How do you prove that path of a satellite or a planet is a second degree curve? In other words, how do you prove Kepler's law which states that planets move in elliptical paths?
How can analytically be  the ?   I found some extremely synthetic equations which from the  (in particular $\mathbf{F} = m \mathbf{a}$) tried to obtain the Kepler's laws, but even if it seemed to be a nice procedure they were too much incomplete.
Let a,b,c,d be real or complex numbers with absolute value less than $1$. Is the following true:  $$|ab-cd| \leq |a-c| +|b-d|?$$ Why can't I press the Install button when installing applications from unknown sources? I'm trying to sideload an application, as seen in the picture below.    I have allowed the installation of applications from unknown applied actions in settings, but I can't seem to press the install button. The cancel button works correctly and installing applications via adb install works correctly. What's the problem?  EDIT: For those who have this problem, using ChainFire's  will correct it because the app uses hardware compositing, and Android doesn't notice a "layer" on top of the current screen. I am able to parse strings containing date/time with time.strptime  &gt;&gt;&gt; import time &gt;&gt;&gt; time.strptime('30/03/09 16:31:32', '%d/%m/%y %H:%M:%S') (2009, 3, 30, 16, 31, 32, 0, 89, -1)   How can I parse a time string that contains milliseconds?  &gt;&gt;&gt; time.strptime('30/03/09 16:31:32.123', '%d/%m/%y %H:%M:%S') Traceback (most recent call last):   File "&lt;stdin&gt;", line 1, in &lt;module&gt;   File "/usr/lib/python2.5/_strptime.py", line 333, in strptime     data_string[found.end():]) ValueError: unconverted data remains: .123 If you have a conducting hollow sphere with a uniform charge on its surface, then will the electric field at every point inside the shell be 0. The reason the electric field is 0 at the center is clear from the symmetry of the sphere, but for a point at a certain distance from the center, shouldn't a net electric field exist?  I saw a similar question on the site but it was vaguely explained. I've been trying to play with a rigid body simulations.  I prepared a project of a building made of domino tails. I've placed all objects very tight, but as soon as I start animation it looks like there was some tiny gap between objects, so they all fall down a little bit. For a high building it leads to a construction disaster as the whole building colapses.  Here is an example:  (I'd suggest to use 0.25x speed).  How can I fix it? I have installed some apps through the Ubuntu Software center. How can I find the corresponding terminal command? For many apps, this is not the same as the displayed name. For example, the app called Text Editor can also be launched by typing "gedit" in the terminal, but how can I find this for other apps? Custom Post Type Archives by Year & Month? How do you display the archives of a Custom Post Type by Year &amp; Month? Regulatory bodies and authoritative dictionaries for English Am I Running as a Service If we fail to reject the null hypothesis in a large study, isn't it evidence for the null? Preview Breaks with Invalid Tag Name [tag:+] In the formatted preview for Questions &amp; Answers, typing a tag link with an invalid tag name "crashes" the preview. As soon as you type the following the preview stops updating and an error can be observed in the Javascript console.   [tag:+]   Observed in Safari 7 and Chrome 31.   seems related to the business rule of not allowing certain characters in tags, but it sounds like a different bug. have lived vs have been living Is it correct to say:     1) I've lived in London for five years.   Or      2) I've been living in London for five years.   I think second one is correct because we use present perfect continuous for actions started in past and is continuing in present. Consider a block cipher with a key of size 128 bits but a small block size, say 32 bits.  Is this kind of block cipher secure?  I would like to know to what extent I can use a small block cipher, like a 32 bit block cipher. What are the constraints so that the use is acceptable in a real life application.  For instance, if we use a one-time key, that is, to encrypt only one message. Besides, the message could be small.  Suppose that when we want so send one file, we perform a key agreement so that we use the key for one message. This scenario is not efficient, but the CPA find-then-guess game is not adequate in this case. Is there an efficient way to copy text from a PDF without the line breaks? What does "causally connected" or "causes" really mean? In a different thread, a user stated the following about events preceding or following other events:     However, if the two events are causally connected ("event A causes event B"), the causal order is preserved (i.e. "event A precedes event B") in all frames of reference.   My question is what does "causally connected" really mean? What does "causes" mean? Further, given that we know that we can have instantaneous effects in typical quantum processes (e.g. flip the polarizer, effect on another a reading light years away, even though we cannot transmit useful information with this), does that not constitute "causing" for the purpose of this statement? Inequality from Chapter 5 of the book *How to Think Like a Mathematician* This is from the book How to think like a Mathematician,  How can I prove the inequality $$\sqrt[\large 7]{7!} &lt; \sqrt[\large 8]{8!}$$  without complicated calculus? I tried and finally obtained just $$\frac 17 \cdot \ln(7!) &lt; \frac 18 \cdot \ln(8!)$$ How to integrate $\int_0^{\pi/2}\frac{\sin^nx}{\sin^nx+\cos^nx}dx$? Possible Duplicate:          How can we integrate $$\int_0^\frac{\pi}2\frac{\sin^nx}{\sin^nx+\cos^nx}\,\mathrm dx , \,\,\,\,\,\,\,\,\, n\in N \quad?$$ Thanks for any hint. What is the fastest, easiest tool or method to convert text files between character sets?  Specifically, I need to convert from UTF-8 to ISO-8859-15 and vice versa.  Everything goes: one-liners in your favorite scripting language, command-line tools or other utilities for OS, web sites, etc.  Best solutions so far:  On Linux/UNIX/OS X/cygwin:   Gnu  suggested by  is best used as a filter. It seems to be universally available. Example:  $ iconv -f UTF-8 -t ISO-8859-15 in.txt &gt; out.txt   As pointed out by , there is an . Gnu  () suggested by  will convert one or several files in-place. Example:  $ recode UTF8..ISO-8859-15 in.txt   This one uses shorter aliases:  $ recode utf8..l9 in.txt   Recode also supports surfaces which can be used to convert between different line ending types and encodings:  Convert newlines from LF (Unix) to CR-LF (DOS):  $ recode ../CR-LF in.txt   Base64 encode file:  $ recode ../Base64 in.txt   You can also combine them.  Convert a Base64 encoded UTF8 file with Unix line endings to Base64 encoded Latin 1 file with Dos line endings:  $ recode utf8/Base64..l1/CR-LF/Base64 file.txt    On Windows with  ():    PS C:\&gt; gc -en utf8 in.txt | Out-File -en ascii out.txt  (No ISO-8859-15 support though; it says that supported charsets are unicode, utf7, utf8, utf32, ascii, bigendianunicode, default, and oem.)   Edit  Do you mean iso-8859-1 support? Using "String" does this e.g. for vice versa  gc -en string in.txt | Out-File -en utf8 out.txt   Note: The possible enumeration values are "Unknown, String, Unicode, Byte, BigEndianUnicode, UTF8, UTF7, Ascii".   CsCvt -  is another great command line based conversion tool for Windows. In a closed system, I know the rider wouldn't be able to change the combined center of gravity of the system by moving his weight around. If he pushes the bike to lean to the right, he would go to the left by the amount that would keep the combined cog the same.  But a bike with tires and a road under it is not a closed system, the tires wouldn't let the lower part of the bike left or right when tryingo to initiate lean. Does this mean it is possible to push with your bodies inertia to the bike, and the combined cog will be changed? I thing if you do so above the cog of the bike, you could, but I am not sure.  Edit: My question is not about if you can move the center of gravity of the bike at all. My question is about if can you change the combine cog of the system by moving around on the bike?  English is not my mother tongue, sorry for the confusion How to prevent SIGPIPEs (or handle them properly)