I just learned about sector velocity and how you can manipulate the equation to show that angular momentum $L$ is conserved by $L/2M$. I know that sector velocity is constant and therefore angular momentum is constant. I have made it that far but I still can't see why a constant angular momentum would explain the coplanar concept.
If I take r as the radial vector of the moving object and v as the velocity vector of the moving object in central force field.   Then r should be perpendicular to r×v . So that depicts that r.(r×v) = 0 . So how does this say that the particle is lying on a constant plane ?
Which kind of functions $f(x, \ y)$ can be written as $g(x)\cdot h(y)$? Someone edited my message on StackOverflow, but it really bugs me out.  I'm not sure what's wrong with it:   As you see, the bigger the circle becomes, the more vertices I need for hiding the straight lines. As you see, the bigger the circle becomes, the more vertices I need to hide the straight lines.   The latter (corrected) sentence just bugs me out for some reason. It would sound better if there was a comma after the word "need", perhaps, but I guess that would be even worse in means of grammatical correctness.  Can someone explain why is the first sentence bad and the second sentence correct? And could there even be better solution to fix the first sentence? Texture packing algorithm What is a good texture packing algorithm?  Technically,  is , so a heuristic is what I'm really after. I was just reading Harry Potter and the Deathly Hallows, and I was wondering, when Hermione Granger changed into Bellatrix Lestrange, she should've obtained the Dark Mark, temporarily.  Now, my question is: would the Dark Mark work if pressed? proof that $f'$ is continuous at $a$ Let $f:I \rightarrow \mathbb{R}$ derivable in set I. if $\lim x_n = \lim y_n =a \in I$ with $x_n \neq y_n$ and $\lim \frac{f(y_n)-f(x_n)}{y_n - x_n} = f'(a)$ proof that $f'$ is continuous at $a$  my attempt $x_n \neq y_n$ so by MVT $\exists z_n \in I$ like $x_n \geq z_n \geq y_n$ with $\frac{f(y_n)-f(x_n)}{y_n - x_n}=f'(z_n)$ for each $x_n$ and  $y_n$ then $f'(a) = \lim\frac{f(y_n)-f(x_n)}{y_n - x_n}= \lim f'(z_n)$   Using $\lim x_n = \lim y_n = a$ and $x_n \geq z_n \geq y_n \Rightarrow z_n \rightarrow a$  if $ \lim_{x\rightarrow a} f'(x) \neq f'(a)$ then $\exists \epsilon &gt; 0$ such $\forall n\in \mathbb{N}$, $z_n \in [x_n,y_n]$ $0 &lt; |z_n - a| &lt; \frac{1}{n}$ and $|f'(z_n) - f'(a)| \geq \epsilon$. So $z_n \rightarrow a$ but will do not have $\lim f'(z_n) = f'(a)$  so $\lim f'(z_n) = f'(a) = \lim_{x\rightarrow a} f'(x)$ when $z_n \rightarrow a$  and thats implies $f'$ continuous at $a$  my question is, that's correct ? if not, can you help me? thanks In my cssh config file, I have:  terminal_font=6x13   this default font is too small for me.   man cssh says, I can specify other font size with the -f argument, while using "standard X font notation".  is a wikipedia page containing some other fonts types. Unfortunately, none of these work for me:  $ cssh host1 host2 -f "7x14" Fatal: Unrecognised font used (7x14). Please amend $HOME/.clusterssh/config with a valid font (see man page).   Why does "7x14" not work?  How can I use bigger fonts with cssh ? Suppose the following dialogue:  ... &quot;I accept only one notion of land property. Namely, 'I am doing my stuff here, therefore I am here&quot;. &quot;But this means,&quot; he responded, &quot;you can break into any place and stay there, using this rule.&quot; &quot;There is another rule, though. Right to act in its most natural sense, 'I am here, therefore I am doing my stuff here.&quot; &quot;But do not these rules put together become circular reasoning?&quot; &quot;Of course, they do,&quot; I put my head closer to him, &quot;and this is exactly that rare case when circular reasoning is not only sufficient, but is necessary.&quot; &quot;But why is that? Circular reasoning never was a correct argument.&quot; &quot;There are many circular things happening in nature. Life forms, for example, exist only in order to produce new life forms or to prolongate their own lifetime. Is there any reason to say this can't be the case for reason itself? Why must reasoning not be circular?&quot; ...  Can circular reasoning ever be justified? For example, we know all the words in our languages can't be defined using other words without the use of circularity. We know logic can't prove itself without circularity. Are these arguments rational? Are there any other arguments where circular reasoning is still rational? To infinitive used after adjective This question is relatively simple. I don't understand why we never use passive form of to infinitive after the adjective unless the subject is "it".  For example:     He is difficult to please.   People consider the example above a correct sentence. But:     He is difficult to be pleased.    People, for example, my teacher, said it sounds wrong and told me not to write this type of sentence. Is it grammatically flawed, or is it just a stylistic choice? Entering Unicode characters in LaTeX Javascript close alert box I want to be able to close an alert box automatically using Javascript after a certain amount of time or on a specific event (i.e. onkeypress).  From my research, it doesn't look like that's possible with the built-in alert() function.  Is there a way to override it and have control over the dialog box that it opens?  Also, I don't want an override that shows a hidden div as the alert.  I need an actual dialog box. How do I convert two lists into a dictionary? How do I deal with a runaway bride? I killed my first wife once I found out there is a mercenary you can marry who gives you up to 300 gold a day (in Whiterun). The only requirement, of course, being that I had to hire her first. So I hired her, and then I popped the question, to which she replied the usual: tell the priest to arrange the wedding.   When we reached Riften I told her to wait, just outside the bee and barb, and arranged the wedding. I went through the process, and the second it finished she left, I followed but as I left she was nowhere to be seen. I have tried going back to my house, the pub where I hired her and that same spot in Riften about 6 times each now, some during the day, some during the night and cannot find her at all.   Now this isn't to much of a problem because I can re-marry...oh wait, to remarry, my spouse has to die, so I can't claim gold off her and can't remarry, and the autosaves have been used up fast travelling to the places I thought she might've been. My last save is something like 6 levels ago, and I don't want to have to load it.   What should I do about this situation? Per User Named Credential and External Identity Users My question is almost similar to one mentioned in 'Auth Provider with per-user Named Credential' (). I am trying to authenticate and make a API call when a new or existing Salesforce community users try to log in. The Authentication is provided by 3rd party (Cognito). So, the requirement is :  User to be authenticated using the 3rd party system for login. After successful authentication and before community page is displayed, the API call is to be made to 3rd party system to get more details about the user.  In order to achieve this:  Created an Open ID Connect Auth. Provider Use the registration handler on the Auth. Provider to create/link a new/existing user. Use a login flow for API call. Use Per User Identity Type Named Credential to make API calls.  No, where I am having issue is once the user has authenticated successfully, how do I allow the user to make API call without authenticating it again. I am getting the error: An Apex error occurred: System.UnexpectedException: You don't have permission to view this data, enter credentials for the named credential in your personal settings. Or ask your Salesforce admin for help. I believe this error is due to the fact that the user is not listed under 'Authentication setting for External Systems'. My requirement doesn't allow me to authenticate the user again, so how do I achieve this using either APEX or any other way? Meta duplicates don't require an answer. Don't suggest there is one when that's not true This request was sparked . The vote to close as a duplicate on meta, in contrast to the main site, does not require for the duplicate to have an answer. Yet, the closure message still says:     This question has been asked before and already has an answer.    ...even when this is not the case. Perhaps we should either only show this particular sentence if there is indeed an answer, or remove this altogether for meta.   Note: I fear this might be a duplicate request, but I was unable to find one. (Not even one without an answer :) ) Question Tag problem! Question:     A man like you should not do this, _______?   Which question tag should I use in the blank space?   should he? should you?   Which would be grammatically correct? I think 1 is true. : So how many named special cases of each modal verb are there, in toto? There's   1. subjunctive should, and   2. mandative should, and   3. , at least;   and I s[up]pose 4. Should we? is suggestive should, and   5. Shouldn't we? is tag **should**, and I can think of a lot more.    I ask about only operative uses of this modal verb including literary and formal usage,  but please omit anything obsolete. I'm trying to classify them and learn the formal terms describing each. Are there any apt others in addition to the ones above? (I added the enumeration below)  1. What's 'subjunctive should'?  Whenever should is conjugated in the subjunctive mood? 5. What's a tag **should** ? 6. Where does  should/would  feature? What's it called? This should is detailed in   or  or . What can cause "Android OS" process to use high percentage of battery? Windows 7 time issues Excel multiple FIND formula I am no expert with excel so any help is appreciated!   I am trying to make one cell do multiple searches within another.  I know that to search one cell for a specific word you would use  =FIND(Blue,C2)   But I need to find multiple different words in one cell. Heres an example of what im trying to do:    I need to show all the allergens in the ingredients cell eg peanuts, gluten, milk, sesame seeds etc   How do I get the result to list all the allergens?   I know that I can do a single find function in separate cells and then concatenate them, but there must be a more simple way?  Thanks url completion in cartoDB info windows