code.js

// SETTINGS
// All of these variables are natural numbers.
var bodiesOnSpawn = 5;
var maxBodies = 5;
var minStartBodiesMass = 3000; // minimum mass of bodies at the start of simulation in 10^20 kg
var maxStartBodiesMass = 400000; // maximum mass of bodies at the start of simulation in 10^20 kg
var minInitVelocity = 50000;
var maxInitVelocity = 4000000;

// GRAVITATIONAL CONSTANT
var speedupFactor = 2000000;
var G = 0.00000000006673 * speedupFactor;
var timeStep = 1 / 50;
var width = 0.0012; // screen width in Astronomical Units
width *= 1.496e11; // convert to meters
var density = 46732037171; //used to render bodies; units are kg / m^2; equals density of Earth were it a flat circle.



onEvent("GSlider", "change", function( ) {
  // GSliderValue ranges across natural numbers from 1 to 30
  var GSliderValue = getNumber("GSlider");
  G = 0.000000000006673 * GSliderValue * speedupFactor;
  setText("GSliderLabel", (GSliderValue * 10) + "%");
  
  console.log("G = " + G);
});

var originalWidth = width;
onEvent("widthSlider", "change", function( ) {
  width = originalWidth * getNumber("widthSlider");
});




// INFORMATION OF BODIES

// These arrays begin as [-1, -1, -1 ... ]
var mass = [];
var radius = [];
var xPos = []; // in meters
var yPos = [];
// These arrays begin as [0, 0, 0 ... ]
var xVelocity = [];
var yVelocity = [];

// setup the arrays
for (var i = 0; i < maxBodies; i++) {
  appendItem(mass, -1);
  appendItem(radius, -1);
  appendItem(xPos, -1);
  appendItem(yPos, -1);
  appendItem(xVelocity, randomNumber(minInitVelocity, maxInitVelocity));
  appendItem(yVelocity, randomNumber(minInitVelocity, maxInitVelocity));
}

var activeBodies = []; // index of simiulated bodies

//FUNCTION TO RESET MASS AND POSITION
function reset() {
  mass[i] = Math.abs(randomNumber(minStartBodiesMass, maxStartBodiesMass));
  
// multiply by 10^20
for (var k = 0; k < 20; k++) {
  mass[i] *= 10;
}

radius[i] = Math.sqrt(mass[i] / density / Math.PI); //radius in meters

//random poisition
console.log("mass of body " + i + " = " + mass[i]);
  xPos[i] = randomNumber(0, Math.round(width));
  yPos[i] = randomNumber(0, Math.round(width));
}


// SPAWN BODIES and add to activeBodies
for (var i = 0; i < bodiesOnSpawn; i++) {
  appendItem(activeBodies, i);
  
  
  // choose random position and random mass
reset();
  
  
  //DEBUG SPECIFIC SPAWNS AND MASSES
  /*
  mass[i] = 6e+24;
  if (i == 0) {
    xPos[i] = width / 2;
    yPos[i] = width / 2;
  } else  {
    xPos[i] = width / 3;
    yPos[i] = width / 3;
  }*/
}
//console.log("width in meters = " + width);




//MAIN SIMULATION
function tick() {
  
  // find the force exerted on body i from every other body
  for (var m = 0; m < activeBodies.length; m++) {
    var i = activeBodies[m];
    // these variables will store the total force on body i in each axis
    var xForce = 0;
    var yForce = 0;
    
    for (var k = 0; k < activeBodies.length; k++) {
      if (m == k) {
        continue; // We can ignore the force that a body exerts on itself, partly due to avoiding dividing by 0
      } else {
      
      
      var j = activeBodies[k];
      //console.log("calculating " + i + " and " + j);
      
      // distance along each axis between body i and body j
      var deltaY = yPos[j] - yPos[i];
      var deltaX = (xPos[j] - xPos[i] == 0) ? 0.0078125 : xPos[j] - xPos[i];
      var angle = Math.atan(deltaY / deltaX); //angle in radians of body j from +x ray, increasing towards +y ray (points down)
      
      //console.log("r^2 = " + (deltaX*deltaX + (deltaY*deltaY)));
      
      // magnitude of Force of gravity from body j = G * mi * mj / r^2
      var F = G * mass[i] * mass[j] / (deltaX*deltaX + (deltaY*deltaY));
      
      // components of Force vector
      xForce += (deltaX < 0 ? -1 : 1) * Math.abs(Math.cos(angle)) * F;
      yForce += (deltaY < 0 ? -1 : 1) * Math.abs(Math.sin(angle)) * F;
      
      //console.log("F = " + F + " Newtons");
      //console.log("Fx = " + xForce);
      }
    } //END LOOP OVER k
    
    
    
    // CALCULATE VELOCITY & POSITION
    // Velocity += accel * t = F / m * t
    xVelocity[i] += xForce / mass[i] * timeStep;
    yVelocity[i] += yForce / mass[i] * timeStep;
    
    // update position; d = v * t
    xPos[i] += xVelocity[i] * timeStep;
    yPos[i] += yVelocity[i] * timeStep;
    
    
  } //END LOOP OVER i
  
  updateScreen(time);
  
  //UPDATE GRAVITY SLIDER
/*  var GSliderValue = getNumber("GSlider");
  G = 0.000000000006673 * GSliderValue * speedupFactor;
  setText("GSliderLabel", (GSliderValue * 10) + "%");*/
  
  //console.log("G = " + G);
}
//END TICK FUNCTION



var time = 0;

// render positions of bodies
function updateScreen(t) {
  // console.log(t == -1 ? "Begin" : Math.round(t * 10) / 10);
  time += timeStep;
  
  for (var m = 0; m < activeBodies.length; m++) {
    var i = activeBodies[m];
    
    // find coordinates of top left corner
    var thisRadius = radius[i]; //radius of actual globe within the icon, in meters
    //center point of body
    var x = xPos[i];
    var y = yPos[i];
    
    // set position of body i, accounting for icon's margin and position of black square
    // top left corner of icon: (x - 1.569 * radius, y - 1.569 * radius + 130)
    var xCorner = metersToPx(x - (0.5686275 * thisRadius)); //x coordinate of top left corner in px
    var yCorner = metersToPx(y - (0.5686275 * thisRadius)) + 130; //shifted down 130
    var iconWidth = metersToPx(thisRadius * 1.5686275);
    
    // RENDER
    setPosition(
      "body" + i,
      xCorner,
      yCorner,
      iconWidth,
      iconWidth
    );
    
    //console.log(xCorner + ", " + yCorner + "width = " + metersToPx(radius * 1.5686275));
  }
}




function metersToPx(x) {
  return x * 320 / width;
}

updateScreen(-1);

var Game = setInterval(function() {
  tick();
}, 1000 * timeStep);