We are talking about nuclear explosions that occur at a range of about one Astronomical Unit or >150 MILLION kilometers. The distance is 300,000 times greater. The energy density impinging on the eye is about 1eex-11.
Put the brightness of a nuclear explosion viewed from one AU in perspective by noting that even if 100% of the yield energy is in the visible spectrum, the brightness is comparable to a moon that is 3,000 kilometers in diameter at one AU. Given the probable energy partition, it is more likely to be comparable to a moon only 1,000 kilometer in diameter at one AU. This is almost as difficult as seeing one of the larger asteroids in the asteroid belt. You need a very good telescope to see an asteroid.
If they have Abby watching the battle with her daddy, may be they should have a really big ass telescope probably in the 50cm range.
gamarus wrote:Thank you very much for this intriguing exposition I looked up the high altitude nuclear tests done around 1960 (wikipedia..) and the best fit is probably Starfish Prime, as it's the highest altitude explosion (400km).
Here's an excerpt from the rapport: "At zero time at Johnston, a white flash occurred, but as soon as one could remove his goggles, no intense light was present. A second after shot time a mottled red disc was observed directly overhead and covered the sky down to about 45 degrees from the zenith..." The rapport goes on to describe the intense auroras that followed but that isn't really relevant to us.
It seems the nuclear flash occurs even at an exoatmospheric detonation and is of sufficient duration to be readily observed.SWM wrote:[continuing the physics calculations]
The limit of detection with the naked eye is an apparent magnitude of 6, but I don't believe you could detect a momentary flash that faint. So let us suppose a detection limit of apparent magnitude 5. That means the explosion would have to be 20 magnitudes brighter, or 1.0e10 times brighter. To do that, we move the explosion 1.0e5 times closer. Absolute magnitude is the apparent magnitude at a distance of 10 parsecs, or 32.6 light-years. Dividing by 1.0e5, we see that the explosion will very briefly be apparent magnitude 5 at a distance of 2.8 light-hours. 10 times closer will be 5 magnitudes brighter (i.e. magnitude 0, as bright as Sirius).
Conclusion: a nuclear explosion 17 light-minutes away might be (very briefly) as bright as Sirius, and potentially visible much further. Very interesting!
Mitigating factors: I'm not sure how long a flash has to be before it is actually detected by the eye. The flash lasts longer than 100 microseconds, of course, but it decays rapidly. I'm not sure exactly how rapidly, and I'm not sure how to model the light-integration of the eye. So this is a big guesstimate here--I easily could be off by several magnitudes brightness.