Overall I think we’ll discover that they are more common than we think which makes me wonder if we could use them to piggy back probes on them to the outer solar system and beyond since they move quite darn fast.
In short: to have any sort of survivable encounter with the object the relative velocities need to be so small you have essentially "matched their speed". Those last 0.5 km/s you might gain aren't important compared with the 29.5 km/s you need to put in.
you don't match deltav, you'd match trajectory. you may be able to do that at the cost of more or less deltav, depending on how clever and patient you are. once you've matched trajectory, you'll (basically) stay matched, as you're in space and there's nothing to disturb you.
That remark makes more sense in the context of missile defence than when talking about space travel.
From what I know from reading on Helios-A and Helios-B, we already have a probe which can go over twice the speed of what I thought I saw the comet is traveling at. So couldn’t the probe match its velocity (dunno why I said Delta V before) to the comet, if even just for long enough to land without total destruction?
And if you don't match it well enough that you end up roughly the same place you're going to have a fast, and therefore violent, encounter.
Elsewhere I saw what I thought was the speed of the comet, which was around 69k mph. Didn’t Helios 1 and 2 do something like ~150k mph[0]?
Assuming those numbers are correct (please say so if not), then what would stop an intercept from being technically possible (even if very very very hard)?
To actually hitch a ride with another object you have to match their velocity _and_ their location at the same time.
If the object you are trying to catch started further from the sun than you, and was already moving faster than you, then you can't match its speed and location by falling toward the sun: when you arrive at the same location, it will have fallen further than you and hence picked up more kinetic energy per unit mass than you did, and it started off moving faster than you to start with, so it's still moving faster.
Dunno why I said DeltaV, but clearly it was inappropriate.
Yeah, but we could go to other stars already, in like a zillion years. Voyager is on an interstellar path, although it isn't pointed at a nearby star. If the object has made the journey it might take the same delta-V for us as an interstellar trip, but it would happen a whole lot faster.
Some of these objects are also not very dense so some ablative enclosure might also work.
In either case, you are going from 0 to 60 more or less instantly and the results on your fleshy meat body will be the same.
You could try to run real fast in front of the car, away from it, but you are limited by your meat body's technology to ~10mph. You still hit the car at a difference of 50mph. Meat paste once again.
To avoid a painful collision, you'd need to get up to speeds of about 57mph, which is pretty hard for your body to do. And if you could get up to 57mph, why do you need tha car? There's no friction in space, so you'd just keep going until something bumped you.
On impact, only the nearly massless front bit of the net needs to accelerate instantly. The acceleration gradually spreads back to the probe, which is then accelerated gradually to match the object.
After it matches, there is still a great deal of energy in the stretched-out net, which in principle could accelerate your probe to be as much faster than the object as it started out slower than.
Another way to think of this is with a non-stretchy tether perpendicular to the object's path. The object hits one end, and the probe swings around behind it, gaining 2x before it gets to the other side. It could let go at various other points to head off in some other direction at less than 2x.
This is not too different from what we do when we fly probes past planets to give them a speed boost. In that case, the tether is gravity.
It would take about 47 seconds, and the spring would elongate by a maximum of 530 km. To withstand this tension (100 kN), the steel wire (ultimate tensile strength ~400 MPa) would need to have a cross-sectional area of 250 mm², or diameter of 16 mm.
Given this wire diameter, and a Young's modulus for steel of 200 GPa, the spring itself would require a diameter of ~42 cm and ~200,000 turns, if we allow it to stretch completely during acceleration. Fully relaxed, the spring would be 3.2 km in length.
This works out to at least 130 m³ of steel, or 1000 metric tons, which is somewhere around USD$500k. Eminently affordable.
Of course, that's a drop in the bucket compared to the cost of launching a 3.2 km long, 1000 metric ton slinky into outer space.
I am actually more worried about the propagation of tension in the tether being restricted to the speed of sound in the material. It seems like the end would just snap off, for any realizable material.
For comparison, the New Horizon probe to Pluto and beyond left at 23 km/s.
With a thousand km of graphene-fiber tether standing perpendicular to the object's path, it would take 45s to accelerate the probe at a peak of 484 km/s/s. For a 10kg probe, that would put 4.8e9 N of tension on the tether.
Graphene has a tensile strength of 130000 MPa, or 1.3e11 N/m^2, so the cable would need to be some 20cm thick.
Boosting to a higher speed would reduce the cable thickness needed proportionally. At 19 km/s, quite doable, it's 10 cm. However, boosting 1000 km of 10cm cable to 19 km/s would take quite a fair bit more fuel than just boosting the probe itself to the target speed of 41 km/s.
(If my maths are right, and the rail of the US Navy's 2km/s railgun is 10m, the projectile has an initial accelleration of about 20,000 gs. Though its internal complexity is fairly low.)
Keep in mind that if you manage to harpoon your extrasolar whale, you haven't landed, you've only attached yourself to it. If you thought ahead and packed a bungee cord, rather than a completely inelastic cable, you could take up the initial acceleration, but would then find yourself dealing with the elastic rebound. You'd eventually contact at twice the original negative delta, assuming elastic limits on the cord weren't exceeded.
(Keep in mind that you were initially travelling faster, slower, or with some relative motion to the interstellar whale, and hence are implicitly counting on your harpoon cord to take up the difference. Unlike Ahab, you don't have the medium of water to supply friction or shock absorption.)
You could carry airbags to cushion the impacts. This was actually done for the Mars Pathfinder mission. The critical differences between Pathfinder and Extrasolar Ahab is that Pathfinder had an aeroshell and parachutes, all of which reduced the terminal impact eleasticity accelleration to well below Mars escape velocity, as well as a substantial surface gravity to deal with, while Extrasolar Ahab has the cold hard vacuum of space and a microgravity measured in single-digit metres/s^2. Rather than bounce and come to a rest, you'll bank off. Instead of Ahab, you're now "Fast Eddie" Felton, and your balls are no longer on the felt.
The problem in both these cases is elasticity, so what you're looking for is something that's deformable rather than elastic, probably at both the 'poon cord and crash buffer side. The longer you can stretch out (so to speak) the accelleration and impact, the softer your ultimate kiss.
https://invidio.us/watch?v=E65F86kMu48
At which you've probably got one more question:
https://invidio.us/watch?v=uJixQ16L5zc
To which I can only reply: as you wish.
The question specifically addressed lithobraking. Which means a terminal state on the surface with matched velocity.
But how much delta-v one can extract from a bungee jump is just as interesting a problem as how do you break from a huge delta-v and no atmosphere. Maybe one can even direct the jump into a useful direction: interstellar body based propulsion.