How much more likely is it for a colony on Mars to receive a damaging meteorite hit than a similar structure on Earth?

Question

Meteorite damage probability is low both on Mars and Earth, but Earth has a thick atmosphere, which Mars does not. The thinner atmosphere on Mars should yield some increase of impact probability.

Is it possible to estimate the following:

1. How often will meteorites hit some Martian city with an area of several square kilometers?
2. How energetic will they be? Will a once in a hundred year strike be enough to break a solar panel, a greenhouse window, or an actual roof of some pressurized surface building? Many folks will stay underground to avoid radiation but may to up to the surface to enjoy the view once in a while.

Answer 1

This is an interesting question! Partial answer!

I don't know about the frequency of Martian meteorites, but for a given one we can estimate its terminal velocity (if it reaches it) and kinetic energy.

If it doesn't reach terminal velocity, then it's going to be going a heck of a lot faster and have a heck of a lot squared more kinetic energy.

A 1 cm radius iron meteorite will have a terminal kinetic energy of 27 Joules on Earth but 540 Joules on Mars!

At 10 cm it's 240 kiloJoules and 5.4 megaJoules!

But most meteorites are small.

The bigger ones are extremely infrequent.

If you collect all the dust and dirt off of a flat-roofed building and sift through with a strong magnet you can collect iron-containing micrometeorite debris, and if you drag a lot of powerful magnets around in a desert you can collect a lot of larger bits, but these are not likely to do any damage to a colony or be noticeable at all actually.

Their terminal velocity will be faster on Mars due to the lower air density, the lower gravity only does a little bit to mitigate that effect.

From Wikipedia's terminal velocity:

$$ v_T = \sqrt{\frac{2mg}{\rho A C_D}}$$

where $m$, $A$ and $C_D$ are the mass, cross-sectional area and drag coefficient of the meteorite, and $\rho$ is the density of the atmosphere near the surface.

For the calculation below I've chosen a density of $\rho$ of 7.5 g/cm^3 typical for an iron meteorite.

    r (cm)            0.01       0.10        1.00       10.00   
------------        ---------  ---------   ---------   ---------
vt_earth  (m/s)      3.88        12.29       38.85      122.85 
vt_mars   (m/s)     19.29        60.99      192.87      609.92 
KE_earth   (J)       2.37e-07     2.37e-03    2.37e+01    2.37e+05 
KE_mars    (J)       5.84e-06     5.84e-02    5.84e+02    5.84e+06

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From this answer to Who discovered “Egg Rock”? The Curiosity rover or people?

...Cropped section of image of "Egg Rock" from redplanet.asu.edu/?p=21047 showing the spots where Curiosity's ChemCam laser has ablated material.

See also (and references and answeres therein):

• Have “frosty meteorites” ever been observed soon after landing? Are there photos?
• Why don't iron meteorites on Mars rust or oxidize? Why are they shiny?

Python script for plot:

import numpy as np
import matplotlib.pyplot as plt

def vt(r, g, rho_m, rho_a):
Cd = 1.
A = np.pi * r**2
m = rho_m * (4/3) * np.pi * r**3
v_terminal = np.sqrt(2 * m * g / (rho_a * A * Cd))
KE = 0.5 * m * v_terminal**2
return v_terminal, KE

np.set_printoptions(precision=2, suppress=False)
r = np.logspace(-4, -1, 4) # meters
r_cm = 100 * r

rho_meteor = 7500 # kg/m^3

vt_earth, KE_earth = vt(r=r, g=9.81, rho_m=rho_meteor, rho_a=1.3)
vt_mars, KE_mars  = vt(r=r, g=3.72, rho_m=rho_meteor, rho_a=0.02)

print('    r (cm):           ', r_cm)
print('    vt_earth (m/s):   ', vt_earth)
print('    vt_mars (m/s):    ', vt_mars)
print('    KE_earth (J):     ', KE_earth)
print('    KE_mars (J):      ', KE_mars)

fig, axes = plt.subplots(2, 1)
ax1, ax2 = axes
fs = 12
ax1.plot(r_cm, vt_earth, '--g')
ax1.plot(r_cm, vt_mars, '-r')
ax2.plot(r_cm, KE_earth, '--g')
ax2.plot(r_cm, KE_mars, '-r')
ax2.set_xlabel('meteorite radius (cm)', fontsize=fs)
ax1.set_ylabel('terminal velocity (m/s)', fontsize=fs)
ax2.set_ylabel('terminal kinetic energy (J)', fontsize=fs)
for ax in axes:
ax.set_xscale('log')
ax.set_yscale('log')
plt.suptitle('meteorite CD=1.0, density = 7.5 g/cm^3')
plt.show()

Answer 2

Uhoh's answer neatly covers the damage a given meteorite would have upon impact.

I'll add to that approach the likelihood that a meteorite even strikes Mars or Earth.

A Martian year is 1.6 times longer than an Earth year (686.96 days versus 365.25). At first approximation, on average, a planet is just as likely to be hit by a meteorite at any point in its orbit (that isn't exactly true and that's why we have yearly meteor showers). In other words, I'm assuming here that the distribution of meteorites comes from a uniform direction in the inner solar system.

Moreover, the radius of Mars is 3397 km compared to Earth's 6378 km. Assuming the planets are spherical, the interception plane (think of it as a "target") of the meteorite traveling in a straight line would be a disk whose radius is the radius of the planet. The area of that disk is what matters here. And the radio of the area of the Earth over the area of Mars is about 3.525 ($A=r^2\pi$).

Therefore, Mars is about 5.6 times less likely to be struck by a meteorite, but if it does, the damage is waaaay worse.

Answer 3

The original OP's question

Could meteorites prevent Mars exploration?

has been transformed into another question that was answered, though partially, into energetic calculations and probabilistic calculations. I will try to answer the original question.

First, how can a meteorite prevent colonization of a planet? You must accept that when people take all the risks of a 9+ month journey in space, and spend $$$, it is not because of a breaking window/solar panel, or even a direct deadly hit on an installation that make them think twice. Like the past adventurers, they will rebuild, they will bury their deads and move on. So, to prevent colonization, we must think of a catastrophic event, one that, due to its ramifications in the established ecosystem, can exterminate almost all livings, like the meteorite that hit Earth 66 millions years ago (at Chicxulub).

Now, for the sake of quick-and-dirty estimation, let's say that in 10,000 years the probability of being hit once is 10^-4 times the probability being hit once in 100 millions years (I know it is wrong math, but I am on the safe side). Furthermore, assume that for Mars, the probability of being hit once in 100 millions years is 1. At least for Earth, it is much less, from the geological records.

The Chicxulub crater has a radius of 90 km. Probably any living animals in a radius of 2x90 km were killed by its kinetic energy. This is a circle of ~100,000 km², or about 7% of Mars surface (R=3400 km). Hence, if you put at random a city on Mars, the probability that, over 10,000 years it is erased by a Chicxulub-like event is 7 in one million. In 100 millions years, your city has 93% of being spared, although we assume certainty for the catastrophic event.

As crucial remark, it was not the kinetic energy of Chicxulub that exterminated 75% forms of life on Earth. It was the ramifications of its impact on the atmosphere and the global cooling that resulted from Sun-blocking ashes. Hence, my calculation above is pointless if I cannot predict - which I can't - the impact on the atmosphere of Mars of a big meteorite hit. In fact, my calculation would hold if Mars were completely devoid of atmosphere, since in this scenario it's only the kinetic energy that harms.

Therefore, the answer: with the present knowledge, the likelihood that meteorites constitute a concern for a Martian colonization is non-existent. Even taking into account the facts that Mars is closer to the asteroid belt and its atmosphere is non-protecting.