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OrbitTrackPlotMiscellaneous Functions

7.4 The OrbitPlot and OrbitPlot3D Functions

OrbitPlot plots the elliptical orbit of an object or objects about a common center.

Plotting the shape of an orbit.

In the two-dimensional form, the horizontal axis is aligned so that the right points to the zero hour of right ascension, and the vertical points to the 6 hour of right ascension. You can switch these axes off by using the normal option setting Axes -> False. The graphic returned is that seen by an observer situated above the ecliptic plane looking down.

You can show the orbital layout of the planets using these functions.

A plots of the orbit of the outer planets shows that Pluto is in an elliptical orbit, which can take it just inside the orbit of Neptune.

In[22]:=OrbitPlot[{Jupiter, Saturn, Uranus, Neptune, Pluto},
Distance -> 48*AU];

A related function is OrbitPlot3D, which does essentially the same thing as OrbitPlot except that it shows the full three-dimensional orbit. Use the option ViewPoint to adjust the viewpoint.

Like OrbitPlot, OrbitPlot3D accepts the option PlotStyle to let you select an individual style for each orbit.

This three-dimensional plot makes it clear that Pluto is in an orbit tilted to the plane of the other planets.

In[23]:=OrbitPlot3D[{Jupiter, Saturn, Uranus, Neptune, Pluto},
Distance -> 48*AU,
PlotStyle -> {RGBColor[0.9,0.8,0.6],
RGBColor[1.0,0.8,0.6],
RGBColor[0.3,0.9,0.2],
RGBColor[0.5,0.7,1.0],
RGBColor[1.0,1.0,1.0]},
Background -> GrayLevel[0.5],
PlotRegion -> {{-0.4,1.4},{-0.4,1.4}},
SphericalRegion -> True];

There are many ways to use the functions OrbitPlot and OrbitPlot3D. For instance, you can show the shape and orientation of the orbit of Comet Halley. You can also show the orbit of satellites around the Earth.

In the case of Comet Halley, you would first add its orbital elements to the package. It is then an easy matter to display its orbit relative to, say, Earth and Jupiter.

This adds a new object called Halley. Note OrbitalPeriod is used rather than OrbitalSemiMajorAxis. See the end of Section 7.1 for the conversion.

In[24]:=SetOrbitalElements[Halley,
ViewPoint -> Sun,
Date -> {1986, 2, 9.4589, TimeZone
/. GetLocation[], 0, 0},
OrbitalEccentricity -> 0.967277,
OrbitalInclination -> 162.2422*Degree,
OrbitalPeriod -> 27757.7 * Day,
MeanAnomaly -> 0 *Degree,
PerigeeArgument -> 111.8657*Degree,
AscendingLongitude -> 58.8601*Degree];

Comet Halley follows the elliptical orbit approaching from the top left.

In[25]:=OrbitPlot[{Halley, Earth, Jupiter}];

The orbital elements of Comet Halley are such that its inclination is 162.2 degrees, which is greater than 90 degrees. Comet Halley, therefore, travels in the opposite direction (i.e., clockwise) to the main planets, which orbit counterclockwise around the Sun.

In the case of a satellite, such as the Hubble Space Telescope (HST), you must have current orbital elements.

Here are the two-line orbital elements for the Hubble Space Telescope.

In[26]:=SetOrbitalElements[HST,
"1 20580U 90037B 97046.42217324 .00050250 00000-0 48781-2 0 9267",
"2 20580 28.4680 94.8927 0005837 191.3643 168.6802 14.91366889174923"];

This plots the three-dimensional shape of the orbit. Note that because the orbit decays with time, you need to specify a date.

In[27]:=OrbitPlot3D[HST, {1997,2, 19},
Distance -> 8000*KiloMeter,
PlotRegion -> {{-0.4,1.4},{-0.4,1.4}}];

OrbitTrackPlotMiscellaneous Functions



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