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What is the best way to determine direction, force, and velocity in three dimensional Cartesian coordinates?

Explanation: I am writing a program to do some star motion simulations. I will edit in some stars, give them their mass, along with initial position and velocity, and see what happens. My plan is to track the position and the velocity with the X, Y, and Z Cartesian values. The distance is simple but I am uncertain as to calculating the force and resultant accelerations and velocity in 3 D.

Will it work our right if I calculate each of the X, Y, and Z values separate from each other? By that I mean work each axis one at a time, do the force, acceleration, and velocity calculations in each axis, and ignore the other two? That sounds like it would work but seems too simplistic.

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# 3D cartesian arithmetic

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