If I understand your objection correctly, you're saying that there are two directions that maintain constant bearing between the missile and the target, one bea

If I understand your objection correctly, you're saying that there are two directions that maintain constant bearing between the missile and the target, one bearing that brings the missile closer to the target, and one bearing that sends the missile farther away. This is true, but in reality it doesn't ... make any sense. If the pilot points the missile in remotely the same part of the sky, the closing bearing is the only bearing in the front quadrant of the missile. Historically, I don't think any missile designed to target aircraft has ever been fielded which use the strategy you suggest. (lots of air to ground missiles do) It works fine if the target is flying straight and level, and you fire from directly behind them. But if the target has even a shallow turn towards you, the rate at which the missile will need to increase its rate of turn will increase exponentially as it closes with the target. If the target is aware it's being shot at and from what angle, all it takes to avoid the missile is to keep it at your 3/9 o'clock positions (steadily turning towards it) and it will miss every time. The first generation of radar guided air to air missiles in the 1940s use beam riding. The missile would attempt to keep itself between the target and the shooter. The first generation of (infrared) AIM-9 Sidewinder missiles in the 1950s used a mechanical system to perform proportional navigation; it spun the sensor at a fairly high rate of speed, causing it to act as a gyroscope. The sensor was pointed towards the target on an internal gimbal. But since the sensor was a gyroscope, if corrections had to be made, this meant the target was not at a continuous bearing. So the same corrections were sent to both the gimbal and the missile's control surfaces. These days, everything just has a microcontroller in it, so there's no need to design such electro-mechanical Rube Goldberg contraptions to get proportional navigation to work.