Moving a object directly towards another object?

You don't need angles for this. "Calculating the difference in x,y" is precisely the right thing to do. If your missile starts at (10,10) and needs to move to (400,420), it needs to add (390,410) to its initial position. You can do it progressively, by adding only a fraction of (390,410).

Missile_position_at_time(t) = (10,10) + (390,410) * t

If you need to rotate your missile to face in the direction of movement, you can normalize the vector (390,410) to obtain a unit-length vector in the direction the missile is facing. That's all that should be needed to do the rotation. If you are using an API that insists on using angles to express rotations, you can compute atan2(410,390) (notice the order of coordinates!).

Much better is computing the direction and magnitude separatly:

- Get the difference between those positions and calculate the magnitude of it pj - pi.

- Normalize the difference, by dividing it by its magnitude - this gives you the unit vector/direction

- Initialize the velocity of the rocket to = Normal * Magnitude / DT. (DT = Delta time in seconds - for example 0.016 - 60 fps)

- Initialize the position to (10, 10)

Now its just a matter of simple euler integration to let the rocket fly :-)

rocket velocity += rocket acceleration * DT (In your case acceleration is zero)

rocket position += rocket.velocity * DT

Also with damping enabled of your integrated velocity, you can achieve a speed increasing or decreasing rocket.

rocket velocity += rocket acceleration * DT (In your case acceleration is zero - so you can skip this step)

rocket velocity *= 1.025 // Slight speed-increase over time

rocket position += rocket.velocity * DT

Are you using a physics engine (e.g. Box2D, Chipmunk, etc.) or are you doing this by controlling the positions of a sprite as your "moving thing"?

Something you might have overlooked is that the target the missile is moving towards is also moving. The target position must be re-calculated. I suggest not doing this every frame, but doing this every couple of seconds maybe?

This gives the target of the missile a fair chance to evade if they are fast and maneuverable enough.

I once wrote a similar system to this which had homing missiles of a similar nature, the only difference was that the missiles would always go towards the nearest target, so if during the process of seeking out an enemy another got too close, they would go for that one instead. I used simple pythagoras for that to calculate which enemy was closest "as the crow flies".

Let me know if you have any questions!