The Moon has a very thin (practically non-existent) atmosphere so the foot print left by Neil Armstrong won't be eroded for centuries. But there are solar winds. Is it possible that solar wind would have enough strength to erode the legendary foot print? If so how many years will it take to completely erode?

(The answer can be approximate.)

source: NASA


Space.com has an interesting article that discusses this very question. Basically, it postulates that everything will eventually go away, due to micrometeorite bombardment, etc. It has the following to say about the rate of deterioration:

From past studies of moon rocks collected by astronauts during the Apollo missions, researchers have learned that the rocks erode at a rate of about 0.04 inches [1.0 mm] every 1 million years.

Given that rate, how long would it take the footprints to disappear? I'm going to guess that the footprint is about an inch (25 mm) deep at it's tallest, and the detail is about a quarter inch (6 mm) (The tread). Given those numbers, it'll take about 6 million years before you won't easily be able to recognize it as a footprint, and about 25 million years before it's completely gone. This assumes that the area doesn't get struck by a particularly large meteor, which would accelerate the rate, and that nothing is done to protect the area in the mean time.

It's worth noting that the provided erosion rate is for rock. The dust might have a higher rate, as it does on Earth, but it likely won't be that much higher. This will be slightly complicated as well that there is a small dust storm that happens at the terminator of the moon. I strongly suspect that the footprints will be gone in a million years, if nothing is done to prevent it from happening.

  • $\begingroup$ Speculation: There was a question that asked "would rocks impacted by a lunar lander shoot off into space like bullets?" I'd assume that, if a meteor were to impact the surface, even in a location not near the footprint, it could actually shoot ballistic dust in a ring that would disperse itself over the moon based on the impact force. The dust could then settle back to the surface-- it may even get filled in by rogue dust before it gets hit by a meteor :)! $\endgroup$ Jun 29 '18 at 20:55

Wind, whether solar or not, is not going to be the main erosion issue.

It will over time strip particles away, but over those sorts of timeframes there will be numerous impacts, whether dust or larger bodies, which may scatter dust over the footprints, or in the case of impact on or near the footprints, may scatter or destroy the footprints themselves.

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    $\begingroup$ Don't forget Moonquakes! They would also cause the lunar soil to shift and settle. An asteroid hit on the other side of the moon might obscure the footprint just as much as a near hit. $\endgroup$
    – john3103
    Oct 1 '13 at 14:01

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