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Mary Hatcher |
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A consistency problem |
1. Nov 11, 2013 #1 |
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Suppose we have a point mass system that consists of ##m + n## particles. There are ##m## normal visible point masses and ##n## invisible "dark matter" point masses. The point masses interact gravitationally with a ##1/r## potential. |
Now when someone observes the motion of the visible masses, he will notice that they are not consistent with Newton's laws of motion (of course, because the invisible masses perturb the trajectories of the visible masses). |
The question is, can such an observer calculate how many dark matter point masses there must be in the observed system to make the system self-consistent, and what are their masses and trajectories? In what cases a unique solution exists to this problem? |
2. jcsd |
3. Nov 13, 2013 #2 |
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I probably didn't express this clearly enough... (English isn't my native language) I have seen that the observed rotational motion of galaxies is explained with a hypothesis that there is a "halo" of dark matter around all galaxies. How does one deduce the required density distribution of dark matter from the obse... |
4. Nov 13, 2013 #3 |
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Staff: Mentor |
This technique has been used to show the existence of astronomical bodies that aren't directly visible - for example, we infer the existence of a dark companion when we observe a bright star making otherwise unexplained motions. It's harder in a more complex many-body problem, of course, but in principle it's still... |
The solutions need not be unique in any practical sense, because two bodies of mass M close enough to one another and distant enough from the other objects will be observationally indistinguishable from one body of mass 2M and located at their center of mass. |
5. Nov 13, 2013 #4 |
That question is much easier to answer (The previous question is very interesting but not trivial at all). |
It is very easy. Find out the force required to keep a star in circular motion around the center of the galaxy using F = mv2/r. |
Compare that with the force produced by the gravitational force due to the visible mass. |
Assume the difference between the two numbers is due to a spherically symmetric distribution of dark matter. |
Compare that with the gravitational force produced by such a spherical mass distribution in order to figure its mass. |
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6 July 2006 |
Why the "loudness wars" are killing today's music |
collision detection: |
"Pull out a vinyl record from the 70s or early 80s, and listen to it. Odds are it'll have a big dynamic range -- it'll be whisper-quiet in some parts and booming loud in others. You'll pick up new nuances every time you listen to it. Now listen to any music track recorded in the last ten years, and it'll be radically d... |
Guardian Unlimited Film | Interviews | What a difference a day makes: Has an article with Kiefer Sutherland, which is not a bad read. I like this part |
24 things you didn't know about 24 |
1 Jack Bauer has killed 112 people over the five years of the show. Season 4, during which he dispatched 44 'hostiles', was his best ever; in the first season he managed a lacklustre 10. |
2 Kiefer Sutherland heard that American college students use 24 as a drinking game, downing a shot every time Jack Bauer says 'damn it'. So he changed the script in one episode to have Jack say 'damn it' 14 times in one hour. |
3 Another frat-house game is to monitor Jack's flouting of the Geneva Conventions. In season 2 he shot a key suspect under interrogation in the heart before beheading him. In season 3, he executed a colleague on the president's orders. |
4 Jack's entry codes for CTU (Counter Terrorism Unit) are 4393 and Q22Q17 |
5 For season 2, a prototype script was written in which each (non real-time) episode would span 24 hours, but execs decided to stick to the original format. |
6 During season 4 an incoming call number was shown on a character's mobile phone. More than 50,000 fans dialled the number - only to find it was real and belonged to one of the crew. |
7 More than 20 lead characters have died in seasons 1-5. |
8 Jack Bauer has actually died twice. In season 2 he was tortured, burned and tazered to death before miraculously coming round. In season 4 he was shot dead; then Tony Almeida injected him with epinephrine and he recovered. |
9 Executive Producer Evan Katz once said: 'We make a lot of it up as we go along.' |
10 24 was the first TV show to embrace real-time - the clock keeps ticking during ad breaks and there are no flashbacks. |
11 Of course, it's not quite as simple as that. Three minutes are in fact gradually added to the timer during the ad breaks. |
12 Almost all scenes are shot at head height. |
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