Unformatted text preview: . TI83 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. TI83 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) .
TI83 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. TI83 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. TI83 Plus Conic Graphing Page 9 Variables Used or Modified by the Application
Conic Graphing modifies various calculator and window
variables.
• Yvars 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.
 Fall '13

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