# Centripetal acceleration with vector components

I'm working on solar system simulation and I need to implement centripetal acceleration. The problem is I don't know how it looks like in vector form. I mean I have these formulas:

1. Velocity $$velocity.x = initialVelocity.x + (acceleration.x * motionTime.x)\\ velocity.y = initialVelocity.y + (acceleration.y * motionTime.y)\\ velocity.z = initialVelocity.z + (acceleration.z * motionTime.z)$$

2. Position $$position.x = initialPosition.x + ((initialVelocity.x * motionTime.x) + (acceleration.x * (motionTime.x * motionTime.x) * 0.5f))\\(...)$$

I'm looking for similiar form for centripetal acceleration. Now I have: $$acceleration.x = ((velocity.x * velocity.x) / distance) * direction.x\\(...)$$ But it doesn't work. Could you help me?

• I think you have everything you need in your first two sets of equations. There is no force called "centripetal force" in the sense that there is a gravitational force, an electrostatic force, a normal force, a tension force, etc. The centripetal force is the resultant of all the real forces, not a separate thing. You are good to go, as long has you have the gravitational acceleration correct. – garyp Oct 19 '16 at 19:12
• Time is a scalar and does not have 3 components. All $motionTime$ values should be the same. – ja72 Oct 19 '16 at 23:02

$$F_{gravity} = \frac{G M_{sun}M_{planet}}{r^2}$$
where r is the separation of the planet and the sun. Once you have the force acting on the planet, divide by $M_{planet}$ to get its acceleration.