It is well-known that measurements of the velocity profile in galaxies are not compatible with Newtonian laws. A way to circumvent the problem is to assume that galaxies are surrounded by a spherical halo of Dark Matter. The density of mass of this Dark Matter can then be computed from the velocity profile with Newton's laws.   My question is the following: the formation of a galaxy involves essentially only the gravitational interaction. According to Newton (and General Relativity too), the trajectory of a particle does not depend on its mass. As a consequence, I do not understand how usual matter and Dark Matter could have followed different trajectories leading to such different mass distributions nowadays. Can somebody explain this (apparent) paradox ?
I'm a complete layperson. As I understand, dark matter theoretically only interacts with the gravitational force, and doesn't interact with the other three fundamental forces: weak nuclear force, strong nuclear force, and electromagnetism.  Those are my understandings going in. If I'm wrong, please correct me. I've done some googling, and I haven't found anything confirming or denying that dark matter is affected by either of the fundamental nuclear forces.  So since dark matter only interacts with gravity, what causes any dark matter particle to be repelled from another? If they can pass freely through each other, and they are gravitationaly attracted to each other, why don't such particles clump together in a single 'point' in space?   It seems to me that particles occupying a single 'space' are philosophically not distinct particles, but I don't know how actual physics would play into this.  Edit , author's credentials unknown, but implicitly claims to be a physicist or astronomer, says "...[P]hysicists generally take all dark matter to be composed of a single type of particle that essentially interacts only through gravity."  Edit 2 The author is this , "Professor of Science on the physics faculty of Harvard University."
Some items in Terraria drop only very rarely from certain enemies. It's a pain having to farm so many enemies to try to get these rare items. Is there any way to make them drop more often? Where should I put  tags in HTML markup? When embedding JavaScript in an HTML document, where is the proper place to put the &lt;script&gt; tags and included JavaScript? I seem to recall that you are not supposed to place these in the &lt;head&gt; section, but placing at the beginning of the &lt;body&gt; section is bad, too, since the JavaScript will have to be parsed before the page is rendered completely (or something like that). This seems to leave the end of the &lt;body&gt; section as a logical place for &lt;script&gt; tags.  So, where is the right place to put the &lt;script&gt; tags?  (This question references , in which it was suggested that JavaScript function calls should be moved from &lt;a&gt; tags to &lt;script&gt; tags. I'm specifically using jQuery, but more general answers are also appropriate.) I can't play online. I can only play solo. I have bought Minecraft so it should work fine, but, when I try to connect to a server, it says:  Internal client error: java.net.UnknownHostException: session.minecraft.net   I have tried over 20 different servers and it says the same thing for every single one.   Note: These are not Hamachi servers. I'm attempting a direct connection. Sequences in $C(X)$ converging uniformly implies uniform boundedness and equicontinuity Let $X$ be a metric space and let $\{ f_n \}_{n \geq 1}$ be a sequence in $C(X)$. Show that if $\{ f_n \}_{n \geq 1}$ converges uniformly on $X$ then $\{ f_n \}_{n \geq 1}$ is both uniformly bounded and equicontinuous.  Could I get a hint? Let $\int_{- \infty}^{\infty} f(x) dx =1$. Then show that $ \int_{- \infty}^{\infty} \frac{1}{1+ f(x)} dx = \infty.$ Why is $H(k\mathbin\Vert x)$ not a secure MAC construction? Why does evolution not make life longer for humans or any other species?  Wouldn't evolution favour a long life? Can graduated Stack Exchange sites get closed too? The Python docs say:     re.MULTILINE: When specified, the pattern character '^' matches at the beginning of the string and at the beginning of each line (immediately following each newline)... By default, '^' matches only at the beginning of the string...   So what's going on when I get the following unexpected result?  &gt;&gt;&gt; import re &gt;&gt;&gt; s = """// The quick brown fox. ... // Jumped over the lazy dog.""" &gt;&gt;&gt; re.sub('^//', '', s, re.MULTILINE) ' The quick brown fox.\n// Jumped over the lazy dog.' Problem: If   $$C_0+\frac{C_1}{2}+\cdots + \frac{C_{n-1}}{n}+\frac{C_n}{n+1} =0,$$  where $C_0,...,C_n$ are real constants, prove that the equation  $$C_0+C_1x+\cdots +C_{n-1}x^{n-1}+C_nx^n=0$$  has at least one real root between $0$ and $1$.  Source: W. Rudin, Principles of Mathematical Analysis, Chapter 5, exercise 4. Word meaning the reverse of 'Xenophobia' Xenophobia refers to the irrational fear or hatred of foreigners. But recently I've seen people displaying (in newspaper articles and other places) an irrational fear or hatred of their own countrymen. Is there a word for that? There are many red and black spots in my photos,what are those? Is WUBI freely available? I checked the link to download WUBI and the only way to proceed is by giving some amount as donation. I will surely do it, but I don't have a Paypal account and I am in urgent need to install Ubuntu. Can someone help me? Returning from a finally block in Java I was surprised recently to find that it's possible to have a return statement in a finally block in Java.  It seems like lots of people think it's a bad thing to do as described in ''. Scratching a little deeper, I also found '' which shows some pretty horrible examples of other types of flow control in finally blocks.  So, my question is, can anyone give me an example where a return statement (or other flow control) in a finally block produces better / more readable code? I'm trying to use biblatex and when I compile my document I get an error like the following:  Windows  data source C:\Users\&lt;username&gt;\AppData\Local\Temp\par-5061756c\ cache-890efc00b3ca6b775c7d44a325c1349fb2a3a3bd\inc\lib/Biber/LaTeX/recode_data.xml not found in .   Mac  data source /var/folders/v2/rld0ls7d2935gkvqv5hfr1x00000gn/T/par-616c616e/ cache-cdd483146f82a9655ce063f848d5139480fbf872/inc/lib/Biber/LaTeX/recode_data.xml not found in .   Linux  data source /tmp/par-6963617269756d/cache-f37ab610b7d79b2720a8ee3732849c6821705520 /inc/lib/Biber/LaTeX/recode_data.xml not found in . Factorial of $i$ With $i^2=-1$, what is $i!$ ?  I'm not sure if it is $i$ or if it is an infinite product $i(i-1)(i-2)(i-3)(i-4)(i-5)\dots$  It would make sense either way.  Is it not defined? Let $\vec{k}$, $\vec{v}$, and $\vec{u}$ be vectors, where $\vec{u}$ is unknown and $\vec{k}$ and $\vec{v}$ are known vectors. Given:     $\vec{u}\cdot\vec{k}=c$  $\vec{u} \times \vec{k}= \vec{v}$   From this relations, how can i determine the vector $u$? I tried to construct orthogonal coordinate system from $(\vec{k}, \vec{v},\vec{k}\times \vec{v})$ but i couldn't proceed from there. Any idea? Can't run my hello world in C How does "proof of effort" make a question better? It seems like many questions by new users are downvoted immediately.  Sometimes there is a comment to the tune of "lacks research", "we're not here to do your homework", or "show us some effort".  Now I wonder, what does it matter how much work someone has done before posting?  If someone can ask a good question in 5 seconds, more power to them.  To illustrate this point, look at how you could "improve" a question to include proof of effort.  You could put in 5 failed code snippets and their in- and output.  This would make for very long questions with a high noise ratio.  Another suggestion is to add "research".  By "research", I suppose most programmers mean "Google".  So this is basically a suggestion to add a list of fruitless Google queries.  That doesn't sound interesting either.  How can "proof of effort" turn a bad question into a good one? I just updated my iMac to Mojave, and am still trying to setup my preferences.  I tried dark mode, but did not like it (half of me apps seem to ignore it anyway).  I switched to light mode, but this too has problems. The File Save dialog shows a list of Directories and existing files, but the latter are very light grey, almost indistinguishable from the background.    I have searched the Preferences menu, but can't seem to find any setting to set normal contrast levels like in High Sierra.