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In this answer, it's mentioned that

However, IR missiles (AIM-9 Sidewinder, AA-11 Archer, MICA IR, ASRAAM) do not emit any EMR that indicates they're incoming; they use a passive FLIR sensor to identify and track the heat source they were told to kill (they don't even require a radar lock; the seeker can be cued to a pilot's helmet, or it can be "uncaged" and will lock on to the most significant heat source in front of it).

Emphasis added.

Given this, is it possible, given some very bad luck, for a fighter jet to fire an IR missile, only for it to get turned around somehow (for instance, by some sort of momentary combustion instability in its rocket motor, or by some very bad turbulence) and end up locking onto and shooting down the jet that fired it?

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    $\begingroup$ Reminds me of near the end of The Hunt for Red October, where a Soviet torpedo hits the sub that fired it. (Interesting, although certainly not authoritative.) $\endgroup$ – Daniel Griscom May 5 '18 at 20:57
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    $\begingroup$ Seems like a more likely (but still involves highly questionable Hollywood-style physics) would be for the aircraft to drop the missile before the missile's engine fully engages. Aircraft then moves ahead of missile, missile locks on to aircraft, boom. $\endgroup$ – James Moore Jun 17 at 23:10
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Yes, but not in the way you're thinking

As a general rule, a missile shouldn't get turned around like that -- if it did so as a sustained maneuver, it'd be vastly short on energy and thus easy to evade in addition to being well out in front of the launching aircraft, making a "circular running missile" self-shootdown scenario improbable.

However, it's still possible to shoot yourself down with a missile, even if it never locks onto you, as Grumman test pilot Pete Purvis and his RIO "Tank" Sherman found out the hard way during testing of the F-14 Tomcat. Stores separation can be an aerodynamically tricky business, and getting torched with rocket exhaust is a good way to find yourself on fire.

While an IR guided missile will have a smaller rocket motor than a big radar-guided missile like the AIM-7 that did Pete and Tank's test Tomcat in, it's not beyond the realm of plausibility that an IR-guided missile could still cripple an aircraft simply by failing to separate from said aircraft correctly during the launch sequence.

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Not really, it would take any of these missiles so long to turn 235 degrees (way more than 6-10 secs), which is generally the maximum burn time of most of their rocket engines. Plus, if it did somehow, get turned around 235 degrees, the energy (airspeed) bleed from such a large turn would leave it without any energy to intercept the launch aircraft even if by some miracle it acquired an IR lock

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Unlikely but possible

It might be possible assuming that the missile does not read or request any IFF signals. If the motor on a missile were to malfunction enough or the missile was to experience enough turbulence to turn it around then it would probably destroy the missile or leave it having a hard time tracking a target. Maybe if it was fired at an aircraft that the managed to get behind the firing aircraft this could happen.

There was a large number of similar events with the first homing torpedos, however sonar based homing has a larger angle of view that the sensor can pick up.

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Highly unlikely. It is however easily possible for two aircraft armed with IR guided missiles, which can nowadays acquire targets in the head on aspect, to shoot each other down.

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