Just curious, what's your background in batteries? From my understanding, sodium based batteries are safer than lithium, but I would defer to anyone with real expertise in the subject.
Yes, 100% agree. We've spent so much time chasing down what makes our build slow. Obviously that is less important now, but hopefully they've laid the foundation for when our code base grows another 10x.
This is amazing. Everyone that picked TS for a big project was effectively betting that someone would do this at some point, so it's incredible to see it finally happen. Thanks to everyone involved!
Where does the uncertainty (1%) come from? For example, is it more from our ability to precisely determine the orbit based on limited observations, or is it because orbits for objects like this just aren't predictable years out, or something else?
It's a bit of both, observing has uncertainty in a lot of places, if you are on the ground you get atmospheric effects, imprecision of timing, imprecision of optics, etc etc. You are also observing an object where you dont know how far away it is. That distance has to be solved by basically doing a sort of triangulation, which requires either the observer or the object to move enough.
So if you observe over a short time (hours for example), you can see it is moving, but it is hard to tell distance.
Once you have an estimated orbit, if it has any interactions with planets (IE: flyby of Earth), small differences in positions during the close encounter make LARGE differences decades later. Add to this the effects of photons from the sun pushing on the smaller asteroids or dust, or out-gassing /dust from comets cause these objects to slightly drift from just the basic gravitational forces. Generally inner solar system asteroids (inside mars) are very chaotic over hundreds of years, though typically predictable less than a century.
Note that I am not an expert on impact calculations, I just know a bit about and and can do back of the envelope ones.
There are a number of ways to get to the ~1%, the orbit fits have uncertainties on them and those can be propagated forward in time. However there are all sorts of complexities with doing that, and often the easiest method is to sample the uncertainty region a few hundred thousand times (Monte-carlo), and propagate those and see what hits.
Very cool. How are samples drawn from the uncertainty region? MCMC or does it simplify down? I'm guessing that this would drive the final percentage values that you guys determine, since the orbital dynamics would be deterministic.
I can tell you how I do it, but again I am not an impact study person. It helps to understand a bit of the background of how we fit orbits in general:
1) someone with a telescope sees something moving (typically these days these are bigger surveys)
2) These observations are submitted to the Minor Plant Center (MPC), the clearinghouse of all asteroid/comet observations.
3) Several groups pull observations from the MPC to fit orbits, including JPL Horizons (MPC also fits orbits)
4) You now have a pile of observations which you have to figure out which observation links to other observations, which is a complex math problem on its own. Solve that.
5) JPL Horizons for example then fits the orbits to the observations, and since the observations may be 100 years of data of wildly varying quality, from hand written notes in the 1920s through to modern data, this is very difficult. They publish a covariance matrix with the associated fit (IE: basically a gaussian error fit for the parameters).
6) I grab that covariance matrix and sample from it using some pretty vanilla statistics to build orbits.
7) Propagate and see what happens.
Here is an example of an observation from 1950:
https://caltech-ipac.github.io/kete/tutorials/palomar.html
The image was developed on a glass plate, this one was never even sent in to the MPC, the guy taking the observation just wrote down "Asteroid" on the cover slip for the image. It was not formally discovered until the 1980s. We now know its orbit very well, so this particular observation is not that interesting other than as a curiosity.
Note the "condition code" on the right, which is a score of how good their orbit fit matches the data, 0 means we know the orbit with high precision. This one is an 8, meaning we have a fit, but its not that great. Most likely because we only have 31 days of observations.
Parent mentioned Monte Carlo simulations, which allow you to simulate across a range possible scenario parameters and see what % result in some outcome (like a collision with Earth or the moon).
I'm sure there's a reason, but it seems like an unusual use of Monte Carlo - it's all deterministic and there is no opposing player making choices. Must have something to do with uncertainties in projected orbits or imperfect simulations maybe?
>it's all deterministic and there is no opposing player making choices
It's not deterministic, it's chaotic. That is the nature of the N-body problem. We can only approximate trajectories in such a system using numerical methods, within a certain margin of error. In principle, the object is gravitationally interacting with everything else in the solar system. But for the most part, most interactions are negligible and could be ignored (eg, other small objects far away), except of the large bodies. But there are many unknowns (as stated before), where initial conditions will affect the outcome of the trajectory simulation, and errors will certainly amplify over time. I'm guessing Monte Carlo is used to "fuzz" the simulations with randomised initial conditions to account for the range of unknowns, and see what the outcome is under these different scenarios.
Chaotic doesn't mean non-deterministic, it just means that small changes in initial conditions result in a large change in the trajectory. The system itself can be both chaotic and deterministic.
It's also a reasonable question to ask, because the simulations are deterministic. It's just that because the system is also chaotic and there's noise in the measurement, that can result in a large spread of deterministic trajectory simulations.
It's only deterministic in the sense of the mathematical constructs that models the system, like differential equations that drive the simulations at each finite time step. But the information or the state which the simulation is applied on is always chaotic. That is because delta at each time step is an approximation with some error. It's impossible to make the state in the system behave deterministically, because that requires time deltas to approach to zero (or infinite amount of infinitely small differential steps).
Energy drift doesn't make the system non-deterministic, it just means that the time evolution has some error. The error is still deterministic. If you simulate a deterministic but chaotic system like n-body orbitals with a non-symplectic integrator, you'll always get the same result for the same initial conditions. The drift created by the finite timestep will also be the same.
It’s the error with the ground truth that you can’t predict. Otherwise you would just be able to cancel it out. You can only predict probability distributions..
If you're saying that it's the uncertainty in the initial measurement, then we're in agreement. If the initial measurement were perfect, the only source of error would be the finite timestep. N-body simulation itself is deterministic, and so the only source of randomness is our uncertainty about the object's true mass, size, shape, position, velocity, etc.
The N-body _reality_ _might_ be deterministic. The N-body simulation using digital computers will technically still introduce errors because of the time steps even if you had perfect knowledge of initial conditions.
The errors are deterministic. Determinism has nothing to do with the existence of errors, it's about uncertainty. They're different things. A system that is deterministic will produce the same results every time given the same initial conditions. If there are numerical errors, they will be identical for each run. A non-deterministic system will give you different results every time given the same initial conditions, with some variance. You can still have numerical errors in such a system.
Ironically, reality probably isn't deterministic. It definitely isn't at small scales (e.g. radioactive decay). If it's non-deterministic at a macro scale, the effect is small enough that we don't see it.
That’s the point, reality isn’t deterministic,so you can’t really use deterministic math to describe it. That’s just an approximation, regardless of errors in the simulation. That’s also why you run Montecarlo simulations, not to even out simulation errors, but to compute as many probable outcomes as possible and then have a probability distribution that represents your best bet at guessing the non deterministic reality that you are trying to predict. If you “run” reality twice your not gonna get the same result
We don't know the configutation it's in precisely. We don't know the initial conditions. Small unobservable differences will lead to large difference in outcome. That's the chaotic part.
I get that. I'm pointing out that these are separate factors. Chaotic does not imply non-deterministic, and vice versa. The only source of randomness here is the uncertainty in the observation of the object, because (as you point out) multiple combinations of parameters could produce the same observation, and each one will have a different trajectory. The randomness doesn't come from the chaotic nature of the system, it comes from noise in our measurements. It also doesn't (as other posts are claiming) come from energy drift in the simulation, because that's also deterministic.
The observations are not 100% certain. There are a variety of body states and configurations that might result in the same (few) pixels being lit up in the few measurements collected so far. As additional measurements are collected, some possibilities may be eliminated and the uncertainty of the trajectory can be reduced. This usually results in the impact probability converging toward 0%.
...or 100%. But yeah, the MC comes in this way. You have a current most probable value for the position and some distribution around it, depending on the precision of the measurement device etc. That can be a high-dimensional space. You draw some (many) random points from this space and propagate them all deterministically. Taking into account how likely a certain random point was in the first place, you can then estimate the hit probability.
MC is numerically approximating an integral. Here it replaces the high-dim integral over the start parameters.
I would assume that it is because we have imperfect knowledge of the state of the asteroid (i.e. mass and current position/velocity/...). This imperfect knowledge is characterised by a probability distribution. Similarly the state of all other objects in the solar system is only known up to some distribution. To propagate the information forward in time to impact requires a complicated function f(state of solar system; state of asteroid). If all of the data was known (and expressible numerically) with perfect accuracy, and f were computable with perfect accuracy then all would be good. But as noted, (state of solar system; state of asteroid) is a probability distribution, and there are very few distributions and very few types of maps f that are amenable to analytic transformation. For example if the state was a normal distribution with mean x and covariance P, and f were a linear transformation, then x,P mapped through f is also normally distributed with mean y and covariance P_y, you can get the mean of the transform as y=fx, and P_y = fPf' (where ' indicates transpose). Needless to say our knowledge of the state of the asteroid and the solar system is probably a rather complicated distribution, and the n-body problem is not a linear transformation. Monte-carlo simulation is often used to propagate probability distributions through non-linear transformations.
My guess is that small objects like this suffer greatly from the 3-body problem, and multiple trajectories are generated from various starting points inside our measured error bars for the current states of these objects. Small inaccuracies compound over the years.
The planets, sun and all planetoids orbit the barycenter of the solar system, which in our case happens to be inside the sun. They all affect each other, making more than 3 bodies problematic.
> My guess is that small objects like this suffer greatly from the 3-body problem
What bodies? My impression is that the only objects around Earth with enough gravity to significantly impact trajectories are the Earth and Moon. Will the other small objects have any significant gravitational impact on this body?
I also understand that in cislunar space, the Earth-Moon dynamic does create a three-body problem and trajectories are fundamentally unpredictable, with some exceptions. I wonder how that affects objects such as this one if they pass through the Moon's gravitational well.
Also, the gravity of asteroids or small planetary bodies like moons that it passes close to will have some small effects that can add up over a long time period.
Even if you're just doing a 2-body problem around the moon you'll get wildly wrong orbits over a timespan of just months if you treat the moon as a point mass (the way that's relatively safe to do with Earth, in comparison). Lunar mascons are so strong you can't even rely on a plumbob to point straight down if you want just tenth-of-a-degree accuracy. These perturbations are so severe there are only effectively only four (instead of 90) stable inclinations for low lunar orbits.
Literally every body in the solar system acts on every other body at all times. All asteroids in the asteroid belt are perturbed by Mars and Jupiter, right? Except if you recognize the need to include Mars in calculating their trajectories, you need immediately to at least also account for the 4 Gallilean moons, who sum to about the same mass as Mars, and now you have a 7-body problem. You won't get correct results on trajectories of Earth approaches if you discount the mass of our moon, nor if you discount the rest of the asteroid belt (4% of our moon's mass)... etc.
Gravity has unlimited range, the patched conics method you think of is a good approximation on short time spans, but breaks down surprisingly quickly. Keep in mind the Sun moves all the water in Earth’s oceans all the time…
There's going to be some degree of measurement error, which will likely be greater for objects which have not been observed many times. Multiple observations should allow both better estimation of the object attributes (average out the noise), and allow some judgement of the quality of predictions given what you think you know about it.
The only announcement I want from AWS about databases is that the price for RDS is going down. Not that they have new chip that is more expensive but offers better price/performance, but that my bill is actually going to drop.
I don't trust them enough to use non-portable technology like this until they give me confidence they are committed to lowering prices.
> The only announcement I want from AWS about databases is that the price for RDS is going down.
If the price hasn't been going up in line with inflation then it's been going down in real terms. Not as nice as the number going down, too, but it's not nothing. Over time AWS prices have significantly declined in real terms simply by not having been raised in nominal value.
Of all the services AWS has, RDS is one of the best values and lowest risks. The peace of mind and reliability it gives you on something as important as a DB is well worth the cost.
Made me think of Factorio (game in which you bootstrap automated factories on an alien planet) where all the robot arms run at reduced speed when power demand exceeds supply.
- lessons are presented based on what you already know (e.g. you can't choose to study a topic before you've demonstrated mastery of all topics it depends on)
- I pick the next lesson from a very small set (usually 5 options, sometimes fewer), so there's no wasting time choosing what to study next
- really great spaced repetition system that prevents forgetting
They don't grant degrees or diplomas. As such it is presumably accredited as a Supplementary Education Program and (like JHU CTY, Stanford ULO, and AoPS) do not grant credit. Such programs can be the basis of credits if your "real" high school accepts them, though.
Right, ymmv for transfers at either a hs or college. But the accredited status makes it possible to get approval. MA say they can make the documentation available manually and will automatically in the future.
