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... but couldn't tell until recently that Apophis won't hit Earth around 2030?

What's the catch in these calculations? Are the numbers just so incredibly big that the 28,000 km distance in which 2012 DA14 passed Earth on Friday last week are already amounting to a precision that you just cannot achieve over longer time frames?

When looking at the Wikipedia article Palermo Technical Impact Hazard Scale one oddity is that (29075) 1950 DA has the highest likelihood to hit Earth around 2880. So over a very long time frame they can tell there's a high probability but over a shorter time frame they can't? Or is it because all forecasters will have died by 2880 and therefore won't get taunted? ;)

TL;DR: how can they calculate one with seemingly utter precision over a very long time frame (2012 DA14 for the remainder of this century or (29075) 1950 DA in the year 2880) but cannot for another case (ruling out Apophis will hit Earth around 2030)? Note: they only established it for Apophis last year!

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closed as off topic by Christian, Sklivvz Feb 25 '13 at 1:15

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What claim to you question specifally? –  Christian Feb 18 '13 at 17:40
    
Assuming you mean "do". The claim that one can be calculated with utter precision, while the other cannot. It seems odd and doesn't add up. So I'm wondering how this can be. I'm not sure what's unclear in the question in that sense. But I can sure improve it if you see ways to improve it. –  0xC0000022L Feb 18 '13 at 17:55
    
So is your questions why can they calculate one with extreme precision and one without? –  Cruril Feb 18 '13 at 18:27
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I suspect that projecting an orbit forward over time requires precision measurements over an angular distance, the larger the better. So a "near miss" provides a lot of very good data for the orbit while a distant object will move less slowly (or there may be other reasons why observations are lacking) and have lower precision. –  Larry OBrien Feb 18 '13 at 18:55
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This is probably a better question for Physics –  Chad Feb 19 '13 at 16:54

2 Answers 2

up vote 7 down vote accepted

Nasa has an excellent page on 1997 XF11 which contains two diagrams which show this really well:

This diagram is from early calculations, so only a few data points:

enter image description here

Note the "uncertainty ellipse" - as there were only a few data points, and the measurement of these points is subject to some uncertainty, it is a very large ellipse, indicating there could be a risk of collision.

Now when they include pre-discovery observations:

enter image description here

The error margin is dramatically reduced, because all the extra data points help to accurately pinpoint the orbital path, so the uncertainty ellipse no longer comes close to the Earth.

The web page also offers the data points and analysis for download if you want to review it yourself.

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First off NASA thought it might hit in 2029, but it was a 1:233 chance that it would. They do know now that Apophis will not, or is extremely unlikely to impact Earth.

The first announcement of Apophis was on December 24, 2004. So it only took 3 days for them to conclude that the original calculations were off because of the incomplete/inaccurate information that they had at the time.

On December 27, 2004, in the afternoon, a precovery increased the span of observations to 287 days which eliminated the 2029 impact threat. The cumulative impact probability was estimated to be around 0.004%, a lower risk than asteroid 2004 VD17, which once again became the greatest risk object.

Doing the calculations without all of the correct information is what led to the inaccuracies.

Criticism of older published impact probabilities rests on the fact that important physical parameters such as mass and spin that affect its precise trajectory have not yet been accurately measured and hence there are no associated probability distributions....Small uncertainties in the masses and positions of the planets and Sun can cause up to a 23 Earth radii of prediction error for Apophis by 2036.

As to why astronomers/scientists can roughly calculate DA 1950 so far out there...

That 1950 DA has one of the best-determined asteroid orbital solutions is due to a combination of:

an orbit moderately inclined (12 degrees) to the ecliptic plane (reducing in-plane perturbations)
high-precision radar astrometry that is more accurate than visual-wavelength measurements
a 60-year observation arc
an uncertainty region controlled by resonance

It as been seen twice (1950 & 2001) and been able to record how it moved. We will see it again in 2032 and be able to more accurately calculate if it may hit or not. As of right now the uncertainty is caused by several things.

If 1950 DA continues on its present orbit, it will approach near to the Earth on March 16, 2880. However, over the intervening time, its rotation will cause its orbit to slightly change as a result of the Yarkovsky effect. Available radar and optical data suggest two possible pole directions; one trajectory misses the Earth by tens of millions of kilometers, while the other has an impact probability of roughly 1 in 300

If it continues uninterrupted there are two paths that they think it will take. One will miss earth by millions of kilometers and the other only has ~ a 1:300 chance of striking Earth.

For a much more detailed description you can check out this NASA PDF detailing the probabilities of the DA 1950 collision.

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Wow, thanks. Need to digest this first. Will probably accept, but perhaps there are others who can provide additional insight. –  0xC0000022L Feb 18 '13 at 19:33
    
Yea, its a bit. Basically though the calculations were right once they had all the information. The initial report on Apophis was released with incorrect info, which they knew within 3 days and release the correct information that is is extremely unlikely to impact us. –  Cruril Feb 18 '13 at 19:45
    
Where did you get that the original calculations were off? To me it seems that the conclusions were right, given the data available at the time. The original calcuations simply lead to more interest into gathering more data and thus better calculations. –  Christian Feb 18 '13 at 19:47
    
I was more meaning that the estimate was off because of the incomplete/inaccurate information that they had at the time. I had stated that partway through my answer, but I have edited my answer to better phrase what I was trying to say. –  Cruril Feb 18 '13 at 20:00
    
Yes - the correct terminology is that with more observations you can reduce the assumed error margins, and once those margins are low enough it can be shown that a hit will not happen. –  Rory Alsop Feb 18 '13 at 20:50

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