How to Create an Animation
of an Orbiting Object
Jim Hannon
Norman Sperling suggested the development
of computer astronomical animations in The
Sperling Files: Creating New Astronomical Computer Graphics
and Animations (The Citizen Scientist,
13 January 2006). Here I suggest a program that is useful
for making at least some of the animations he suggests
and for many more illustrating scientific principals.
The program is POVRay.
This program is a very powerful method of making images
and animations based on equations and computer programming-like
commands. Have a look at some of the truly awesome artwork
at the POVRay web site. Another really neat feature
is that the program is free.
POVRay
works by tracing what happens to the photons emitted
by the light source(s) when they strike objects in a
scene. This way shadows and reflections are accurately
depicted in the image without having to program them.
To see how POVRay would work for an astronomical animation,
I programmed a simple spherical object orbiting another
in a circular orbit. Here is the code for the entire
animated image:
#include "colors.inc"
background { color Black }
camera {
location <0, 2.6, -4>
look_at <0, 1, 2>
}
sphere {
<0, 1, 2>, 0.5
texture {
pigment { color Yellow }
}
}
sphere {
<0, 1, 2>, 0.2
texture {
pigment { color Green }
}
translate<2.5*cos(2*pi*clock),0,2.5*sin(2*pi*clock)>
}
light_source { <8, 2, -12> color White}
First, an include file lets you describe
simple colors with their name rather than specifying
their RGB values.
The background color is set to black.
It is outer space.
A camera location and direction are
then specified. The coordinates are X,Y,Z. X is left
to right, Y is down to up and Z is in to out on the
screen. The units on the coordinates are arbitrary,
and you can use any scale you want.
Next, the central planet or sphere
is described in terms of its location and color. Then
the orbiting moon is described. It is placed at the
same location as the planet and then translated by the
equations of a circle to its "orbit."
The last statement places the light
source and describes its color. You can insert some
background "stars" by placing various light
sources behind the existing scene.
The program will render the image multiple
times by incrementing the variable "clock."
I chose to make 60 images for one orbit of the moon.
What you end up with is 60 bmp image files of the scene.
Figure simple50.gifxx is one image from the set that
shows the shadow of the moon on the planet.
I then used a shareware program written
by a friend of mine called PolyView
to convert the bmp files to gif files and then to an
animated gif file. Figure 2 shows the resulting animation.
For this article I chose to make an
animated gif from the bmp images, because I knew how
to do it and the animated gif is compatible with web
browsers. Once you have the bmp images, it is possible
to make any sort of computer animation file, including
an MPEG-2 video with sound. I have arranged the light
source (sun) to be nearly in the same plane as the orbit,
so you can see both types of eclipse as the moon orbits.
You can transform any of the parameters in the program
into variables to make it easy to change the conditions
that make the image. 
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