Once in a book ( I think title was Mathematical Physics, no idea who the author was) saw the proof of instability of planetary orbits in 4 dimensions, cant remember the details of derivations only the final conclusion of the result. Been trying to do something similar myself, but still with no success, how ever pondered if there is any reading material that shows for dimensions higher than 3 the orbits become unstable. I remember there were problems that were easier to solve for general cases than the low specific ones. So maybe there is a simple trick that would take care of that problem. My question is are there any higher dimensions were the orbits remain stable? Is this a mathematical curiosity or was there any body knowledge in physics that considered such cases but ultimately came to conclusion that there is nothing worth pursuing in these lines of thinking?
I have heard from  that stable orbits (ones that require a large amount of force to push it significantly out of it's elliptical path) can only exist in a three spatial dimensions because gravity would operate differently in a two or four dimensional space. Why is this?
Zip all files in directory? Is there a way to zip all files in a given directory with the zip command? I've heard of using *.*, but I want it to work for extensionless files, too. "Images with street signs" CAPTCHA impossible to solve What canon evidence is there that Stormtroopers are/are not still clones? Reading this article about , my nerd-rage started flaring as they claimed that Stormtroopers were still Fett-Clones 20 years after the rise of the Empire.  As I started thinking about it, I realized that everything I had read saying that Modern-Day Stormtroopers not being clones was from the EU - C Level books or games.   One of the quotes often cited for backing the idea that the Stormtroopers are clones comes from Princess Leia:     Aren't you a little short for a Stormtrooper?   But through the movie, paying close attention, Stormtroopers are often shown to be slightly different heights. One even hits his head in the doorway while others walk through uninjured.                                  Is there any G Canon fully canon (non-Legends/Infinities) evidence to support the idea that Stormtroopers are, or are not still clones at the time of Episode IV? Where does the term $|\psi\rangle\langle\psi|$ come from while calculating the expectation value? How to add custom objects to the "add object" menu? What is the difference between "I have a doubt with ...." & "I suspect there is a problem"? Prove that If $m'$ is a common multiple of $s$ and $t$, then $m | m'$. Here $m$ is the LCM of $s$ and $t$.    Although the statement is intuitively clear to me I don't know how to prove. How to find the smallest $n$ such that $n^a\equiv 1 \pmod p$ Given a prime $p$ and number $a$, how do I find the smallest $n$ such that $n^a\equiv 1 \pmod p$? Is there a non trial-and-error method?  Edit: obviously removing $n=1$! how to *completely* turn off automatic updates in Windows 10 I have disabled the services &quot;Windows Update&quot; and &quot;Windows Update Medic Service&quot; in using services.mcs. Furthermore, I made changes to the registry, creating a key HKEY_LOCAL_MACHINE\SOFTWARE\Policies\Microsoft\Windows\WindowsUpdate\AU with a DWORD (32-bit) Value &quot;AUOptions&quot; with value set to 2. I still see frequent queries to ctldl.windowsupdate.com sent to my DNS server. Which services need to be disables to completely shut this down? Can I give a creature trample after blockers have been assigned? I declare my attack with a 3/3 creature &amp; then my opponent assigns a 1/1 creature to block.  Am I allowed to use the ability of an  (1 Green Mana - Target creature gains trample until end of turn) on my original 3/3 creature to make sure that, in addition to his creature dying, he receives 2 damage to himself as well?  Or would that give my opponent the chance to go back and assign a secondary blocker? Normal subgroup of prime index Android Respond To URL in Intent I want my intent to be launched when the user goes to a certain url: for example, the android market does this with  urls. so does youtube. I want mine to do that too. how to hard-bypass the input of a line driver with a switch? Ocean modifier and foam data export? It is there any way to export the foam data generated from ocean modifier to use it in other render engine, like LuxRender? The manual says that the foam data is stored as vertex color data, but there isn't a way to access the vertexColor data. I know that can be accessed from Cycles from attribute's node. LuxRender supports vertex color and I tried to bake the texture to vertexColor and an image but only get a plain black texture. Prove that if $ f\mathrm{(}z\mathrm{)} $ is analytic at the infinity  ,then :  $ {\lim}_{{z}\mathrm{\rightarrow}\mathrm{\infty}}{f}\prime{\mathrm{(}}{z}{\mathrm{)}}\mathrm{{=}}{0} $ Indenting a whole paragraph How do I indent a whole paragraph at the same distance from my left margin, with the simplest command or environment? Duplicate id in list My service is working fine for single record insert when i send bulk records at that time it showing soapenv:ClientSystem.ListException: Duplicate id in list: 01ti0000002gUP1AAM Class.Sample.behaviourOfWebService: line 235, column 1  the error line is Database.upsert(pList)     p.productCode = pCode;    p.name =pName;    pList.add(p);  } $X=(-\infty,0]\cup\left\{{1\over n}:n\in\mathbb N\right\}$ with subspace topology Then $X=(-\infty,0]\cup\left\{{1\over n}:n\in\mathbb N\right\}$ with subspace topology. Then   $0$ is an isolated point $(-2,0]$ is an open set $0$ is a limit point of the subset $\left\{{1\over n}:n\in\mathbb N\right\}$ $(-2,0)$ is open set.   $0$ is not an isolated point of $X$ as every nbd of $0$ contains a point of the form $1\over n$ so  $3$ is true and $1$ is false, $2$ is false as $0$ is not interior point, $4$ is true as every point is interior point. Am i right? Showing that $\frac{z^n}{1+z^{2n}}$ is real for $|z|=1$. How does the Commander interact with Banishing Light or Oblivion Ring? What happens if a commander is sent to the command zone via  and then enchantment is destroyed? Can the commander return to the battlefield from the command zone?.  I think that  would not allow that to happen.