It would seem that I haven't posted here in nearly four years. Life has been busy, and further, I find other social media outlets capture my attention more. But I shall try to post here now and then. So what has happened in physics in the last four years? Too much to write! But here are a few things:
• The Large Hadron Collider has pinned down many of the properties of the Higgs boson.
• Alas, there are few hints of anything unexpected, except for a "bump" in the data at six times the mass of the Higgs boson, which might be some new elementary particle. Stay tuned!
• Quantum mechanics has passed all tests thrown at it. There has been great progress in using it to improve communication security and computation--though that is still a ways off.
• There has been a lot of work in constructing materials from the small scale on up.
• Gravitational waves have been directly observed.
The last one was reported just a few months ago. Two giant black holes merged a billion light years away, and scientists were able for the first time to detect the resulting jiggling of spacetime, just as Einstein predicted. It was a stupendous achievement, and opens our ears to a whole new side of the Universe.
Showing posts with label astronomy. Show all posts
Showing posts with label astronomy. Show all posts
Saturday, May 7, 2016
Science over the last four years
Thursday, February 14, 2008
Saturday, January 12, 2008
More on Why Asteroid Will Miss Mars
As you can see, the dots are bunched around the most probable value and taper off in either direction—in the same way that the the area under a bell curve decreases away from the center. s, the distance from the blue line to Mars divided by the size of the error, is 3.7, giving a probability of 10,000:1.
Here is what the asteroid figure looked like two weeks ago:
Notice that the scale here is 500,000 km, so this is zoomed out by a factor of 5 from the 9 January picture. Two things have happened in the fortnight. First, the position of the blue line has changed a little. More importantly, the size of the error was a lot bigger two weeks ago. Back then the error was large enough so that the distance from the blue line to Mars divided by the error was only 2.2, giving a probability of 25:1.So the probability changed from 25:1 to 10,000:1 over the last two weeks mainly because the error in the path decreased, making s increase (again, s is the distance from the blue line to Mars divided by the error, and it is also the position on the bell curve of the previous post).
Friday, January 11, 2008
Why Asteroid Will Miss Mars
Last month, it was reported that a very small asteroid had a 1-in-75 chance of hitting Mars, which was very exciting. It would be awesome to see the effects of such a collision. Then the number was 1-in-25, which was even more exciting. Now the number has dropped to 1-in-10,000, so it is very unlikely to happen. How could the numbers change that much?
[see also next post, More on Why Asteroid Will Miss Mars]
Suppose it was your job to calculate the probability the asteroid would hit. You would take the most accurate measurements of the asteroid, extrapolate its position, and come up with your best estimate of the path for the asteroid. Now there would be some uncertainty in your estimate for the path. Let's call s the distance of closest approach to Mars of your best guess for the path. The plot of probabilities is given by this bell curve (also called a Gaussian curve):
If you calculated that s=0, that the most likely path just grazes the surface of Mars, then all paths to the right of s=0 would hit Mars, and you'd say that the probability of hitting was 1/2 (half the area under the curve is to the right of s=0). If you calculated that s=2.2 (which they did in December), then only paths more than 2.2 standard deviations from the most likely path would hit Mars, a chance of 75 to 1 (less than 2.1%). And if your calculation shifted just a little, so that s=3.7 (the value now), then only the paths more than 3.7 standard deviations from the most likely path would hit Mars, a chance of 10,000 to 1. It takes only a little shift out on a bell curve to make the probability plummet.
And so a small refinement in measurements of the asteroid positions made the impact probability... crash.
[Notice that I did not put any units on s, because s is really distance/error-in-path-estimation, so that s=1 corresponds to whatever 1 standard deviation is in this case. We don't need the actual distances in km because we are taking a ratio.]
[image from here, arrows and text added by me (feel free to use)]
[confidence: likely, my qualifications: informed]
Saturday, December 22, 2007
Happy Solstice!
The solstice occurs now, on 22 December 2007 at 1:08 AM EST (06:08 UT). It is the moment that the Sun is farthest from the celestial equator. It is when the Earth's axis is aligned with the line between the Earth and Sun such that the Northern Hemisphere is tilted away, and the Southern Hemisphere towards the Sun.
This makes today the shortest day of the year and the start of winter here in the Northern Hemisphere, and the longest day of the year and the start of summer in the Southern Hemisphere.
Above is the oldest solar observatory in the Americas, in Chankillo, Peru. It has been there since the 4th century BC, but it was just discovered this year. The point where the Sun rises moves up and down the 300m length of the hill, from solstice to solstice.
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