[diverjohn (OP)]

If I worry about an asteroid hitting earth and killing everyone, including me, are my odds better if I hitch a ride from Elon Musk and move to Mars? On the one hand, the Earth has a stronger gravitational attraction to asteroids, but Mars is much nearer to the asteroid belt. Is there a clear winner here?

[paul cotter]

The lack of a breathable atmosphere rules out Mars for human habitation except in the most limited forms of existence. Don't tell Elon Musk!- I think we should all start a gofundme to pay for his transit.

[Eternal Student]

Hi.

    A brief survey of the evidence suggests that you'd be at higher risk of meteoroid impacts on Mars.

Why?
     The explanation usually given is that the atmosphere is too sparse.  Small meteoroids don't seem to break up or burn up in the atmosphere anything like as much as they do around Earth.

What evidence?

....  The Mars Global Surveyor, active from 1997 to 2006, was the first spacecraft able to image Mars in high enough resolution to detect new impacts, with a resolution of up to 1.5 meters (4.9 ft). The first detected impact, a 14.4-meter (47 ft)-diameter crater in southern Lucus Planum, happened between 27 January 2000, and 19 March 2001.[2] Since then, over 1,200 new impact craters have been found on Mars......

  .... Due to Mars's tenuous atmosphere, with just 0.6% the surface pressure of Earth's, incoming meteors are much less prone to breaking up..... 

[Extracts taken from Wikipedia]

More discussion and further references on this Wikipedia page:   https://en.wikipedia.org/wiki/Impact_events_on_Mars 

Best Wishes.

[evan_au]

At present, there are estimates about the quantity of meteors hitting the Earth's atmosphere, but only a small fraction of them (larger than 1 kg) actually survive to hit the ground.
- Smaller ones are more frequent than more massive ones, but we don't have good statistics on them

The LUMIO space probe (planned launch in 2027 or 2028) will study meteorite impacts on the far side of the Moon (but only while it is also the dark side of the Moon).
- It will look for flashes as meteorites strike the Moon, vaporising the lunar rock
- They expect to detect meteorites as small as 1 gram
- This will give a better idea of the size distribution of meteorites - even a 1g meteorite could destroy an above-ground lunar habitat.

https://www.sciencedirect.com/science/article/pii/S0094576522001424

[alancalverd]

Gravitational attraction increases with the cube of the radius of a planet, and surface area increases with r², so in the absence of an atmosphere the probability of any point being struck by a meteorite increases with r³ /r². Thus you are safer on a smaller planet.

The atmosphere adds a significant nonlinear element. Small particles will burn up in an atmosphere and the dust from disintegrating medium-sized meteors is harmless, but the residue of a Tunguska or Chicxulub event will kill you.

A really dense atmosphere might ablate the bigger rocks but the surface of Venus is even less welcoming than Mars. So how about a really deep atmosphere? Problem with the giant planets seems to be an absence of actual rocks to stand on.

My choice: stay here and let the dice roll.

[Petrochemicals]

From a geological point of view, as Mars has no internal heating and is quite cold to begin with, it has limited energy recources also. In the event of the big one our underground refuges would be considerably more comfortable on earth. I can imagine Mars would be a serious threat to one's mental health under normal circumstance, after a meteor apocalypse it would be a disaster.

[Eternal Student]

Hi.

Gravitational attraction increases with the cube of the radius of a planet, and surface area increases with r2, so in the absence of an atmosphere the probability of any point being struck by a meteorite increases with r3 /r2.

    I like the approach you've taken and can see what you're doing.  However, what reason do we have to assume the size of an objects gravitational attraction would be directly proportional to the number of meteors that strike it?    In the absence of any atmosphere, as you state, two objects generally heading toward each other will form an orbit almost all the time.  I agree that an object with a greater gravitational attraction may have more objects in orbit around it - but we don't really care about that too much, it's only the actual meteor impacts on the planet surface that matter.
    It's only when the approach of the meteor toward the planet was almost perfectly "head-on" that an impact would occurr instead of an orbit (either a closed elliptical or else a hyerbolic escape orbit) being the final result.   So, you'd have thought, the cross-section of the planet seen by the approaching meteor is a fair estimate of the critical solid angle for the approach that does result in an impact,   so that cross-sectional area is a circle, with area ~  r².

Best Wishes.

[alancalverd]

An object at grazing incidence will be slowed by the upper atmosphere and will eventually descend, which accounts for practically all the meteors and meteorites we see. And for some reason NASA and suchlike organisations are more worried about preventing future impacts than the gradual accretion of orbital dust, which seems not to have happened to any great extent - apart from the anthropogenic junk we have carefully launched into precise orbits in the last 70 years or so.

[Eternal Student]

Hi.

...but you ( @alancalverd ) were the one who said....

so in the absence of an atmosphere the probability of any point being struck .....

    In the absence of atmosphere, collisions between objects broadly heading toward each other are extremely rare,  they just orbit in some way.    For example, when the entire Andromeda galaxy finally reaches us and starts occupying much the same space as the Milky Way galaxy,  head-on collisions of the stars, planets, asteroids and other stuff are still generally thought to be rare events.   Instead the "damage" will be done just by changing the orbits of stuff in our galaxy upto and including the possibility of having some astronomical bodies thrown out into deep space.

Best Wishes.

LATE ADDITION:
     The interesting and relevant point is that gravity isn't some problem or destroyer of worlds.    Actually, gravity is quite helpful , it's the great creator of solar systems, galaxies and most of the structure in the universe.   Everything about it, such as Newton's inverse square law, seems to be well crafted so that most bodies are kept safely away from each other and just orbit.    Your original inference, that the number of meteor impacts would be proportional to the gravitational attraction of the planet, just seems to be entirelly unfounded.   Your giving gravity a bad name which it doesn't deserve.
    Given a choice we'd probably be a lot safer on super-super massive planet.  I'd like to be the quivalent of the sun and just have everything spinning around me rather than being one of the little planets held in it's gravitational pull and made to move around in an orbit that could cross paths with all the other flotsam and jetsam that orbits the sun.

    However, I'm only being this critical because you ( @alancalverd ) aren't going to worry about it.   Most of the time you give sage advice.