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3.3 The Coordinates Function
Coordinates is useful for producing various three-dimensional plots.
Calculating an object's position in x,y,z coordinates.
The three-dimensional coordinate system used by Coordinates is aligned so that the z coordinate is perpendicular to the plane of the Earth's orbit about the Sun, and the x coordinate points in the direction of the 0h line of right ascension. For historical reasons, the 0h line is called the first point of Aries, even though the point is currently in the direction of Pisces. Several thousand years ago the 0h line of right ascension was in Aries, but precession has been slowly moving it, so that now it lies in Pisces and is moving into Aquarius.
Output position is given in astronomical units.
The Coordinates function gives you the x,y,z coordinates of Mars on the given date.
In[18]:=Coordinates[Mars, {1993,11,17,3,20,0}]
Out[18]=
Here Coordinates gives the x,y,z coordinates of the Moon.
In[19]:=Coordinates[Moon, {1993,11,17,3,20,0}]
Out[19]=
A default viewpoint of Earth is used here, but any viewpoint is allowed.
This plots the orbit of Mercury as viewed from the Sun. You can see the expected elliptical orbit with the Sun centered at one focal point. Observe the somewhat eccentric shape of the ellipse.
In[20]:=ListPlot[
Table[Take[Coordinates[Mercury, {1993,1,d},
ViewPoint -> Sun], 2],
{d, 1, 89, 2}],
PlotJoined -> True, AspectRatio -> 1];
Using Earth as the viewpoint, it becomes clear that Mercury makes roughly three close approaches to the Earth each year.
In[21]:=ListPlot[
Table[Take[Coordinates[Mercury, {1993,1,d},
ViewPoint -> Earth], 2],
{d, 1, 366, 5}],
PlotJoined -> True, AspectRatio -> 1];
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