The Probability of Apocalypse
Posted by Science Oxford on October 4, 2010 | comments
Article By Jeannie Moulton
How Do Scientists Compute Probabilities for Near-Earth Object Collisions with Earth?
OK, there will probably not be an Apocalypse, but scientists did discover an asteroid that has a 1 in 1000 chance of hitting Earth in 2182. It’s really far away and a pretty low probability, so why should anyone
care? Well, it’s not quite like 1 in 1000 chance that someone will lose 100 bucks in a stupid bet or a 1 in 1000 chance that it rains on someone’s wedding day. This is a 1 in 1000 chance that millions, billions (or trillions by that point?) of humans beings and countless other species may be vaporized. That’s why. 172 years is not exactly a long time on the scale of the universe either.
How do scientists come up with this probability? They could just be making it up and no one would know the difference…but they’re not. They use a technique called Monte Carlo simulation. They make a mathematical model of the situation at hand – in this case, an asteroid and the Earth in orbit around the Sun. The orbit of the Earth is very well-known, but the orbit of the asteroid is not known as well and may even change a bit. Many simulations – or trials – are run, each with slightly different conditions. The different conditions may be, for example, slight variations on current position, size, speed and rotation of the asteroid based on what is already known about it from measurements. The number of simulations run must make it so that the determined probability of the event in question – in this case, the asteroid hitting Earth – is statistically significant.
Statistical Significance and Rare Events
As an example of what statistically significant means, imagine flipping a coin. Each flip is a simulation. If the coin is flipped twice, it may land head-head by chance. One could say from the two simulations that a coin has a 100% probability of landing heads up, but this is incorrect. It happened by chance that there were two heads. If the two-flip experiment were run again, the experiment would probably not yield the same results.
Many simulations have to be run so that nothing is left to chance. If the coin were flipped 100 times, there would probably be close to 50 heads…if it were flipped 1000 times, it would probably be even closer to
500 heads, meaning that the probability of getting heads is approaching 50%. An experiment of 100 coin flips gives a statistically significant estimate, where two flips does not. The two-flip experiment would change a lot between different experiments, but the 100-flip experiment would not change that much between experiments. This is the crux of statistical significance.
The number of simulations required depends inversely on how likely the event is. If the event is rare, like an asteroid hitting Earth, 1000 simulations may be run, all of them without the event occurring. This doesn’t mean that the event will never occur. It is just likely that it doesn’t occur in the first 1000 simulations, so many, many more simulations need to occur.
As more and more simulations are run, it is less and less likely that something happened by chance and a more accurate probability can be determined. Possibly millions of simulations are needed to determine the probability of such a rare event with any statistical significance. The lack of respect for statistical significance leads to a lot of bad science.
Why this asteroid is significant (in the non-statistical context)
This isn’t the first asteroid discovered that may collide with Earth someday, but this asteroid is special. It was determined that if this asteroid needed to be deflected to avoid hitting Earth, it would have to be deflected before 2080 because of the uncertainty in its path due to the Yarkovsky effect. The Yarkovsky effect changes the trajectory of the asteroid because it is radiating absorbed heat from the sun while rotating, which causes a force on the asteroid.
Discovering this asteroid suggests that the window for searching for Earth-bound asteroids should be extended beyond the current window of 100 years, because if this asteroid were not discovered until 2080, we would not be able to change its course with technology we have available today.
What do you think?