If you are randomly shooting a rock through the solar system, “close approach of mars within 100,000 km” is 870 times as likely as “hitting mars”. That brings a ‘once in 100 million years (really roughly guessing based on what I know of earth’s geological history)’ event down to the order of ‘once in a hundred thousand years’, and the proper reference class of things we would be considering ourselves this lucky to see is probably more like ‘close approach of a large comet to a terrestrial body’ rather than singling out mars in particular. I don’t know enough about distributions of comet orbital energies to consider different likelihoods of comets having parabolic orbits that bring them closer to the center of the solar system versus further away to compare the odds of things going near the different terrestrial planets with different orbits.
The gravity of a planet actually slightly increases the fraction of randomly-shot-past-them objects that hit them over just sweeping out their surface area through space, but for something with a relative velocity of 55 km/s (!) that effect is tiny.
If so, we are indeed very lucky to observe an event, which happens every 100 000 years or so.
OTOH, I’ve conclude, that it is in fact less likely for a planet to be hit by a random comet than it is for a big massless balloon of the same size, to be hit by the same comet.
Why is that? Roughly speaking, if the comet is heading toward some future geometric meeting point, the planet will accelerate it by its own gravity and the comet will come too early and therefore flies by. It’s a very narrow set of circumstances for an actual collision to take place.
A bit counter intuitive but it explains why we have so few actual collisions, despite of the heavy traffic. Collisions do happen, but less often than a random chance would suggest. The gravity protects us mostly.
If you are randomly shooting a rock through the solar system, “close approach of mars within 100,000 km” is 870 times as likely as “hitting mars”. That brings a ‘once in 100 million years (really roughly guessing based on what I know of earth’s geological history)’ event down to the order of ‘once in a hundred thousand years’, and the proper reference class of things we would be considering ourselves this lucky to see is probably more like ‘close approach of a large comet to a terrestrial body’ rather than singling out mars in particular. I don’t know enough about distributions of comet orbital energies to consider different likelihoods of comets having parabolic orbits that bring them closer to the center of the solar system versus further away to compare the odds of things going near the different terrestrial planets with different orbits.
The gravity of a planet actually slightly increases the fraction of randomly-shot-past-them objects that hit them over just sweeping out their surface area through space, but for something with a relative velocity of 55 km/s (!) that effect is tiny.
Should we bring Shoemaker-Levy into this discussion?
If so, we are indeed very lucky to observe an event, which happens every 100 000 years or so.
OTOH, I’ve conclude, that it is in fact less likely for a planet to be hit by a random comet than it is for a big massless balloon of the same size, to be hit by the same comet.
Why is that? Roughly speaking, if the comet is heading toward some future geometric meeting point, the planet will accelerate it by its own gravity and the comet will come too early and therefore flies by. It’s a very narrow set of circumstances for an actual collision to take place.
A bit counter intuitive but it explains why we have so few actual collisions, despite of the heavy traffic. Collisions do happen, but less often than a random chance would suggest. The gravity protects us mostly.