CODEWITHSUNDEEP
javascriptmathgravitynumerical-methods
user2394418
user2394418

Reputation:

JS - How can I implement gravity?

How can I implement gravity? I have made this: http://jsfiddle.net/X2XvC/5/ but all dots simply follow your cursor (that's not gravitation). I heard about Eulers method, but I don't know how to implement it into my code.

what I found:

void update(float dt)
{
    position += velocity * dt + acceleration * 0.5 * dt * dt;
    velocity += acceleration * dt;
}

Upvotes: 5

Views: 3357

Answers (1)

Nico Schertler
Nico Schertler

Reputation: 32597

As Pointy already suggested, you have to affect the points' velocity vector.

Gravity is a force that is calculated by:

F_G = gamma * mass1 * mass2 / distance^2

Where gamma is the Gravitational constant and mass1 and mass2 are the objects' masses. You get the resulting acceleration with:

F_G = a * mass1
a = F_G / mass1
  = gamma * mass2 / distance^2

And you'll see that the acceleration is independent of the moving object's mass. What remains is gamma * mass2 which you can set to an arbitrary constant. Whichever meets your needs best.

Now we have the length of the acceleration vector. The direction is of course normalize(cursorPosition - pointPosition). So the overall acceleration is:

d = cursorPosition - pointPosition
a = constant * d / length(d)^3

Knowing this, you can update the point's velocity and speed in every frame by:

velocity += a * dt
position += velocity * dt

where dt is the duration of the last frame.

Here is your changed example code. The line if(distance < 6)... is used to cap the acceleration (if a point moves through the gravity center, it is infinitely accelerated).

Upvotes: 5

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