The chances of an asteroid hitting Earth...

They only have a few observations yet to predict the orbit - and these have uncertanties of measurement.

So you run the calculation lots of times, using all the most extreme possible values for the observations. For example, if you measure a speed as 60 +/- 2, you run the calcs for 58 and 62.

The uncertain orbit of the NEO (Near Earth object) puts it somewhere in a cone from its present position - sort of like a shotgun spread pattern. At some point in the future, you can predict a certain sized sphere (or elipsoid) of space that the object will be in - the further into the future, the bigger that sphere gets.

So you work out how big the sphere is at the time when it comes close to the Earth, and divide the cross sectional area of the place it might be in by the cross sectional area of the Earth, using suitable probabilty weightings (the object is more likely to be near the centre of the cone than the edges). The ratio of the areas, weighting adjusted, gives the chances of a hit.

As they take more measurements over the next few weeks, the uncertainty will grow less. Pretty soon, they will be able to say it is definitely going to miss (we hope).
 
Diamond said:
...are 909,000 to 1
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I like those odds...

Everything on 17 black...

*click click click click... click... click... click*

28 Red, house wins.

:(
 
ceptimus said:
They only have a few observations yet to predict the orbit - and these have uncertanties of measurement.

So you run the calculation lots of times, using all the most extreme possible values for the observations. For example, if you measure a speed as 60 +/- 2, you run the calcs for 58 and 62.

The uncertain orbit of the NEO (Near Earth object) puts it somewhere in a cone from its present position - sort of like a shotgun spread pattern. At some point in the future, you can predict a certain sized sphere (or elipsoid) of space that the object will be in - the further into the future, the bigger that sphere gets.

So you work out how big the sphere is at the time when it comes close to the Earth, and divide the cross sectional area of the place it might be in by the cross sectional area of the Earth, using suitable probabilty weightings (the object is more likely to be near the centre of the cone than the edges). The ratio of the areas, weighting adjusted, gives the chances of a hit.

As they take more measurements over the next few weeks, the uncertainty will grow less. Pretty soon, they will be able to say it is definitely going to miss (we hope).
Click to expand...

Thanks for that. I always wondered how such a calculation was done.
 
There is an update to that story, it now says that there is no chance that the asteriod will hit the Earth.

Sleep well.
 
Diamond said:
...are 909,000 to 1

http://story.news.yahoo.com/news?tmpl=story&u=/ap/20030902/ap_on_sc/britain_asteroid_watch_1

How do you calculate odd like that? It seems awfully exact.
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Collision probabilities are calculated first by estimating the uncertainty in the orbital elements calculated from a set of observations by one of several means. Each observation of an object has some estimated uncertainty, i.e., we send in the right ascension and declination of the asteroid at some time and in reality, it can occupy an area of about 0.5 arcseconds, typically, in radius in that direction on the sky (and it can, in principal be at any distance in that direction at least until we compute an orbit or beam it with radar). After 3 or more observations, using celestial mechanics allows one to compute a preliminary orbit fitting through those observations and later use differential correction techniques to fit the orbit through the entire set of observations (again, each observation has some estimated uncertainty, so one way to estimate the uncertainty in the orbital elements is to use a Monte Carlo scheme to fit a variety of slightly different orbits through the region surounding each observation bounded by that estimated uncertainty in the astrometric position measurement.

One can then project the uncertainty ellipsoid of the orbit into the future to the time of a close approach to some planet (like Earth!). You also project the uncertainty ellipse of Earth (or whatever planet) to the same time and the collision probability is then the intersection of the two uncertainty ellipsoids divided by the total area (really volume) of the uncertainty ellipsoids. The size of the uncertainty ellipsoid of an asteroid shrinks, of course as more observations are made and as the arc of observations is extended and of course grows as you extrapolate the orbit farther into time away from the arc of observations. The ellipsoids shape is generally very long and nearly circular in width. They can by 100s of thousands of kilometers long by maybe a few thousand kilometers wide.

I would say that there might be a few too many significant figures in the 1 in 909,000. I would probably have rounded it off to 1 in 900,000 or 1 in 910,000. Of course, in any case, new measurements of the asteroid have moved the uncertainty ellipsoid in 2014 away from Earth so that it is zero (or very nearly zero).

Jim.
 
All these observations are discripitions of events that have occured or the postulated average of near earth collisions. If theres one thing I have learned lately is that there are more things in heaven then can be drempt of in our ability to detect them ( apoligies to the Bard) I.E There are NECs that go undected until after the event or events we notice that take place hours before they come into the near earth field. So without knowing the entire mass and number of the asteroids ( and comets) that exist under the influence of the solar systems gravitational field we are guessing. The whole question of orbit and periodicity of the bodys make anything but a guess at a trend to be dissmisable.
 
TillEulenspiegel said:
All these observations are discripitions of events that have occured or the postulated average of near earth collisions. If theres one thing I have learned lately is that there are more things in heaven then can be drempt of in our ability to detect them ( apoligies to the Bard) I.E There are NECs that go undected until after the event or events we notice that take place hours before they come into the near earth field. So without knowing the entire mass and number of the asteroids ( and comets) that exist under the influence of the solar systems gravitational field we are guessing. The whole question of orbit and periodicity of the bodys make anything but a guess at a trend to be dissmisable.
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No, our knowledge of the asteroid impact rates are much better than mere guesswork. Once an object is discovered, we can estimate its orbit with decent precision once enough observations are made to project its path far into the future. Having discovered the various objects, we can estimate the total population size and get a very good estimate of the average time between impacts. We expect to have found nearly all of the near-Earth asteroids (NEAs) bigger than about 1 kilometer diameter within less than 10 years and the orbits for all those objects can be extrapolated many decades into the future looking for close approaches such as the one that just made the news. Once we have found the estimated 1500 or so kilometer or larger NEAs, there will no longer be any of them that we don't expect making close approaches. Smaller ones will be the ones we sometimes find after close approaches and I expect that eventually, we will have surveyed to completion objects closer to 100 meters across.

One of the goals of science is to remove the guesswork and actually measure things and that is what NEA research has successfully been doing with the population of NEAs during the last 20 years or so.

Jim.
 
Well I agree that the staticstical model is becoming more accurate as time goes by, but it's still a model. In the past 15 yrs or so we have had 4-5 flybys by NEAs that were planet killers and either did not detect them until they were right on top of us or had passed. (right on top of us in terms of space could mean anything from inside the moon orbit to a few million miles. The objects we know about approach the earth with much more frequency the most people are aware. Ten since 8-21-03 till 9-4-03. The gravitational waltz they perform also makes long term trajectory prediction problematic.

Complicating the picture still further is that possible new threats to the Earth are being created continually by the collisions of large asteroids with each other.

We do have programs ( NASA's Space Watch and others) that are cataloging NEAs and the original statistical population model number has been downwardly adjusted from 2000-900.

It's not a chicken little catastrophe, just some observations.
 
A 10 km asteroid hits the Earth, on average, once every 100 million years. (Easy to remember, I find, since its 65 million years since such an impact marked the KT boundary.)

Impact rates scale with impactor diameter with a factor somewhere betweem 10^2 and 10^3. (Crater counting on the Moon and elsewhere makes this rock solid.)

So the chance of a 1km asteroid hitting the Earth in any given year is somewhere between 1 in a million and 1 in 100,000.

So this story was a real non-story - the calculated probability of a 1 km asteroid hitting the Earth in 2014 didn't change significantly even when we thought it was in the 1 in 900,000s.
 
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