在3D中计算力的方向

Question

I'm trying to build a 3D simulation of a solar system but i'm having difficulty in finding the 3D equivalent of this 2D python code

# Compute the force of attraction f = G * self.mass * other.mass / (d**2)

# Compute the direction of the force.
    theta = math.atan2(dy, dx)
    fx = math.cos(theta) * f
    fy = math.sin(theta) * f
    return fx, fy

Answer 1

The 2-D code is ridiculously inefficient. You don't need any trigonometry at all. It's just multiplying the magnitude of the of the force, f , by a unit vector in the (dx, dy) direction. Given that you already know the length of the vector, d , all you need is

fx, fy = f*dx/d, f*dy/d

In 3-D

fx, fy, fz = f*dx/d, f*dy/d, f*dz/d