Moonbase issues: falling rocks

Help me out with some lunar physics.

a one gram feather
dropped from one hundred miles high
hits the ground how fast

  • How much energy does that feather deliver? What is a real-world equivalent? (bullet? fisticuffs punch? Kitten slap?
  • I assume a one gram rock would create a different effect from a one gram feather owing to the surface area receivig the energy–significant?
  • Rocks are probably more prevalent in space than feathers, and I reckon they would hit the moon with considerably more force than one that was dropped from 100 miles.
    -----What’s THAT one gram rock gonna feel like when it hits you?
    -----What does a moon resident do to keep from getting hurt?
    -----If the tiny rocks aren’t a problem, how big do they need to be to present more than a mere nuissance?
    -----What precautions can/should I take to protect my huge lunar solar array?

From this calculator.

Speed at impact:1775.85 m/s or 6393.06 km/h
Time until impact: 181.21 s
Energy at impact: 1576.82 joules

As noted on the page, all friction is ignored in the calculation.

1576.82 joules

My Wiki-foo tells me that 1 joule = a smallish (100gram) apple hitting the ground after a 1 meter drop (on earth). So 1576.82 joules = a considerable whack. Yes?

Roughly in the range of a 5.56 rifle or a .44 Magnum revolver.

Guys, that calculator is using 10 m/s[sup]2[/sup]. That’s fine for free fall on earth but the g of the moon is 1.64 m/s[sup]2[/sup].

:smack::smack::smack::smack: Forgot that little detail.

“Bill always knew a feather would get him one day…”

kinetic energy is mgh

m = 0.001 kg
g = 1.63 m/s[sup]2[/sup]
h = 161,000 m

KE = 262 J

Just looked it up this morning when writing a test. Explorer 1.

Actually I did look it up today for a test I wrote and I suppose we can neglect air resistance. d = 0.82t[sup]2[/sup] and 100 miles is 160934.4 m which gives me very close to 443 seconds meaning it hits the Moon at 726.54307 m/s or just over 1625 mph :eek:.

No biggie, divide the previously calculated energy figures by 6 (and divide the speed figures by the square root of 6).

The calculator running coach linked to uses Earth gravity, not Moon gravity.

The mass of the moon is 7.35x10[sup]22[/sup] kg, and its radius is 1.74x10[sup]6[/sup] m. Acceleration due to gravity is GM/R[sup]2[/sup], so gravity at the surface of the moon is 1.62 m/s[sup]2[/sup].

Assuming constant acceleration, speed at impact would be √(2gh) = 722 m/s. Kinetic energy = 1/2*mv[sup]2[/sup] = 261 J.

However, gravity isn’t constant. At 100 miles above the surface of the moon, gravity would only be 1.36 m/s[sup]2[/sup], which is enough that it needs to be taken into account.

For that, E = GMm*(1/r[sub]1[/sub] - 1/r[sub]2[/sub]) = 239 J. v = √(2E/m) = 691 m/s

To check CurtC, my answer is a touch under 264J of energy.

Here’s a research paper addressing your question. Their conclusion:

A 150 square meter surface on the moon will experience about one impact per year from micrometeoroid that’s 1/2 a millimeter in diameter or larger. Such an object will be moving on average about 13 km/s. That’s enough energy to blast a crater in an aluminum plate 2 mm in diameter and 1 mm deep.

Feathers or rocks don’t fall from 100 miles up. Because there’s no source up there to create them.

Rocks falling down a cliff or off a mountain are realistic threats. Smart campers don’t erect tents at the base of cliffs. Smart Moon campers do the same.

Assuming we have dumb Moon campers … For a walnut-sized rock falling from the top of a tallish Moon mountain to the basin below (3,000m fall) you’re talking about a couple hundred J of energy. Enough to hurt, or maybe damage flimsy structures. But well under a bullet’s energy.

The Hamster King has some nice data on micrometeors. For which acceleration due to gravity is immaterial. Their velocity relative to the Moon is entirely a matter of their and the Moon’s orbital velocity around the Sun & Earth.

Shouldn’t it be the other way around?

I’m totally clueless about physics and geometry, but don’t rocks on earth fall due to erosion or being dislodged by an animal or human? With no erosion to speak of and no living things on the Moon, isn’t it unlikely for a rock to roll down a mountain or off the edge of a cliff? Again, I’m totally ignorant and willing to have my ignorance tackled.

Sounds right.

Thermal changes could account for a very small amount of rockfall (or perhaps dustfall). And meteors occasionally strike. But without weather or life or volcanism or seismic activity, there can’t be much.