Or I could send smaller probes—but they’d be slower to industrialize at the other end. And either of those changes would also make them more vulnerable to collisions with space debris, which already destroy over 99% of the probes I send out.
Why smaller probes end up more vulnerable to collisions? This sounds sort of counter-intuitive to me, should not this dependency between size and vulnerability go in the opposite direction? (I guess my model is that every hit is fatal, and that hit/no-hit is a binary thing which only depends on size.)
Why smaller probes end up more vulnerable to collisions?
In my model of that claim, it would be true, but the claim was phrased in a confusing way.
I’d build them to be very slender, so instead of “bigger” I would say “longer”, and in a sense their vulnerability to collisions would be roughly the same under changes in length (they’re moving ahead much faster than debris is moving laterally, so they’d mostly take hits from the front, which doesn’t have to expand much when we elongate them), so I would say instead that they’re more resilient, because they have more shielding (or because they have more redundancy and they retain data/functionality at the square of their in-tact mass).
Why smaller probes end up more vulnerable to collisions?
Smaller probes are probably more vulnerable to collisions per unit mass. (Unsure if this was the intention in the story.)
In particular, suppose the probability of collisions is proportional to total surface area. Then, if our probe is spherical, collisions are quadratic in radius while mass is cubic.
probes probably want a very skinny aspect ratio. If cosmic dust travels at 20km/s, that’s 15k times slower than the probe is travelling, so maybe that means the probe should be eg 10cm wide and 1.5km long
I expect that the engineering constraints kick in way before that, but yeah, seems broadly correct.
Perhaps the correct strategy here is for the probe to be multi-stage, but with each stage behind the next, so that it drops off after spending all its fuel.
Oh actually… I think 15k isn’t the right number here, both because of threshold effects, but also because these are relativistic collisions. I’m not sure exactly how to do it but intuitively it should be something like 15k times the Lorentz factor (around 70 for 0.9999c). So more like 10cm wide and 100km long, lol.
i thought about this for a minute and landed on no counting for lorentz factor. Things hitting on the side have about the same relative velocity as things hitting from the front . Because they’re hitting the side they could either bounce off or dump all their tangent kinetic energy into each other. like because all the relative velocity is tangent, they could in principle interact without exchanging significant energy. But probably the side impacts are just as dangerous. Which might make them more dangerous because you have less armor on the side
I think there’s probably a variety of more complicated factors involved that we haven’t considered. Doesn’t really matter for the story, it’s sufficient to leave stuff unsaid as long as the currently understood boundaries of the possible are respected.
Would the probe emit an ‘ablative antimatter particle shield’ which coasted alongside the probe and eliminated dust particles approaching from the sides?
Launching a probe with a laser probably involves an umbrella shaped probe with the umbrella shaft being the ‘true’ probe, and the umbrella canopy being a ‘first stage acceleration’ disposable parabolic mirror made of something like mylar and carbon fiber. The mirror gets jettisoned at some point. Fun to speculate about, but not really critical to planning the next few decades. A far smarter mind than mine will have time to work out these details before they’re needed.
Yeah, the intended intuition is that the size of collision required to derail a probe is proportional to the probe’s mass, and that there are many tiny collisions (e.g. with stray atoms) that wouldn’t derail bigger probes but might derail smaller ones.
But not particularly confident on either of these.
Thanks, that’s great!
I wonder how does this work:
Why smaller probes end up more vulnerable to collisions? This sounds sort of counter-intuitive to me, should not this dependency between size and vulnerability go in the opposite direction? (I guess my model is that every hit is fatal, and that hit/no-hit is a binary thing which only depends on size.)
In my model of that claim, it would be true, but the claim was phrased in a confusing way.
I’d build them to be very slender, so instead of “bigger” I would say “longer”, and in a sense their vulnerability to collisions would be roughly the same under changes in length (they’re moving ahead much faster than debris is moving laterally, so they’d mostly take hits from the front, which doesn’t have to expand much when we elongate them), so I would say instead that they’re more resilient, because they have more shielding (or because they have more redundancy and they retain data/functionality at the square of their in-tact mass).
Smaller probes are probably more vulnerable to collisions per unit mass. (Unsure if this was the intention in the story.)
In particular, suppose the probability of collisions is proportional to total surface area. Then, if our probe is spherical, collisions are quadratic in radius while mass is cubic.
probes probably want a very skinny aspect ratio. If cosmic dust travels at 20km/s, that’s 15k times slower than the probe is travelling, so maybe that means the probe should be eg 10cm wide and 1.5km long
(Agreed, I was just trying to describe the spherical cow of probe designs, a spherical probe.)
I expect that the engineering constraints kick in way before that, but yeah, seems broadly correct.
Perhaps the correct strategy here is for the probe to be multi-stage, but with each stage behind the next, so that it drops off after spending all its fuel.
Oh actually… I think 15k isn’t the right number here, both because of threshold effects, but also because these are relativistic collisions. I’m not sure exactly how to do it but intuitively it should be something like 15k times the Lorentz factor (around 70 for 0.9999c). So more like 10cm wide and 100km long, lol.
i thought about this for a minute and landed on no counting for lorentz factor. Things hitting on the side have about the same relative velocity as things hitting from the front . Because they’re hitting the side they could either bounce off or dump all their tangent kinetic energy into each other. like because all the relative velocity is tangent, they could in principle interact without exchanging significant energy. But probably the side impacts are just as dangerous. Which might make them more dangerous because you have less armor on the side
I think there’s probably a variety of more complicated factors involved that we haven’t considered. Doesn’t really matter for the story, it’s sufficient to leave stuff unsaid as long as the currently understood boundaries of the possible are respected.
Would the probe emit an ‘ablative antimatter particle shield’ which coasted alongside the probe and eliminated dust particles approaching from the sides?
Launching a probe with a laser probably involves an umbrella shaped probe with the umbrella shaft being the ‘true’ probe, and the umbrella canopy being a ‘first stage acceleration’ disposable parabolic mirror made of something like mylar and carbon fiber. The mirror gets jettisoned at some point. Fun to speculate about, but not really critical to planning the next few decades. A far smarter mind than mine will have time to work out these details before they’re needed.
Yeah, the intended intuition is that the size of collision required to derail a probe is proportional to the probe’s mass, and that there are many tiny collisions (e.g. with stray atoms) that wouldn’t derail bigger probes but might derail smaller ones.
But not particularly confident on either of these.