Great question!
Whether a footprint will stay nicely formed or will be erased depends on a variety of things.
On earth, you get the clearest footprints which last the longest
when the particles (dust, mud, or whatever) adhere to each other much
more than they do to the sole of your boot (otherwise you end up
pulling up a sticky mess, as in some muds). Furthermore, the
self-adhesion of the particles is responsible for the footprint
retaining its shape over time. If you make a boot print in sand on the
beach, the shape of the impression will immediately change once your
boot is gone because sand likes to flow down hills. There is a maximum
steepness to a hill of sand, and if a hill is any steeper than that,
the sand will spontaneously flow in little or big avalanches until that
steepness is attained. That's why when you pour sand on a pile (say in
an hourglass) the conical pile you get always has the same steepness.
Sand flows in this way because the grains are large and the
cohesive forces between sand grains are small. Gravity pulls down on
sand grains and they will rearrange themselves until the forces balance
out. If you wet the sand, you increase the cohesive forces between
grains because water is electrically polarized and attracts the sand
grains electrostatically, "wetting" them. Other fluids may have the
opposite effect (pouring, say, freon on a sand pile may actually make
it reduce in height).
On the moon, there is a layer a few meters deep of very very fine
rocky dust, with the consistency of dry talcum powder. The individual
grains are smaller than usual sand grains. The cohesive forces are
small, but on the moon, gravity is also quite low. What's important is
the relative size of the electrostatic cohesive forces and the weight
of each particle of dust, and it appears from the fact that the
footprint doesn't collapse under its own weight, that the cohesive
forces win out. This may not be the case in another region of the moon
where there may be larger grains of rock covering the ground. Although
the stuff that's there is very fine powder because it is ejecta from
meteor impacts, and the entire moon may be covered in nothing but this
stuff.
Tom
(published on 10/22/2007)
