Ti 83 plus conic graphing page 5 getting started work


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Unformatted text preview: . TI-83 Plus Conic Graphing Page 5 Getting Started Work through this exercise to become familiar with the basic features of the Conic Graphing application. In this exercise, you trace the trajectory of Haley’s comet. One of the more common uses of conics is to show the orbits of planets and other astronomical bodies. Planets have closed orbits that are almost circular, while comets have highly elliptical orbits. For example, Haley’s comet follows a long path out from the sun, but passes very close to the sun when it returns to the solar system. It has a major axis of 36.18 astronomical units, and an eccentricity of 0.97 (Larsen, Hostetler, and Edwards. 1997, 821). You can use Conic Graphing to trace the trajectory of Haley’s comet. Note To complete this exercise, you need to set your calculator to radian mode before you start the Conics application. To do this: 1. Press ]. 2. Move the cursor to Radian, and press ¯. 3. Press s to exit the mode screen. TI-83 Plus Conic Graphing Page 6 2ep 1. We know the following: r = 1+e sin T , e = 0.97, and 2a ≈ 36.18. Find p, the halfway point of the distance from the focus to the directrix. 2ep 2ep r1 = r2 = π 3π 1 + e sin 1 + e sin 2 2 2a ≈ 36.18 ≈ r 1 + r 2, then 2ep 2ep 36.18 ≈ + π 3π 1 + e sin 1 + e sin 2 2 Thus, p = .551 2. Select ELLIPSE from the CONICS main menu. 3. Press ] to display the CONIC SETTINGS screen. 4. Select POL to change the mode to polar. 5. Select Man so that you can manually change window settings. 6. Select ESC to return to the ELLIPSE screen. 2ep 7. Press h to select equation 4, R = 1 + e sin (T) . TI-83 Plus Conic Graphing Page 7 8. Enter these parameters for e and p, as defined above in step 1: e = 0.97, p = .551 9. Press T to display the CONIC ZOOM screen. 10. Select Zoom Conic so that the aspect ratio on the screen is square. The graph of the ellipse is drawn. S The center (0, 2 ) is the sun. The graph shows the path around the sun. To see this graph, press T, and select ZStandard, then press T, and select ZoomIn. Press ¯ with the cursor near the origin. TI-83 Plus Conic Graphing Page 8 11. Press R to exit the graph screen. 12. Press e ? to find the foci. One focus is the sun at S distance 0, angle 2 , ≈ 1.5708 radians. (If the calculator is in degree mode, the distance is 0 and the angle is 90 degrees. To change to degree mode, you must exit Conic Graphing.) 13. Press U to trace the trajectory. Note Conic Graphing does not allow for continuous tracing. For example, after you trace the entire ellipse, the tracing stops. You can then press the opposite direction arrow to trace the object in the opposite direction. TI-83 Plus Conic Graphing Page 9 Variables Used or Modified by the Application Conic Graphing modifies various calculator and window variables. • Y-vars in the list below are modified, but are not restored when you exit the application. • Real number variables in the list below are modified, but are restored after you exit the application. • If any of the variables were archived, Conic Graphing unarchives them, but does not archive them again after...
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This document was uploaded on 12/31/2013.

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