Lunar Libration

http://www.wolfram.com/applications/astronomer/index.html

Terry Robb. <terryr@wolfram.com>

setup

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Lunar Libration

The Moon always presents the same face towards the Earth. We never get to see the back of the Moon.

However, for various reasons, the Moon slightly rocks from side to side about the mean state. This effect is known as libration.

We can produce an animation of lunar libration during a given month.

Double click on the graphic to animate it. Alternatively select the cell and look under the menu Cell/Animate Selected Graphics. Use the number keys to speed up or slow down the graphic.

Do[PlanetPlot3D[Moon, {1996,1,d},
      Shading->False,
      PlotRange->{{-1,1},{-1,1}} 0.3],
   {d,1,30,3}]

The setting PlotRange -> {{-1, 1}, {-1,1}}*0.3 is used so that a fixed 0.3 degree radius field of view is used. The default is otherwise to fit the image  into the available box.

Similarly, we can produce an animation of lunar libration for all the full moons in one year.

Do[PlanetPlot3D[Moon,
         Lunation[1199.5+m],
         Shading->False,
         PlotRange->{{-1,1},{-1,1}} 0.3],
   {m,1,12}]

Note that at some full moons we get to see slightly around the eastern edges of the Moon, but at other full moons we get to see more of the western edge.

If you take photographs of the Moon at extreme libration, you can make a 3D stereographic image of the Moon.

Two such extreme librations take place on 1997 March 24 and 1997 September 17.

crosses = {RGBColor[1,0,0],
     Line[{{0,2},{0,-2}}],
     Line[{{-2,0},{2,0}}],
     Line[{{45,2},{45,-2}}],
     Line[{{43,0},{47,0}}],
     Line[{{-45,2},{-45,-2}}],
     Line[{{-43,0},{-47,0}}],
     Line[{{0,43},{0,47}}],
     Line[{{-2,45},{2,45}}],
     Line[{{0,-43},{0,-47}}],
     Line[{{-2,-45},{2,-45}}]};
p1=PlanetPlot3D[Moon,{1997,3,24},
             Shading->False,
             Features->crosses,
             DisplayFunction->Identity];1;
p2=PlanetPlot3D[Moon,{1997,9,17},
             Shading->False,
             Features->crosses,
             DisplayFunction->Identity];1;
Show[GraphicsArray[{p1,p2}],
     DisplayFunction->$DisplayFunction];1;

Converge your eyes to see the above in 3D.