chongo's Journal: 2003-CR20 asteroid update for 2003-Feb-02 23:30 UTC

We have a new entry near the top of the current impact risks . It is an asteroid called 2003-CR20.

This asteroid appears be about 520 m in diameter. Its impact velocity, IF it were to hit the Earth is in the high end of the range: 24.95 km/sec.

IF 2003-CR20 were to hit the Earth on land, its impact would result in sub-continent scale devastation. IF 2003-CR20 were to hit the Earth in the ocean, it would create a tsunami the size and speed of which have not been seen in recorded history. Such a tsunami would would inflict total devastation along adjoining coastlines and in some cases spread destruction far inland.

The 2003-CR20 asteroid has a Torino impact hazard scale value of 0. It also has a cumulative Palermo Scale value of -1.86, mostly because of its many (234) potential close approach scenarios over the next 100 years.

The chance of impacting the Earth in the next 100 years is low: about 1 in 233,000. Even so, at those odds there is a 99.99957% chance that it will NOT hit the Earth in the next 100 years.

The 1st close approach is not until 20 Sep 2006. The model shows over the next 100 years the closest approach could be a close as 875 km. The most of the approaches in the next 100 years range from 10000 km to 700000 km above the Earth's surface.

Normally close approaches occur around one day of the year. That is, the asteroid's orbit crosses near Earth's orbit at only one point as the asteroid comes up thru (ascending node) or drops down thru (descending node) the plane of Earth's orbit. An interesting aspect of this model is that both nodes of 2003-CR20 pass close to Earth's orbit. 2003-CR20's orbit passes close to Earth's orbit near the 20-Sep position AND near the 15-Mar position.

It is very likely that over the next few days or weeks, additional observations will allow the model for 2003-CR20 to be refined. It should be noted that 2003-CR20's listing is preliminary with only 11 observations spanning only about 3 days ... not much on which to form a super accurate model.

P.S. There is no change is status for 1997-XR2. That asteroid remains as the only other non-zero Torino impact hazard scale object. The only reason why 2003-CD30 is listed higher than 1997-XR2 is because its cumulative Palermo scale is higher.

How are the odds calculated

[andrel]

I ain't afraid of no asteroid -- I've got plenty of duct tape and plastic sheeting.

How do you calculate the odds an asteroid will impact with Earth? Are you saying something like "X fraction of the orbits consistent with our current observations extrapolate to a collision"? Or do you look at more than just measurement error by trying to quantify future orbital peturbations?

Re:How are the odds calculated

[chongo]

I ain't afraid of no asteroid -- I've got plenty of duct tape and plastic sheeting.

One could always go to the hardware store, buy a few km^3 of the stuff and fling it at the asteroid. :-) Just be sure that your giant duct taped plastic ball doesn't swing back around and smack into the Earth during some future orbit. :-(

How do you calculate the odds an asteroid will impact with Earth? Are you saying something like "X fraction of the orbits consistent with our current observations extrapolate to a collision"? Or do you look at more than just measurement error by trying to quantify future orbital peturbations?

The 0-order estimate, given a path, yields a center-line and 1 sigma error estimate. So a path in a model might say:

Center line miss of 29147km +/- 154080 km

The +/- part refers to the 1 sigma distance:

1. You have a ~68.269% chance that the object will be within 1 sigma of the center line.
2. You have a ~95.4500% chance that the object will be within 2 sigma of the center line.
3. You have a ~99.7300% chance that the object will be within 3 sigma of the center line.
4. You have a ~99.99366% chance that the object will be within 4 sigma of the center line.
5. You have a ~99.9999994% chance that the object will be within 5 sigma of the center line.

In this 0-order estimate, one would use an ~68% impact chance. But the 0-order estimate is a very crude estimate.

The 1-order estimate takes the size of the Earth into account. We assume a sphere with a 6420km radius. There is a little extra thickness to account of the atmosphere.

In the previous example, the Earth was within the 1 sigma (~68.269% chance) window of 7.459e10 km^2 (area of a 154080 km circle). But the Earth has a target area of only 1.295e8 km (area of 6420 km circle). So the Earth is only 1/576-th of the 1 sigma circle, so the impact chance is now ~68.269% / 576 == 0.11852%. One can improve on the 1-order estimate.

The 2-order estimate integrates the impact probability over each point on the disk that represents Earth's target cross section.

Using a Confidence Internal [wolfram.com], one can determine the Standard Deviation [wolfram.com] (or sigma) for a given distance. So a target spot on the Earth may represent a 2-sigma distance (~95.45%) to the center line.

You discover that you have a arc of points on Earth's target that are all 2-sigma distant from the center line. Due to Earth's size, that 2-sigma arc may only be 1/10000th of the entire 2-sigma circle about the center line path. So those points on Earth's target represent ~0.009545% chance (95.45%/10000). By integrating over the entire Earth target, one might come up with an overall 0.01% chance of impact. Frequently the 2-order estimate is sufficient.

3-order estimates are sometimes needed. We take into account that the 1-sigma distance may vary depending on which direction you are going from the center line. That is, the 1-sigma distance is not a perfect circle, but rather a distorted one. One determines the sigma value for each point on Earth's target and integrating over the whole disk to get a better estimate.

Higher than 3-order estimates also exist, but are only used in extreme cases.

On top of all that, the model may require you to split into multiple paths. As a result of the 19-Sep-2018 approach of 2003-CR20, and as a result of the conditions for the Sep-2019 approach, we split our model into 5 paths.

Each path has its own close approach distance and time. Each path comes with a %-age chance that it will be taken. That is, we clump the range of potential paths into 5 tracks with, say a 0.1%, 1%, 4.9%, 14%, and 80% chance that it is taken. We compute the 2-order or 3-order estimate for each path and mulitply that by the %-age chance that the given path will be used.

Hopefully this will give you some insights into how odds are calculated.

Re:How are the odds calculated

[andrel]

Thanks, that helps!

Although I'm still not sure how the original error-bar ("Center line miss of 29147km +/- 154080 km") is calculated.

What I'm actually trying to understand are the (unpublished) error bars around the odds estimate. They're obviously huge, that's why the odds change so much with each additional week of observation. Here are the things I can think of that contribute to that error:

1. Uncertainty about the position/momentum of the asteroid. Additional observations help a lot here.
2. Uncertainty about the position/momentum of the rest of the solar system.
3. Roundoff and other numerical errors in the N-body solver used to predict future position/momentum of Earth and asteroid.
4. Modeling error in the N-body solver. For example, it might ignore relativistic effects. And it is a good bet it incorrectly models the Yarkovsky effect, if it even tries.

The first three points should be straightforward to deal with in the error analysis. But the fourth one is a lot harder, since modeling error is usually thought of as bias, not a source of variance. However the magnitude of the modeling error increases with time so one might try to fold it into the error bars.

I'm trying to get a feel for how accurate the odds are and what can be done to make them more accurate.