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:
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.
> 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 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.
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 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.
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.
> 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.
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.
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?)
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.
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?
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.
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.
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.
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 :)
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.
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.
(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.
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