large orbits take a long time to complete an orbit )*+  ! 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