Earth orbit simulation has incorrect speed

Question

I'm very new to programming and I've gotten a school assignment for which I have to create a simulation of the earths orbit around the sun in p5.js . We were offered a simplified way to compute the gravitational pull but I wanted to use the actual formula (Fg = GMm/r^2). In my code, one pixel equals 10^9 meters or a million km. If I use the actual masses of both the sun and the earth, as well as the actual distance between them, I have to put the speed at which the earth travels at around 1 pixel per second or a million km/s, which is around 30,000 times the actual speed of the earth in orbit. My code:

x = 550;
y = 400;
vy = -1;
vx = 0;
dt = 1;
sunSize = 80;
planetSize = 10;
// 1 pixel equals 1 million km
canvasSize = 800;
starAmount = 600;

function setup() {
  frameRate(60);
  noStroke()
  solarXY = 0.5 * canvasSize;
  xSun = solarXY;
  ySun = solarXY;
  createCanvas(canvasSize, canvasSize);
  M = 1.989 * pow(10, 30);
  m = 5.972 * pow(10, 24);
  background(0);
  for (i = 0; i < starAmount; i++) {
    starX = Math.random() * canvasSize;
    starY = Math.random() * canvasSize;
    starSize = Math.random() * 3 + 1
    ellipse(starX, starY, starSize, starSize);
  }
  fill(255, 192, 0);
  ellipse(xSun, ySun, sunSize, sunSize);
}

function draw() {
  r = sqrt(sq(xSun - x) + sq(ySun - y)) * pow(10, 9);
  Fg = 6.67 * pow(10, -11) * m * M / sq(r);
  if (x >= xSun) {
    angle = atan((ySun - y) / (x - xSun));
  } else {
    angle = PI + atan((ySun - y) / (x - xSun));
  }
  xOld = x;
  yOld = y;
  Fgx = cos(angle) * Fg
  Fgy = sin(angle) * Fg
  ay = Fgy / m;
  ax = -Fgx / m;
  vy += ay * dt;
  vx += ax * dt;
  y += vy * dt;
  x += vx * dt;
  fill(30);
  ellipse(xOld, yOld, planetSize, planetSize);
  fill(0, 0, 192);
  ellipse(x, y, planetSize, planetSize);
}

<script src="https://cdnjs.cloudflare.com/ajax/libs/p5.js/1.0.0/p5.min.js"></script>

Do you know what the cause could be? Thanks in advance.

Answer 1

You appear to have acceleration in meters per second ², and velocity in pixels per second. Then you combine them:

vy += ay * dt;
vx += ax * dt;

Your gravitational accelerations are a billion times too strong. So your planet must move about 31,623 times faster than normal to keep a circular orbit.