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[Math!] When will the next big meteorite crash on earth?
This might seem like an astronomy question, but read on and see the math.
Scientists believe that in 1908, a big meteorite crashed in Siberia, destroying thousands of square kilometre of woods.
They also believe that crashes like this happen every 100 years.
With the knowledge that it hasn't already come, when will the next one come, on average?
Please explain what you think.
Scientists believe that in 1908, a big meteorite crashed in Siberia, destroying thousands of square kilometre of woods.
They also believe that crashes like this happen every 100 years.
With the knowledge that it hasn't already come, when will the next one come, on average?
Please explain what you think.
Well, if they came like clockwork, we'd be due for a big one right about now (2012 perhaps... ^.^). But, they don't. You can calculate the probability of getting hit quite nicely, but the length of time that has passed since the last hit does NOT factor in to that calculation.
| ocalhoun wrote: |
| Well, if they came like clockwork, we'd be due for a big one right about now (2012 perhaps... ^.^). But, they don't. You can calculate the probability of getting hit quite nicely, but the length of time that has passed since the last hit does NOT factor in to that calculation. |
I know. So when, on average, they come once every 100 years, that would mean the next one is in 2108 right (again, average)? A physics teacher mentioned the 100 years on tv so it should be quite correct. Or would that be 2058? That's my first intuitive thought, but I can't find a rational explanation for it.
It's weird because some very smart people don't believe me when I say 2108 is the most likely date.
| ocalhoun wrote: |
| Well, if they came like clockwork, we'd be due for a big one right about now (2012 perhaps... ^.^). But, they don't. You can calculate the probability of getting hit quite nicely, but the length of time that has passed since the last hit does NOT factor in to that calculation. |
That depends on how you go about calculating it. If you use past impact data to predict future impacts, then the time since the last impact would be quite useful.
But Stubru Freak, you just don't have enough data there to say anything about it. All you have is the average... that's just not enough. You'd need to know the probability distribution of the impacts at least... and if you assume it's Gaussian you'd need to know the standard deviation, too. For example, something like 100 ± 20 years with 95% confidence... now that is useful information. The mean alone is just not enough.
^ So, if we get hit by one today, then it will affect the probability of getting hit by one next year?
The problem, as stated, is a classic example of a Poisson Distribution. The mean time between events is 100 years, and the expected waiting time till the next ocurrence is 100 years (since we are looking at starting from now). So we're looking at 2108 (almost 2109!)
Suppose we simplify the problem...
We have a bag with 30 marbles in it.
Only one is blue.
Once per minute, we draw one out, check if it is blue, and put it back in (and mix the bag up).
So, given that, we should draw a blue marble once every half hour, statistically, and it will average out to that.
However:
Suppose we draw a blue marble at 4:30.
The chances of drawing a blue marble at 4:31 and at 5:00 are still exactly equal at 1/30.
(In case anyone needs an explanation:
The blue marble is the large impact.
The one we drew at 4:30 is the most recent large impact.
The drawing at 4:31 is analogous to the chance of getting hit tomorrow.
The drawing at 5:00 is analogous to the chance of getting hit on a specific day in 2108.)
We have a bag with 30 marbles in it.
Only one is blue.
Once per minute, we draw one out, check if it is blue, and put it back in (and mix the bag up).
So, given that, we should draw a blue marble once every half hour, statistically, and it will average out to that.
However:
Suppose we draw a blue marble at 4:30.
The chances of drawing a blue marble at 4:31 and at 5:00 are still exactly equal at 1/30.
(In case anyone needs an explanation:
The blue marble is the large impact.
The one we drew at 4:30 is the most recent large impact.
The drawing at 4:31 is analogous to the chance of getting hit tomorrow.
The drawing at 5:00 is analogous to the chance of getting hit on a specific day in 2108.)
Jupiter had a string of collisions in 1994 with the impact of Comet Shoemaker-Levy 9. The comet broke up and the result was some massive impacts. As far a Earth goes, NASA does track comets that could possibly impact us, here is thenk to their asteroid risk site: http://neo.jpl.nasa.gov/risk/ Unfortunately it looks like we have a busy future ahead of us.
| ocalhoun wrote: |
| ^ So, if we get hit by one today, then it will affect the probability of getting hit by one next year? |
That would depend on the probability distribution you chose. If you chose Gaussian (which i used as an example in my earlier post, just because everyone knows it), then yes, it would. Obviously that makes no physical sense, which is why you wouldn't choose Gaussian under normal circumstances.
As infinisa mentioned, if this were a question on a homework assignment, or if you were just going to assume a distribution, the obvious ("classic") choice would be a Poisson distribution (in which case, getting hit today would not affect the probability of getting hit tomorrow). That's probably a good guess for modelling the real situation, too, but who can say how good a guess it is with the limited information we have? There's just not enough info.
^Well, come to think of it, getting hit today does affect it in one tiny way...
There's one less rock on an Earth-crossing orbit out there! ^.^
There's one less rock on an Earth-crossing orbit out there! ^.^
| Stubru Freak wrote: |
| This might seem like an astronomy question, but read on and see the math.
Scientists believe that in 1908, a big meteorite crashed in Siberia, destroying thousands of square kilometre of woods. They also believe that crashes like this happen every 100 years. With the knowledge that it hasn't already come, when will the next one come, on average? Please explain what you think. |
Is there a possibility of exceptions? I.e., the earth was due for a big meteorite say in 2108, but the meteorite never came? So we have to wait for another 100 years? How do we know?
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