OT: Looking for a good physics site

[Jack Simth]

That's not physics, that's math (mind you, Physics IS math, but nowhere are you actually needing to deal with things like, oh, gravity - you're just looking at acceleration).

A position under constant acceleration vs. time for a given axis has an equation that can be formatted as:

P(T)=(1/2)A(T^2)+VT+S

P(T): Position at time T (the function)
T: Time (the only variable)
A: Acceleration (a constant for this exercise)
V: Initial Velocity (at T = 0; a constant)
S: Starting position (P(0); a constant)

You're looking to calculate an intercept - well, you've got a lot to worry about, but basically, you're looking for a way to get two different position functions at the same point at the same time:

So basically, you have P1(T) = P2(T), and want T and A (do I need to reword that?).

As each object has a different starting position (otherwise, T=0 always works; this is the definition of interception), Acceleration, and initial velocity are likely to be different; you're looking to solve:

(1/2)A(T^2)+V T+S = (1/2)A(T^2)+V T+S

Do note that your intercepting ship can potentially control it's acceleration. Well, let's start manipulating:

(1/2)A(T^2)+V T+S = (1/2)A(T^2)+V T+S

(1/2)(A - A)(T^2)+(V - V)T+(S- S) = 0

Oh, hey - we now have a quadratic equation; sub (1/2)(A - A) with a, (V - V) with b, and (S- S) with c, and T with x. The Quadratic formula will do the job:

x = (-b +/- sqrt(b^2 - 4ac))/(2a)

Note: a is a variable, as the interceptor will need to choose it. You've got a variable on both sides - but that's okay, as you'll want at least two dimensions, and you've got a separate equation for each dimension; you'll end up with a system of equations (one for each dimension) and some relationship between the a on the various axes (usually the Pythagorean therom).

Edit:
That is, of course, assuming you don't want to stop at the end, other than ramming the target....