Why does my 1D gravity simulation not act like a pendulum?

Question

My gravity simulation acts more like a gravity slingshot. Once the two bodies pass over each other, they accelerate far more than they decelerate on the other side. It's not balanced. It won't oscillate around an attractor.

How do other gravity simulators get around it? example: http://www.testtubegames.com/gravity.html, if you create 2 bodies they will just oscillate back and forth, not drifting any further apart than their original distance even though they move through each other as in my example.

That's how it should be. But in my case, as soon as they get close they just shoot away from each other to the edges of the imaginary galaxy never to come back for a gazillion years.

edit: Here is a video of the bug https://i.stack.imgur.com/uRSRI.jpg

Here is a minimal test case to run in processing.

//Constants: 

float v;

int unit = 1; //1 pixel = 1 meter

float x;
float y;

float alx;
float aly;

float g = 6.67408 * pow(10, -11) * sq(unit); //g constant

float m1 = (1 * pow(10, 15)); // attractor mass
float m2 = 1; //object mass

void setup() {
size (200,200);
  a = 0;
  v = 0;

  x = width/2; // object x
  y = 0;       // object y

  alx = width/2; //attractor x
  aly = height/2; //attractor y
}

void draw() {
  background(0);
  getAcc();
  applyAcc();

  fill(0,255,0);
  ellipse(x, y, 10, 10); //object
  fill(255,0,0);
  ellipse(alx, aly, 10, 10); //attractor
}


void applyAcc() {
  a = getAcc();
  v += a * (1/frameRate); //add acceleration to velocity
  y += v * (1/frameRate); //add velocity to Y
  a = 0;
}

float getAcc() {
float a = 0;
  float d = dist(x, y, alx, aly); //distance to attractor
  float gravity = (g * m1 * m2)/sq(d); //gforce

  a += gravity/m2;

 if (y > aly){
 a *= -1;} 
 return a;
}

Answer 1

Your distance doesn't include width of the object, so the objects effectively occupy the same space at the same time.

The way to "cap gravity" as suggested above is add a normal force when the outer edges touch, if it's a physical simulation.

Answer 2

You should get into the habit of debugging your code. Which line of code is behaving differently from what you expected?

For example, if I were you I would start by printing out the value of gravity every time you calculate it:

float gravity = (g * m1 * m2)/sq(d); //gforce
println(gravity);

You'll notice that your gravity value skyrockets as your circles get closer to each other. And this makes sense, because you're dividing by sq(d). Ad d gets smaller, your gravity increases.

You could simply cap your gravity value so it doesn't go off the charts anymore:

float gravity = (g * m1 * m2)/sq(d);

if(gravity > 100){
  gravity = 100; 
}

Alternatively you could cap d so it never goes below a certain value, but the result is the same.

In the end you'll find that this is not going to be as easy as you expected. You're going to have to tune the parameters quite a bit so your simulation works how you want.

Answer 3

Working demo here: https://beta.observablehq.com/@shaunlebron/1d-gravity

I followed the solution posted by the author of the sim that inspired this question here:

-First off, shrinking the timestep is always helpful. My simulation runs, as a baseline, about 40 ‘steps’ per frame, and 30 frames per second.

-To deal with the exact issue you talk about, I think modeling the bodies not as pure point masses - but rather spherical masses with a certain radius will be vital. That prevents the force of gravity from diverging to infinity. So, for instance, if you drop an asteroid into a star in my simulation (with collisions turned off), the force of gravity will increase as the asteroid gets closer, up until it reaches the surface of the star, at which point the force will begin to decrease. And the moment it’s at the center of the star (or nearby), the force will be zero (or nearly zero) - instead of near-infinite.

In my demo, I just completed turned off gravity when two objects are close enough together. Seems to work well enough.