: how does a air-air missile track an aircraft that is constantly changing it’s direction while also traveling supersonic?
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Tracking depends on the missile. Fox 1 and Fox 3 missiles use some form of radar tracking, which is where you emit radio waves and scan for an echo. If you detect that echo, that means there’s something to bounce the waves. Measure how long it took to return and you can calculate distance to the target because you know the speed of radio waves. If you measure the difference in frequency from what you emitted you can also discern how quickly they’re moving relative to you through the Doppler effect. If you know all this, and you track the target’s angle relative to the radar you have all the information needed to calculate it’s exact position and velocity relative to your missile. You can calculate the target’s trajectory from all these values and tell the missile where in that trajectory to go so that it will hit the target.
Infrared missiles are simpler, they listen for infrared waves and point themselves at the brightest heat source. They have no way to tell distance to the target so they simply follow it until they hit, or until they run out of velocity.
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