Simple particles simulation (gravity)

[qwe]

i believe I'm using the correct equations, but the orbit won't work. here is the relevant code for a 2 particle simple orbit simulation. I'm not sure what I'm doing wrong

...

timeStep = 1.0
gravityConstant = 6.67384 * 10.0 ^ -11.0

...

// (initialize particles)
// p[n].m: mass, p[n].x: initial x position, p[n].vz: initial velocity vector along z axis

            p[0].m = 1.0
            p[1].m = 1.0

            p[0].t = 0
            p[0].x = 10.0

            p[1].t = 0
            p[1].x = -10.0

// initial velocity = sqrt(m2 ^2 * G / m1 + m2 * distance)

            p[0].vz = sqrt( ( p[1].m * p[1].m * gravityConstant ) / ( p[0].m + p[1].m * 10.0 ) )
            p[1].vz = sqrt( ( p[0].m * p[0].m * gravityConstant ) / ( p[1].m + p[0].m * 10.0 ) ) * -1

...

// (each loop, for each particle... p[n] is current particle, p[m] is other particle)

                        // calculate distance
                        dx# = p[m].x - p[n].x
                        dy# = p[m].y - p[n].y
                        dz# = p[m].z - p[n].z
                        distance# = sqrt( dx# * dx# + dy# * dy# + dz# * dz# )
                        // calculate force
                        force# = (gravityConstant * p[n].m * p[m].m) / (distance# * distance#)
                        // calculate acceleration, include timestep
                        acceleration# = (force# / p[n].m) * timeStep
                        // calculate unit vector and calculate magnitude of vector (acceleration)
                        p[n].vx = p[n].vx + dx# * (acceleration# / distance# )
                        p[n].vy = p[n].vy + dy# * (acceleration# / distance# )
                        p[n].vz = p[n].vz + dz# * (acceleration# / distance# )

 

[Delta Kilo]

Without going through the code in details:
1. I don't see where you update particle position. I assume you just omitted it for brevity.
2. Gravitation force between 2 1kg masses at 10 meters is not exactly very strong.
3. With a time step of 1s your are going to have a lot of very small steps, running into precision and error accumulation issues
4. Euler method sux. Bite the bullet and code up 4th order Runge-Kutta, then you can increase your step size to a sensible value.

 

[qwe]

am i doing the timestep correctly? the bigger the timestep, the more acceleration applied. that doesn't seem right, the orbit shape changes based on the timestep, but it shouldn't

 

[Khashishi]

Numerical integration suffers problems with accuracy and stability. The simple method you are using is called Euler method and isn't good. As Delta said, you should try 4th order Runge-Kutta.