You're right, there are some very interesting issues here.  No way is it easy
to write something that looks good, and doesn't take FOREVER to get results. 
The way I see it there are at least three issues.

	1) You are right, if his variable "Time" was the total
           time, he would be in real trouble.

            The variable "Time" isn't the total time, it's the
            time between frames.  So, if this time is SMALL ENOUGH,
            the acceleration is pretty much constant, so the
            program IS right.  
	
           The real problem was with defining the units correctly.
           ( i.e. he had accidentally defined the gravitational to
             be WAY too strong )
	
        2) The other issue is the issue of realism. In a lot of
           particle simulations, you don't really care if the
           simulation cheats a bit on the physics.  You just
           want it to look GOOD.  But Peter wants to simulate
           something real, and something we all know.  So if he
           runs the simulation and Mercury falls into the Sun
           he's in trouble!

           That depends something called the "numerical stability"
           of the simulation program.  It depends a little bit on
           the exact method you use to estimate the new positions and
           new velocities, but it mostly depends on the amount of
           time between steps.

           In this case, I got pretty good results for 1 frame =
           3 days, or "clock_delta" = .01 which you get in a 100
           frame animation.

           One really cool way to check this out is to run the
           simulation forward 100 or 1000 steps and then run it
           backward by the same number of steps and see if you
           get your original data back.

        3) This is definitely not the most efficient way of doing 
           things! You could probably make something that looks pretty
           good without solving ANY differential equations.  The
           orbits of almost all the planets and moons in the
           Solar System are pretty circular, which means that they
           travel in circles about the body they orbit at a constant
           angular velocity {i.e. the earth has an angular velocity
           of about 1 degree/day = (360 degrees / 365.24 days) and the
           moon has an angular velocity of about 360/28 degree/day
           around the earth.}

           This method looks good, and is less prone to the
           difficulties listed in point 2.

           Actually computing the paths of the planets this way
           is really only good if you want to see the TINY effect
           that the Sun has on the orbit of the Moon, or the REALLY
           TINY effect that all the other planets have on the orbit
           of Mercury.

           With even 10 objects the rendering time is so much longer
           than the computation time that it just doesn't matter, but
           I wonder what happens when you start tossing in all those
           moons and a few asteroids ...


	This really is a cool topic.  Maybe we could start a thread on simulation
issues or something!

	Until that Day,
	Ben

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