The random walk of cars and their collision probabilities with planets | Hacker News Reader

The random walk of cars and their collision probabilities with planets

arxiv.org

165 pointssndean61 comments

Hanno Rein and Daniel Tamayo are pretty legit dynamicists. For anyone interested in doing calculations like these themselves, they've been working on this amazing N-body library called Rebound:

https://github.com/hannorein/rebound

One of my all-time favorite figures is Fig. 1 of this paper of theirs describing one of the integrators used in Rebound:

https://arxiv.org/abs/1704.07715

Thanks for the link, that paper was a great read: clever idea, and very well written.

By running a large ensemble of simulations with slightly perturbed initial conditions, we estimate the probability of a collision with Earth and Venus over the next one million years to be 6% and 2.5%, respectively

More fortunately, even if it were to "collide", it would likely burn up in the atmosphere like the majority of other, even very large[1], objects that reenter.

[1] https://en.wikipedia.org/wiki/Mir#Final_days_and_deorbit

"Free Tacos for Everyone in the Solar System if Mir hits our Target on Venus!"

Reference for reference: http://news.bbc.co.uk/1/hi/world/americas/1231447.stm

Particularly since there is a potential that it would enter earth's atmosphere at 2-3x the orbital velocity of Mir.

2 questions:

> The repeated encounters lead to a random walk that eventually causes close encounters with other terrestrial planets and the Sun.

What are terrestrial planets? I thought there was only one terrestrial planet; earth. Or is meant 'earth like' planets, specifically Venus, Mars and Earth?

> dynamical lifetime of the Tesla to be a few tens of millions of years

What is the dynamical lifetime? I'd think that with all the rocks out there the Tesla will get some dents from collisions. So many dents that I think in a million years it'll be toast. How does this square with a dynamical lifetime of tens of millions of years?

Terrestrial planets usually means inner 4 in our solar system, and "earthlike" elsewhere

Re. dynamic lifetime: you are right that there are many rocks. You underestimate the vastness of space though. Collisions are extremely rare and the Tesla is pretty small.

What collisions? The whole point of this article is that the most likely rock to hit Tesla is the Earth. Space is very, very, very empty; all the (many) rocks out there are scattered in extremely huge amounts of empty space.

Even in a dense asteroid belt, almost every path encounters zero rocks; and the orbit of that Tesla is not in asteroid belts but in interplanetary space that's quite "clean".

Tesla would be expected to get some abrasion / "wear&tear" from hitting individual atoms and tiny particles of space dust; over a million of years that would likely accumulate to a major change. But it's not likely to hit a rock of "dent-making" size before it gets sucked in by some major planet.

It's also worth noting that Earth is more massive than Mercury, Venus, Mars, the Moon, and the asteroid belt combined.

Since the Tesla doesn't go anywhere near Jupiter's orbit, if it gets sucked in by anything at all, it's likely to be Earth.

I thought there was no way this could be true - I was at the Griffith Observatory yesterday and saw that Venus was nearly 80% the mass of Earth.

But indeed, Mars has only about 1/10 the mass of Earth! And Mercury is about half of that.

https://nssdc.gsfc.nasa.gov/planetary/factsheet/

It's the mass ~ size cubed that's deceptive.

Yeah, Earth is huge!

It also has the highest density of all the planets, thanks to the iron and nickel in the core. Earth is so dense that its surface gravity is higher than that of Saturn and Uranus (for a suitable definition of "surface" for the gas giants) despite the fact that the latter are much more massive as a whole.

We should make note of these facts and use them to burn the aliens if we ever come to an interplanetary rap battle :)

It's as though Earth were a gas giant, but with the outer layers of hydrogen and helium blown away. The magnetosphere is closer in magnitude to Uranus's or Neptune's than Venus's or Mars's. We think it's why we still have water.

That makes me wonder - given that Jupiter and Saturn are so massive as to have solid cores, how do their core sizes compare to Earth's size? never compared those numbers, not sure where to find core size estimates for our four giants.

> What are terrestrial planets?

Terrestrial planets have a solid planetary surface, making them substantially different from the larger giant planets, which are composed mostly of some combination of hydrogen, helium, and water existing in various physical states.

1. https://en.wikipedia.org/wiki/Terrestrial_planet

> In our numerical model, we do not integrate the orbit of the Moon and instead use a single particle with the combined mass of the Earth and the Moon.

Is that a standard assumption for this kind of model? For such a chaotic simulation, would it not be very important to approximate the effects of the Earth and moon very precisely? Especially since these bodies would have such dominating effects early on?

Only the initial launch has the car near the earth and moon, but the calculations are already factoring in a range of starting points - I’d assume the moon’s effects are contained in that range.

After it moves away from the earth the distance ought to be negligible, although even if they do reduce the earth moon to a single point I don’t know if they model a wobble.

The mass of the moon is only about 1.2% of that of earth.

Also, “early on” earth is much, much closer than the moon. The gravitational pull of the sun is >100 times as large as that of the moon there, and both are minute compared to that of earth (you don’t feel much lighter or jump higher when the sun or the moon are overhead, do you?)

Yes, for things "far" away from the Earth. They said they started their simulation on Feb 10, the launch was on Feb 6, to the roadster was far enough away at that time to ignore the Earth and Moon being separate. I didn't see where they mentioned it in their paper, but they likely started with either published location/velocity data, or used observations to compute its position and velocity for the start on the 10th.

Very cool, looks like this partially answers my curiosity https://news.ycombinator.com/item?id=16324894.

It'll be fun to read papers about other projected fates of the various aspects of the Tesla.

I'm wondering about the fate of the paint, plastic, rubber and leather.

https://www.autoblog.com/2018/02/07/tesla-roadster-starman-s...

It’s pretty incredible to imagine that after most of the monuments man has built for man have vanished, Elon’s Tesla might still be orbiting the Sun.

Feels implausible.

Voyager 1 & 2 are the trailblazers here and the chances of them colliding with anything are markedly lower I would assume.

Pioneer 10 and 11 probes left the solar system as well.

I think it’s also likely that all the stuff left on the moon might be longer lived than a car shooting randomly around the solar system.

I sure hope that's not the way things go. Eventually humanity will be extinct, but long before that I'd image we'd build far more out in space than we have on Earth.

Within a couple of hundred years (maybe even much less) someone's going to go and collect it for bragging rights and/or as a trophy. See if they don't.

>> See if they don't.

Hope to live long enough to see you proved wrong.

It will be designated a solar system historical site and be strictly off limits. You can't exactly sneak up on something in space...

Space tourism.

Imagine SpaceX selling tickets to rendezvous with the car, put you in a spacesuit, and sit next to Starman.

What a photo opportunity!

I'd imagine it's still considered to be property of SpaceX and/or Elon Musk, so he should have the right to reclaim it, even if no-one else does.

Aw, that reminds me of a story about the future Mars rover:

https://www.wired.com/2016/12/jon-rogers-a-martian-goes-hunt...

And if someone flies their own ship and catches it, what is Earth going to do about it, exactly?

My theory is that it'll be in a museum within a century.

empty speculation

I only hope it'll be a museum on Mars.

If SpaceX ever gets into asteroid mining, it’ll be good practice to return it to earth.

As high as 6%? In the total vastness of space, 6 in 100 seems like an incredibly high chance that the rocket payload will hit either Earth or Venus... It's a bit like me pulling out a rifle and firing into the air, hoping to hit a specific dinner plate in a back yard two suburbs away on a windy day, isn't it?

Plates a few suburbs away don't exert massive gravitational pulls on their surrounding.

But doesn't gravitational pull mainly deflect objects travelling at high velocity? Hence their use to accelerate spacecraft into different trajectories? If we looked at the 'indentations on a rubber mat' model of gravitational influence, the object would still have to be aimed almost directly at the planet in order to hit it rather than bend around it?

But I guess that comes down to the velocity of the object in question, and after repeated trajectory adjustments due to gravitational pull, it could quite conceivably end up aiming directly at a massive body in space that exerted the pull in the first place...

Currently, the Tesla is aimed almost directly away from Earth. After all, it was launched from Earth!

On the other side of the orbit, that becomes almost directly at Earth.

Go round and round a few million times, and Earth might actually be at a point in the orbit where it can exert a significant gravitational pull on the passing Tesla.

I hope that other members more in the know can clarify, but I thought that the launch into deeper space was done as a 2 stage thing - first, they got the car up into earth orbit, THEN they did a second burn to break orbit. i.e. the second burn was done while the vehicle was moving tangential to the Earth, and not radially away from it?

That just means that when the Tesla returns to the same point in its orbit, it will pass a few hundred miles above Earth's orbit (where the final burn was performed) instead of directly intersecting Earth's orbit.

The difference is virtually meaningless compared to orbital perturbations from other sources. Either way, it's close enough for Earth to affect the Tesla's orbit if it were at the right place at the right time.

The point was made in the paper - since the Tesla was launched from Earth, its orbit has its closest approach to the Sun very close to the Earth's orbit, and this increases the chance of it being affected by Earth's gravity. This is because for part of its orbit, the Tesla will be effectively travelling along approximately the same path as Earth, just a bit faster. This means that it will approach Earth approximately one in every ten orbits. Hence the first interaction in 2091.

After a few interactions, the orbit becomes more funky, and interactions decrease in frequency.

If you do this every day for millions of years, it's reasonable to expect a hit at some point.

Hah. This is cool.

I’ve become so used to reading papers with a footnote that states something about an NSF grant being used to support the research that I was initially surprised when I didn’t see it here. Then I realized what I was reading and chuckled :)

There is one in ACKNOWLEDGEMENTS section:

> This research has been supported by the NSERC Discovery Grant RGPIN-2014-04553.

As if there was not enough junk in space already.

There's junk in low earth orbit. But this object is in solar orbit. There's very little junk there. There's very little anything there.

Very little junk, but _loads of stuff_ in solar orbit in the form of the asteroid belt, the jupiter greeks/trojans and the hildas, the kuyper belt, and the oort cloud.

There is so much there.

For extremely low values of ”so much”.

Maybe, but on the other hand, I expect you've hardly ever used 'so much' to refer to more - since a small fraction of that 'so much' includes Earth and everything on it.

As with everything, it depends on what your comparisons are to.

It's hard to really wrap your mind how BIG it is there.

Those things you mention? They take up so little space they wouldn't even count if not for the fact there's nothing else.

Space is REALLY big, and REALLY empty.

it's really empty unless you need to compute gravitational deviation over the course of decades. Then it's suddenly bloody full.

Gravity obeys inverse square law, so no, all that small stuff doesn't count on timescales of decades.

Like the meteor belt? :P

More like Jupiter.

There isn't, and it's unlikely to ever be.

I like to use this comparison: a single cell you shed from your skin pollutes the Earth more than the Roadster pollutes the Solar System.

I like that analogy - but is there anything to back it up?

The order of magnitude is correct:

https://www.wolframalpha.com/input/?i=(diameter+of+blood+cel...

(convert erythrocyte | diameter to meters)×(convert diameter of Neptune's orbit to kilometers)/(convert Earth | average radius to kilometers) = 11 meters

edit: Of course you could argue with this calculation in all kind of ways - widths vs volume vs mass ... but I think for such a silly analogy this is good enough to say: It is not totally unreasonable.

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