Re: Is there any way a missile's path can be retraced?

Yes it can be done. But it's complicated in real-life cases...

Consider a pure ballistic trajectory and no atmosphere, such as a projectile fired from a gun on the moon.

Once you determine the state vector (position & velocity) of a missile in ballistic (unpowered) flight, you can propagate its path forward or backward in time according to Newtons laws. See any basic physics text, or an orbital mechanics text for a more detailed explanation. So you could propagate the trajectory back to where it intersects the earth to find the launch point.

However, any error in your knowledge of the state vector will grow as you propagate it. So an initially small error could be quite large by the time it is propagated back to launch. To see this, propagate a test trajectory, then add small errors to it and propagate again and consider the growth of the error.

So even in a simple, ballistic, no-atmosphere case, you could end up with significant errors at the launch point, depending on the accuracy of your state determination.

With a missile it gets even worse! For one thing, there is the atmosphere. This will affect the trajectory of the missile in a manner proportional to the Ballistic Coefficient (BA) of the missile. BA is the ratio of the mass of the missile over the frontal area of the missile. High ballistic coefficients will be affected less then low ballistic coefficients. Think of a feather and a bowling ball. So, now you need to know something about the missile density & shape. But it gets worse....

The missile starts off it's flight under power which means the initial portion of the flight is not ballistic. If you propagate the ballistic state backwards, you will (neglecting drag) intersect the point where the flight became ballistic. This point is known as booster-burnout, ie, the point where the rocket engine stops firing. But to get back to launch from that point, you need to know a lot about the thrust profile of the missile launch. You also need to know at what time booster-burnout occured. This is some pretty detailed information!

Despite all of these difficulties, you can be sure that people are working on the problem. You will likely have great difficulty in locating information on it, though, because much of the research is done by the military and is classified.