# My vector math seems to be off in this 2D simulation of a solar system

I intend to simulate gravitational acceleration on a 2D plane (simplified, no gravitational constant). My code is interpreted without any error in the console, but instead of having the two circles slowly accelerate towards each other, they go away from each other. Acceleration seems to stay at 0. I can't understand this behaviour.

// orbiters is gonna be the array containing the two celestial bodies
var orbiters;
var sun;
var earth;
function setup() {
frameRate(.3);
console.log("starting the program")
createCanvas(640, 480);
sun = new Orbiter(10, 0, 0, width/2, height/2);
earth = new Orbiter (1, 0, 0, width/5, height/4);
orbiters = [sun, earth];
}

function draw() {
console.log("starting the loop")
background(15, 40, 20);
// then update position, display position, calculate gravity acceleration for next iteration
orbiters.forEach(function(celBody) {
celBody.update();
})
orbiters.forEach(function(celBody) {
celBody.display();
})
// for each celestial body, accelerate it towards every other celestial body
orbiters.forEach(function(celBody){
orbiters.forEach(function (otherCelBody){
if(celBody != otherCelBody){
celBody.gravityAccelerate(otherCelBody.weight, otherCelBody.pos)
}
})
})
}
// No volume for now: describe a body with weight, velocity, position
function Orbiter(weight, vx, vy, posx, posy) {
this.weight = weight;
this.pos = createVector(posx, posy);
this.vel = createVector(vx, vy);
this.acc = createVector(0, 0);

//this finds an acceleration and an angle and gives out a vector to accelerate a body by
this.gravityAccelerate = function(otherBodyWeight, otherBodyPosition) {

// calculate magnitude of the vector between point a and b (r in the law of attraction where F = G*((m1*m2)/r) )
gravDistance = sqrt(sq(otherBodyPosition.x - this.pos.x)+sq(otherBodyPosition.y - this.pos.y));
// calculate angle of the vector above
// calculate force and divide by own mass(acceleration amount)
// this should represent the force in a = F/m (Newton's 2nd law)
gravForce = (this.weight * otherBodyWeight) / gravDistance;
// calculate gravitational acceleration's magnitude as a vector
gravAccMag = gravForce / this.weight;
// apply amount to angle and give a vector,
// translating the magnitude and direction into a vector
console.log("gravity acceleration = ")
// display gravitational acceleration vector
console.log(gravAccVec.x);
console.log(gravAccVec.y);
console.log("this body's acceleration = ");
console.log(this.acc.x);
console.log(this.acc.y);
// add this vector to the velocity of the celestial body
console.log("this body's position")
console.log(this.pos.x)
console.log(this.pos.x)
}

this.update = function() {
}

this.display = function() {
this.size = sqrt(this.weight * 10);
fill (60, 180, 70);
ellipse(this.pos.x, this.pos.y, this.size, this.size);
}
}


I tried lowering the framerate to better analyze the execution, the initial position of the two circles seems correct. They appear to be repulsed away instead of attracted, and what's even stranger, I see the change in position but total acceleration (this.acc) and gravitational acceleration variation (gravAccVec) have a value of 0 and don't change, and the heading of the gravity acceleration vector is null, so I don't understand what causes the repulsive motion. Changing the weight value doesn't impact the outcome, and even switching sine and cosine for the evaluation of the angle of the gravity vector doesn't change anything:

body1(x,y)  body2(x,y)
320,240     -192,-120
512,360     -704,-480
1216,840    -1920,-1320
3136,2160   -5056,-3480


To execute this code you'll need to import the p5.js library or paste it in the online p5.js IDE.

• Yes @uhoh, thank you for pointing this out, SO's community helped out with an issue that was present in the code, I edited it and understood that the problem is not an issue strictly inherent in code - it's probably more about mathematical representation of subjects more pertaining to this platform. – WildWilyWilly Nov 25 '20 at 12:45
• PS I edited my question in order for it to better respond to your request – WildWilyWilly Nov 25 '20 at 13:11
• +1 Okay great! I see the comments with the physics, thanks! Normally people will use MathJax but I think many people can read it as-is now. – uhoh Nov 25 '20 at 13:13

In the following line:

gravHeading = createVector(otherBodyPosition.sub(this.pos)).heading();


otherBodyPosition.sub(this.pos) is already a Vector. When you try to createVector on that, you're putting a Vector in your Vector, and the .heading() method doesn't know how to resolve that, resulting in the value of gravHeading becoming NaN

So when later in, you have

gravAccVec = createVector(Math.cos(gravHeading), Math.sin(gravHeading));


It resolves to gravAccVec = createVector(NaN, NaN) and assigns the value of the Zero Vector.

As a result, neither the velocity nor the acceleration values of either body are being updated.

I'm not sure why the positions of your objects are being changed, since the objects are not experiencing relative velocity or acceleration.

That said, I do see in the line:

// this should represent the force in a = F/m (Newton's 2nd law)
gravForce = (this.weight * otherBodyWeight) / gravDistance;


You're having the gravitational force represented by an inverse-linear instead of an inverse-square relation. Did you intend it to be the following?

// this should represent the force in a = F/m (Newton's 2nd law)
gravForce = (this.weight * otherBodyWeight) / sq(gravDistance);

• while you're at it, do you think this is answerable as well? How to convert body coordinate from Sun reference frame to Earth reference frame? I can only read English, Math and Python, I've never been able to manage to learn even a little bit of any other languages :-) – uhoh Nov 25 '20 at 14:56
• The distance was already squared elsewhere, I see how that's not very clear at all, but my function was square, not linear (that's why I had marked it as gravDistance... me and my variable names). The first part of your answer was key anyway, thank you a lot. – WildWilyWilly Nov 26 '20 at 15:02