How long until the micrometeorites stop?

In my setting, a The Moon is a Harsh Mistress-style mass driver existed around Mare Tranquillitatis, and was destroyed by a 100 megaton nuke in a preemptive strike. While I understand that the nuclear fallout would dissipate relatively quickly, I don't quite have a grasp on how long afterwards that Earth would be pelted by micrometeorites, and how severely it might impact existing satellites in Earth orbit.

My question: If a 100 megaton nuclear weapon was exploded on the surface of Mare Tranquillitatis, how long afterwards would the Earth see the aftereffects (dust clouds, micrometeorites, falling satellites, etc), what would be the severity, and would this taper off or just stop?

• We still have micrometeorites hitting Earth after 5 billion years from its formation... – L.Dutch Mar 30 '18 at 15:03
• The answer revolves around the velocity at which the ejecta is blasted off the Moon. Anything not travelling greater than 40000 kph would eventually get pulled into the Earth. – RonJohn Mar 30 '18 at 15:19
• Also, 100Mt is a lot. It's 2x as large as we (specifically the Soviets) have ever detonated, and is waaaayyy overkill. – RonJohn Mar 30 '18 at 15:20
• Some nuclear fallout will dissipate within a few weeks. But quite a lot would remain for decades in a cloud around the Moon. – RonJohn Mar 30 '18 at 15:22
• The moon is 240,000 miles away from the earth. It is unlikely that any satellites would be affected. It is unlikely that micrometerorites would have any effect on the earth (the few that reached us would be quickly consumed in the atmosphere). Any radioactive fallout to the earth would be marginal at best, and only barely measurable. – RBarryYoung Mar 30 '18 at 16:11

Not as long as you might think.

This post does some math associated with a Hiroshima bomb class explosion. The key observation is that the core material reaches an average speed of 100 km/sec at about 800 nsec into the explosion.

A bigger bomb would simply have a larger plasma cloud that expands even faster.

Remember that the moon has no atmosphere. So, the gas plasma will continue to expand at essentially full speed. This means the bulk of radioacvtive material will far exceed the escape velocity of the earth-moon system and rapidly cease to be a source of impacts for Earth orbiting satellites.

After a few hours, the radioactive rain would mostly cease. Probably after destroying many/some/none of the existing satellites (the tiniest chunk would do major damage at this velocity). Though answering how many would be another question.

Solar escape velocity in the neighborhood of earth is about 42 km/sec so a lot of the plasma is not coming back to Earth ever.

If you set off the bomb where it will also throws out significant material from the lunar surface, the answer changes considerably as that material will be much slower. Too many variables to actually answer this version of the question. Radioactive fallout could continue for months, or years (depending on what you decide the cutoff value is) and the exact conditions in which you explode the bomb.

You might want to consider No Endor Holocaust. What happens when the Death star explodes near Yavin and the moon Yavin IV, and what happens when the Second Death Star explodes near Endor.

Suppose the bomb explodes and vaporizes a sphere of rock 1 kilometer in diameter. The average distance between the Moon and Earth is 384,399 kilometers. So when some of the vaporized rock reaches Earth the sphere containing the rock should have a volume about 5.6799 X 10 to the sixteenth power times the volume it originally had and thus the density will be very much less than it had before being vaporized. But its speed will be very great.

But if all of the vaporised rock has a narrow range of speeds, it won't expand as a sphere but as a comparatively narrow shell. Thus it will have a much smaller volume than the sphere calculated above and a higher density.

Someone might want to calculate the density of such a shell if it is 1,000 kilometers thick and if it is 1 kilometer thick, for example.

How dense does the expanding shell of vaporized rock have to be to do damage when travelling at a high speed? I don't know.

Triton, the large moon of Neptune, has a very, very, very thin atmosphere. It has a surface pressure of 14 microbars - one 70,000th as dense as Earth's atmosphere. But that is dense enough for clouds to form and for winds in the atmosphere to have detectable effects.

Thus It is possible that the vaporized rock from the atomic blast could have no detectable effects on Earth or wipe out all life on Earth. And it would take calculations to show how much effect there would be.

Back in the late 1950s the USA was considering a plan to send an atomic bomb to the Moon and explode it on the surface, Project A119. The plan would have used a W25 warhead with a 1.7 kiloton yield. Apparently none of the scientists calculated any danger to Earth because that wasn't the reason why the project was dropped.

Of course the plan was to detonate the bomb near the terminator and raise a dust cloud that would be illuminated by the Sun and visible from Earth, while you plan to detonate your bomb near Mare Tranquillitatis, closer to the center of the Moon and making Earth the target for more of the debris. And you plan to fictionally detonate a bomb about 58,823.529 times as powerful.