16
2.50e11
 1.000e11  0.000e00  0.000e00  -2.52664e05 1.000e32 earth.gif
-1.000e11  0.000e00  0.000e00   2.52664e05 1.000e32 mars.gif
 0.000e00  1.000e11  2.52664e05 0.000e00   1.000e32 mercury.gif
 0.000e00 -1.000e11 -2.52664e05 0.000e00   1.000e32 venus.gif
 1.000e07  0.000e00  0.000e00   0.000e00   1.000e01 sun.gif
 0.000e00  1.000e07  0.000e00   0.000e00   1.000e01 sun.gif
-1.000e07  0.000e00  0.000e00   0.000e00   1.000e01 sun.gif
 0.000e00 -1.000e07  0.000e00   0.000e00   1.000e01 sun.gif
 1.000e13  1.000e13 -1.000e06  -1.000e06   2.000e32 blackhole.gif
 1.000e13 -1.000e13 -1.000e06   1.000e06   2.000e32 blackhole.gif
-1.000e13  1.000e13  1.000e06  -1.000e06   2.000e32 blackhole.gif
-1.000e13 -1.000e13  1.000e06   1.000e06   2.000e32 blackhole.gif
 0.000e00  1.414e13  0.000e00  -1.414e06   2.000e22 blackhole.gif
 0.000e00 -1.414e13  0.000e00   1.414e06   2.000e22 blackhole.gif
-1.414e13  0.000e00  1.414e06   0.000e00   2.000e22 blackhole.gif
 1.414e13  0.000e00 -1.414e06   0.000e00   2.000e22 blackhole.gif


// This is a good test case for seeing if the positions are being updated
// properly.
// If there is one big force loop (i.e., program updates position
// before computing all the new forces) the bodies will fly off 
// very quickly.
// If everything is correct, the scenario will play out (four suns
// emerge from center, suns and planets dance around until suns exit,
// planets dance a bit more until black holes come and everyone
// flies off the screen).

Michael Gelbart Fall 06:

This universe is a bit of an optical illusion at first. It starts out with
4 planets supposedly orbiting the sun, but they are actually just orbiting
around their common center of mass, located exactly where the "sun" is. To
determine these orbits I calculated what velocities they must have based on
the radius of orbit and their masses. I did this by equating centripetal
force to the total gravitational force (the sum of all the "inward-pulling"
components of the forces from the other 3 planets - the perpendicular
components cancel out).

After a short amount of time, the sun "splits" into four, as there are
actually 4 suns on top of each other, each one with a small initial velocity
in a different direction. These "suns" are all set to negligible mass (10 kg)
so that they do not apply any significant gravitational force on each other
or on the planets (if they were heavy they would all immediately fly out
at the beginning). However, because we know a = F/m and F is proportional to 
mass, the acceleration (which then defines velocity and position) is
independent of the mass of the suns and therefore they are affected by the
gravitational pull of other planets as if they were very heavy.

Another interesting thing about this universe is the behaviour of the 4 suns
after they leave the center of the planetary orbits. Each one flies outward,
circles around a planet, comes back into the middle, and pauses for a short 
time. This process repeats a few times until finally the suns fly out of the
screen. The entire behaviour just described is very interesting to observe,
and, at least to me, is not at all what I would have expected. The pause 
is especially counter-intuitive as one would think it would require very
precise conditions.

Shortly after the suns depart, eight black holes (which are not really 
black holes as they actually have masses equal to the that of the planets)
fly through the screen at a high speed (they start very far away),
causing the planets to pull inward and then fly out towards the corners.
In conclusion, the main point of interest in the universe is the initial
optical illusion, but the rest of it looks quite neat, too.
