Simulates the motion of particles from forces of gravity.
Click to add objects. The top slider changes the mass of objects, the bottom slider adjusts G, the gravitational constant.
p5js
Using Netwon's universal gravitational law, the force of gravity between two objects can be calculated.
Each of the vectors can be split into X and Y components and summed up. The accelration of each particle can be calculated by F=ma.
Finally the velocity of each object can be calculated by
Where t is the duration of one frame.
From main.js
for (i = 0; i < objects.length; i++) {
objects[i].display()
const M = objects[i].mass;
nF_x = 0;
nF_y = 0;
for (j = 0; j < objects.length; j++) {
// F_g = GMm/r^2
dx = objects[j].x - objects[i].x;
dy = objects[j].y - objects[i].y;
r = dx ** 2 + dy ** 2;
if (r != 0) {
F = G * M * objects[j].mass / r;
theta = Math.atan(dy / dx);
F_x = Math.abs(F * Math.cos(theta));
F_y = Math.abs(F * Math.sin(theta));
if (objects[j].x < objects[i].x) {
F_x = -F_x;
}
if (objects[j].y < objects[i].y) {
F_y = -F_y;
}
const k = (1 / fr) / M;
if ((objects[j].x - (k * F_x + objects[i].x) < 0) == (dx < 0) ||
(objects[j].y - (k * F_y + objects[i].y) < 0) == (dy < 0)
) {
nF_x += F_x;
nF_y += F_y;
}k
}
}
// F = ma -> a = F/m
// v = at -> t = size of one frame
v_x = nF_x * (1 / fr) / M;
v_y = nF_y * (1 / fr) / M;
objects[i].x += v_x;
objects[i].y += v_y;
}Where objects is an array of objects of class Obj defined as follows:
class Obj {
constructor(mass, x, y) {
this.mass = mass;
this.x = x;
this.y = y;
}
display() {
ellipse(this.x, this.y, this.mass, this.mass);
}
}