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Asteroid ZTm0038 with a >3% impact probability

newton.spacedys.com

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Re: Asteroid ZTm0038 with a >3% impact probability

#221

Post by s1artibartfast »

gyrovagueGeist wrote: post #220
s1artibartfast wrote: post #219

Earlier quoted context omitted.

That makes perfect sense. Where it breaks down is if you put percentages on it. If you say the car is a 3% chance of hitting you, it doesn't and you repeat the process a thousand times, and it never hits you something is wrong with your math

The uncertainty is epistemic not aleatoric. The percentage represents our knowledge about the system at the time of measurement propagated through the forward model and is not an inherit random process in the system/model itself.

If your model is consistently wrong in a statistically predictable way, either your measurement or model is inaccurate.

A 3% chance that never occurs is an inaccurate prediction.

Re: Asteroid ZTm0038 with a >3% impact probability

#222

Post by msandford »

s1artibartfast wrote: post #221
gyrovagueGeist wrote: post #220

Earlier quoted context omitted.

The uncertainty is epistemic not aleatoric. The percentage represents our knowledge about the system at the time of measurement propagated through the forward model and is not an inherit random process in the system/model itself.

If your model is consistently wrong in a statistically predictable way, either your measurement or model is inaccurate. A 3% chance that never occurs is an inaccurate prediction.

Right! Yes absolutely!

It's wrong because the measurements are suggestive of possibility, rather than certain of it.

If we observe an asteroid that with two poor measurements is determined to be headed away from Earth, that's the end. Look no further.

If we observe an asteroid with two poor measurements that has some significant chance of hitting, more and better measurements are made. Then very often those better measurements show it was never actually going to hit anyhow.

But we never would have known without the better measurements, and we never would have devoted more time to making better measurements without a reason to do so.

A 3% chance that never occurs is because that 3% is based on data that's at the limit of what the telescopes can provide, not based upon bad math.

Re: Asteroid ZTm0038 with a >3% impact probability

#223

Post by gyrovagueGeist »

MauranKilom wrote: post #166
cfraenkel wrote: post #154

Earlier quoted context omitted.

It's not a model that is poorly calibrated - you seem to be taking a software-centric concept far away from where it's useful. The uncertainty at initial observation is because when you first observe an object, you only have observations covering a tiny bit of the orbit, resulting in very wide error bars. The "model" (Newtonian orbital dynamics) is one of the most precise models we have. Doesn't help when the observa…

Unless one in every 33 asteroids that have 3% impact probability at some point in time actually impacts earth, there is clearly some unwarranted assumption in the error bar/distribution calculation. "The measurement data has noise" does not explain why the noise has a bias towards "the asteroid will hit earth" whereas reality so far has been biased towards "the asteroid will not hit earth". (This assumes that signifi…

To simplfy, let's assume you have perfect knowledge of everything else & that the only variable that matters is asteroids current position. By triangulating observations you have a point estimate. Due to calibrating your instruments in the past you know that they tend to have uniform additive noise that is the same in each dimension. Let's say it shifts measurements by up to 1km randomly.

So the best guess you have is that the true asteroid is 99% likely to be somewhere within a 2km box centered at the observation point.

For each possible location in this box you use it as a hypothetical starting point and run a simulation forward creating a trajectory. In 3% of these trajectories the asteroid hits the earth.

The 3% is only a probability over the measurement uncertainty. It represents our knowledge about the system in a bayesian sense. The true asteroid was always ever going to hit the earth or not. There is no uncertainty inherent in the system.

That many asteroids have non negligible probability only means the physics is sensitive to initial conditions or that the measurements are loose. (Both are true)

Re: Asteroid ZTm0038 with a >3% impact probability

#224

Post by mongol »

chris_va wrote: post #179
throwaway5729 wrote: post #29

Earlier quoted context omitted.

I saw this tweet: https://twitter.com/ByronDrury/status/1691487518590402560?s=... linking to https://cneos.jpl.nasa.gov/scout/#/object/ZTm0038 It has some cool graphs that seem to show a lot of uncertainty in closest approach time [edited to fix second link]

Well, that NASA page has the closest approach going into next week and a ~10% of impact, so... hopefully the big disclaimer at the top is relevant.

Are you sure? I chose another asteroid by random in the selector and it looked even worse.

Re: Asteroid ZTm0038 with a >3% impact probability

#225

Post by canadaduane »

s1artibartfast wrote: post #219
msandford wrote: post #187

Earlier quoted context omitted.

Imagine you see a car 1 mile away as you're preparing to cross the street. 1 sec later, it's a bit closer. You wonder "will this car hit me?". It's hard to say since the car is so far away and your measurements of its speed are so poor. You wait 5 sec and it's still only imperceptibly closer. You realize there is no way it could possibly hit you. You cross the street unconcerned.

That makes perfect sense. Where it breaks down is if you put percentages on it. If you say the car is a 3% chance of hitting you, it doesn't and you repeat the process a thousand times, and it never hits you something is wrong with your math

I wonder if it's the difference between "this asteroid" and "all asteroids". As we learn more about it, we can start to treat it like a process that has repeated, but initially we can't be sure if it's like other asteroids.

Consider a 6-sided dice roll. What is the chance it will roll a 1?

A person might think, "1 in 6". But what if this is a loaded die? In that case, we need more information before we can classify it as "a die like other dice". We can observe two rolls, and try to ascertain whether or not it is like other fair 6-sided dice; however, two rolls is not enough to be sure.

So as we're gathering data, we start to classify this instance of a thing (a die, an asteroid) as part of a series of things we already know about. The more rolls we observe, the more sure we can be that this is a fair die or a loaded die, for instance.

If I'm understanding how asteroids' trajectories are calculated, we can simulate THIS asteroid's trajectory (3% chance of hitting you, based on a little data), or we can just decide to classify it (perhaps prematurely?) in the series "an asteroid like every other asteroid that we've observed" and arrive at a 0.000001% chance of hitting you (I'm making up a number here).

Re: Asteroid ZTm0038 with a >3% impact probability

#226

Post by MauranKilom »

noduerme wrote: post #173
MauranKilom wrote: post #166

Earlier quoted context omitted.

Unless one in every 33 asteroids that have 3% impact probability at some point in time actually impacts earth, there is clearly some unwarranted assumption in the error bar/distribution calculation. "The measurement data has noise" does not explain why the noise has a bias towards "the asteroid will hit earth" whereas reality so far has been biased towards "the asteroid will not hit earth". (This assumes that signifi…

One explanation would be the Anthropic Principle. In 3% of universes you were killed today, you're just not living in one of those.

This only works if there is nothing between "no impact" and "you die the same day as the impact". But we know that's not the case.

Re: Asteroid ZTm0038 with a >3% impact probability

#227

Post by MauranKilom »

jacquesm wrote: post #202
fouc wrote: post #198

Earlier quoted context omitted.

I wouldn't expect earth gravity to affect it sufficiently enough to cause it to crash unless it was moving very slowly, but I'm not sure asteroids ever move that slowly?

Like the moon is moving slowly? About 1 km/second for an object that weighs ~10^18 tons at a distance of 300,000 km? Now think of what that kind of force would do on a much lighter object that moves faster.

I'm not sure I understand your point... The object mass does not impact its trajectory (unless it either touches our atmosphere or is so massive as to measurably change earth's orbit). The gravitational force earth exerts on the moon and some asteroid is also very different, because the force is proportional to both object masses.

Re: Asteroid ZTm0038 with a >3% impact probability

#228

Post by MauranKilom »

msandford wrote: post #222
s1artibartfast wrote: post #221

Earlier quoted context omitted.

If your model is consistently wrong in a statistically predictable way, either your measurement or model is inaccurate. A 3% chance that never occurs is an inaccurate prediction.

Right! Yes absolutely! It's wrong because the measurements are suggestive of possibility, rather than certain of it. If we observe an asteroid that with two poor measurements is determined to be headed away from Earth, that's the end. Look no further. If we observe an asteroid with two poor measurements that has some significant chance of hitting, more and better measurements are made. Then very often those better me…

Then what does 3% mean? Surely it means "given the data we have, one in every 33 will hit". Since that empirically doesn't happen, it must be that "the data we have" has a very low prior probability of being real. In other words, the measurement noise seems distributed in a way that over-represents unlikely trajectories.

Hence it seems that it would lead to more accurate predictions if the measurements and their uncertainties were fitted to a model that corrects for the prior probability of observing an asteroid on a given trajectory/making a certain observation.

This discrepancy between distribution of measurement error vs distribution of actual trajectories is what people are wondering about, because it seems interesting to know more about (e.g. "why are certain trajectories less likely?").

Re: Asteroid ZTm0038 with a >3% impact probability

#229

Post by MauranKilom »

gyrovagueGeist wrote: post #223
MauranKilom wrote: post #166

Earlier quoted context omitted.

Unless one in every 33 asteroids that have 3% impact probability at some point in time actually impacts earth, there is clearly some unwarranted assumption in the error bar/distribution calculation. "The measurement data has noise" does not explain why the noise has a bias towards "the asteroid will hit earth" whereas reality so far has been biased towards "the asteroid will not hit earth". (This assumes that signifi…

To simplfy, let's assume you have perfect knowledge of everything else & that the only variable that matters is asteroids current position. By triangulating observations you have a point estimate. Due to calibrating your instruments in the past you know that they tend to have uniform additive noise that is the same in each dimension. Let's say it shifts measurements by up to 1km randomly. So the best guess you have i…

Given everything you said is true, under those assumptions 3% of those asteroids that we identify as being in said 2km box will hit earth, unless the forward simulation is wrong (implausible) or the measurement error distribution is substantially wrong (also seems unlikely).

What your analysis is not touching on is the prior probability that an asteroid will hit earth (you collapse this to "any asteroid will either hit or not", but that is not helpful for "model calibration" or whatever you want to call this) - or, equivalently, the prior probability of making (a series of) observations with a certain uncertainty/error distribution. If that prior were actually as uniform as each measurement error suggests, I don't see any Bayesian wiggle room left for why we don't have those 3% of impact actually happen.

(I'm no expert, but presumably you need multiple measurements to predict a trajectory, and while their measurement error distributions may be independent, it seems plausible to me that the prior probability of making two specific noise-affected observations, i.e. of the asteroid being on a certain trajectory, is most likely not so uniform. That's the part that I'd like to learn more about though.)

Re: Asteroid ZTm0038 with a >3% impact probability

#230

Post by bulatb »

s1artibartfast wrote: post #219
msandford wrote: post #187

Earlier quoted context omitted.

Imagine you see a car 1 mile away as you're preparing to cross the street. 1 sec later, it's a bit closer. You wonder "will this car hit me?". It's hard to say since the car is so far away and your measurements of its speed are so poor. You wait 5 sec and it's still only imperceptibly closer. You realize there is no way it could possibly hit you. You cross the street unconcerned.

That makes perfect sense. Where it breaks down is if you put percentages on it. If you say the car is a 3% chance of hitting you, it doesn't and you repeat the process a thousand times, and it never hits you something is wrong with your math

You're standing in a four-lane road and see a car approaching. You're looking at an angle and the lanes are poorly marked, so you can't tell which one it's in. Your observation lets you estimate the chance you need to move at 25%.

When it gets a little closer, you can tell at least which half it's on, the left or the right. Now your estimate is either 0% or 50%.

Closer still and you tell which lane it's in, so now you're sure.

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