I think about the precession of the perihelion of the trajectory as the probe comes closer to the sun than Mercury, which was the first successful test for the general relativity.
note: This is a question about relativistic effects. I've included some detail about the spacecraft and its orbit for background, but the question is about relativistic effects and their observability.     When the Parker Solar Probe passes within 8.5 solar radii of the Sun, it will be moving really fast.  A perihelion and aphelion of about 6.6 and 109 million kilometers suggests a semi-major axis of 57.8 million kilometers. The standard gravitational parameter for the Sun is:  $$GM_{Sun} \ = 1.327\times 10^{20} m^3/s^2$$  So using the :  $$v^2 \ = \ GM_{Sun}\left(\frac{2}{r}-\frac{1}{a}\right)$$  the orbital velocity at perihelion will be about 195,000 m/s, or about 25 times faster than a satellite in LEO. This is close to one part per thousand of the speed of light! I think this will be a new record for a spacecraft velocity relative to the solar system.  Depth of a gravitational potential well for an object of mass $m$ is approximately given by:  $$u_G \ = \ -GM_{Sun}\frac{1}{r}$$  At 6.6 million kilometers the spacecraft will be 23 times deeper in the Sun's gravitational well than it would be at 1 AU.  Will there be any particularly unique relativistic effects detectable for the Parker Solar Probe during it's close flyby of the Sun?  Just for example, during one close flyby, how much time will its on-board clock gain or lose compared to some convenient standard solar system timescale? I know there are several different choices, "GPS time" might be one but I don't want to arbitrarily choose an inconvenient one.     above: Parker Solar Probe cropped, from .    above: screen shot from NASA's      note: the link seems to be dead now, but there is plenty of related information available at     above: Illustration of the Parker Solar Probe's orbit, from .
I used source code to build one package such as below:  ./configure --prefix=/usr --sysconfdir=/etc --localstatedir=/var --libexecdir=/usr/lib --with-package-name="Myplugin" --with-package-origin="http://www.ubuntu.org/" --enable-gtk-doc --disable-static make make install   But unfortunately, i discovered that its the latest version, and has lot of bugs, so i need to remove it/uninstall it. But how can i do so? I tried make clean; make uninstall but still i see it exist:  # pkg-config --list-all | grep Myplugin myplugin-.... $ ls /usr/lib/myplugin/libXYZ.so exist....   How do you remove this now? There is (there's) vs.There are What are the roots of the creeping usage of "there's" for both singular and plural predicates? (This seems to be more common in spoken English.) I have 2 theories.  Perhaps it is because spoken communication our society is becoming less formal by the day. Or perhaps it is a reflection of speakers of other languages having increasing contact with native English speakers.  I am aware of German  "es gibt" and Spanish  "hay" constructions. Please comment.  3/06/14 I ran a couple of Google Ngrams and was surprised to find a greater rise in the use of "there's" in English fiction than in general English language books, since the turn of the century.  This would seem to support my contention that informality is behind the shift. Can bosons that are composed of several fermions occupy the same state? It is generally assumed that there is no limit on how many bosons are allowed to occupy the same quantum mechanical state. However, almost every boson encountered in every-day physics is not a fundamental particle (with the photon being the most prominent exception). They are instead composed of a number of fermions, which can not occupy the same state.  Is it possible for more than one of these composite bosons to be in the same state even though their constituents are not allowed to be in the same state? If the answer is "yes", how does this not contradict the more fundamental viewpoint considering fermions? How to see what's going on during Windows shutdown/logging off process? Windows 7 msconfig lets users select the options No GUI boot and OS boot information to have a list of drivers being loaded during boot. Is it possible to have similar detailed messages during shutting down/restarting/logging off? Here's the screen I want disable or give me more details: I am trying to understand what mathematics is really built up of. I thought mathematical logic was the foundation of everything. But from reading a book in mathematical logic, they use "="(equals-sign), functions and relations.  Now is the "=" taken as undefined? I have seen it been defined in terms of the identity relation.  But in order to talk about functions and relations you need set theory.  However,  seems to be a part of mathematical logic.  Does this mean that (naive) set theory comes before sentential and predicate logic? Is (naive)set-theory at the absolute bottom, where we can define relations and functions and the eqality relation. And then comes sentential logic, and then predicate logic?  I am a little confused because when I took an introductory course, we had a little logic before set-theory. But now I see in another book on introduction to proofs that set-theory is in a chapter before logic. So what is at the bottom/start of mathematics, logic or set theory?, or is it circular at the bottom?  Can this be how it is at the bottom?  naive set-theory $\rightarrow$ sentential logic $\rightarrow $ predicate logic $\rightarrow$ axiomatic set-theory(ZFC) $\rightarrow$ mathematics  (But the problem with this explanation is that it seems that some naive-set theory proofs use logic...)  (The arrows are of course not "logical" arrows.)  simple explanation of the problem:  a book on logic uses at the start: functions, relations, sets, ordered pairs, "="  a book on set theory uses at the start: logical deductions like this: "$B \subseteq A$", means every element in B is in A, so if $C \subseteq B, B \subseteq A$, a proof can be "since every element in C is in B, and every element in B is in A, every element of C is in A: $C \subseteq A$". But this is first order logic? ($(c \rightarrow b \wedge b \rightarrow a)\rightarrow (c\rightarrow a)$).  Hence, both started from each other? BAV99 forward voltage I am reading the  From the table on ELECTRICAL CHARACTERISTICS (page 2) (TA = 25°C unless otherwise noted) (Each Diode)     Forward Voltage mVdc     IF = 1 mAdc 715mV   IF = 10 mAdc 855mV   IF = 50 mAdc 1.0V   IF = 150 mAdc 1.25V     On page 3 there is the following VI curve graph:  Clearly at 25°C - 100mA is Vf = 0.9V. There is huge difference between the table and the IV curve.  Which source of information I should trust? Is this (typical) and (maximum) where the table guarantees the diode won't exceed Vf 1.0v at 50mA while the graph is just typical values? How is it the Voyagers are a few seconds closer to Earth than earlier? The  of March 01, 2013 put it's distance at 14 hrs 04 mins 23 secs of light-travel time from Earth. A  (earlier today) tweet says it is 14 hrs 04 mins 22 secs of light-travel time from Earth. An  tweet put it still further out at 14 hrs 04 mins 25 secs of light-travel time.  The Voyager 2 tweets on Voyager 1's proximity to Earth too has reduced similarly to  earlier today from  reported on Feb 28 2013  It could quite simply be a typo ... If not a typo then my curiosity is piqued; I was under the impression the Voyagers are outbound from the Solar System now without any major in-system activities now.   How is it the Voyagers are closer to Earth than before? Apache error "Could not reliably determine the server's fully qualified domain name" When I restart my Apache server using the command  sudo /etc/init.d/apache2 restart   I get the following error:  Restarting web server apache2 apache2: Could not reliably determine the server's fully qualified domain name, using 127.0.1.1 for ServerName ... waiting apache2: Could not reliably determine the server's fully qualified domain name, using 127.0.1.1 for ServerName   Is the server using 127.0.1.1 instead of 127.0.0.1? What causes this error? I have some problems with this exercise. I don't know if it can be done. Consider the polynomial $ x^n - a \in \mathbb{Q} $ Can I compute the Galois group of this over $\mathbb{Q}$? Maybe having a nice "basis.  The splitting field is given by $\mathbb{Q}(\zeta_n,\alpha)$ , where $\zeta_n$ is a primitive root of unity , and $\alpha$ is some number such that $\alpha^n = a $. Well first of all, I want a $\underline{"good basis"}$ for the splitting field. In the sense that the minimal polynomials, of the adjoined elements, are different (in this case the computation of the galois group is very simple).  For example one easy case, it's when $a&gt;0$, then $(a)^{\frac{1}{n}} \in \mathbb{R}$ , so clearly the minimal polynomial of $(a)^{\frac{1}{n}} , \zeta_n$ are distincs, and I'm done. If $n$ is odd then , it's also easy, since one root it's also real, for example $x^3-3 $, the real root is $ \root 3 \of { - 3}  =  - \root 3 \of 3  $ , so I can consider the splitting field as $\mathbb{Q}(-\root 3 \of 3 , \zeta_3 )=\mathbb{Q}(\root 3 \of 3 , \zeta_3 )$. The difficult case is when $n$ is even and $a&lt;0$ , for example  $x^8+20$ or $x^4+20$ in some cases as in the second, there are particular cases since there exist algorithms for the Galois group of quartics, but in general. It can be done?  $\underline{Remark}$ I'm searching a $\underline{"good basis"}$ for the splitting field. In the sense that the minimal polynomials, of the adjoined elements, are different since in this case the computation of the galois group is very simple. In bash, how do I escape an exclamation mark? I want to do something like bzr commit -m "It works!". I can sort of escape the exclamation mark by doing bzr commit -m "It works\!". However, then my commit message includes the backslash. How do I escape the exclamation mark, while still ignoring the backslash? Recently I commented on  question   and the text did got bold but the italic word didn't seem to get italic on Android Chrome(Latest Ver.), but when I saw from the PC browser, it rendered as it should...  I've attached a screenshot of my phone ... Why is (sizeof(int) > -1) false? Harry is a half-blood and Ginny is a pure-blood, so what does that make his children? I've been told it means they are pure-bloods but I can't be sure. What do you think? What does pwd output? Does the command pwd in a shell script output the directory the shell script is in? How to create functions of arbitrary number of variables? $\mathbb{Q}(\sqrt{n}) \cong \mathbb{Q}(\sqrt{m})$ iff $n=m$ Page 105 of D. Burton's A First Course in Rings and Ideals reads     It is not difficult to show that if (I'll call them $n$ and $m$ instead of $n_1$ and $n_2$) $n$, $m$ are square free integers, then $\mathbb{Q}(\sqrt{n}) \cong \mathbb{Q}(\sqrt{m})$ if and only if $n=m$.   Well, it is getting difficult for me, any help or would be appreciated.    My progress so far: Suppose $\phi :\mathbb{Q}(\sqrt{n})\to\mathbb{Q}(\sqrt{m})$ is an isomorphism. Then $\phi(u)=u$ for every $u \in \mathbb{Q}$, so that $\phi(\sqrt{n})^2=\phi(n)=n$. If $\phi(\sqrt{n})=a+b\sqrt{m}$ for some $a,b\in\mathbb{Q}$, then $(a+b\sqrt{m})^2=a^2+b^2m + 2ab\sqrt{m}=n$ implies $$a^2+b^2m = n$$ and $$2ab=0.$$  Then $b=0$ cannot happen since that would imply that $\sqrt{n}\in\mathbb{Q}$, where $n$ is a square-free integer. Also $a=b=0$ cannot happen. Hence $a=0$ and we have $$b^2m=n.$$ If $\psi:\mathbb{Q}(\sqrt{n})\to\mathbb{Q}(\sqrt{m})$ were an isomorphism then there would exist some $s\in\mathbb{Q}$ such that $$s^2m=n,$$ then $s=b$ or $s=-b$. Therefore the only isomorphisms from $\mathbb{Q}(\sqrt{n})$ to $\mathbb{Q}(\sqrt{n})$ are $\phi(u+v\sqrt{n})=u+vs\sqrt{m}$ and $\psi(u+v\sqrt{n})=u-vs\sqrt{m}$.    I don't know if there's an easier way and I don't know if I'm in the correct way here. Thanks beforehand :) Python gives us the ability to create 'private' methods and variables within a class by prepending double underscores to the name, like this: __myPrivateMethod(). How, then, can one explain this  >>> class MyClass: ...     def myPublicMethod(self): ...             print 'public method' ...     def __myPrivateMethod(self): ...             print 'this is private!!' ...  >>> obj = MyClass() >>> obj.myPublicMethod() public method >>> obj.__myPrivateMethod() Traceback (most recent call last):   File "", line 1, in  AttributeError: MyClass instance has no attribute '__myPrivateMethod' >>> dir(obj) ['_MyClass__myPrivateMethod', '__doc__', '__module__', 'myPublicMethod'] >>> obj._MyClass__myPrivateMethod() this is private!!   What's the deal?!  I'll explain this a little for those who didn't quite get that.  >>> class MyClass: ...     def myPublicMethod(self): ...             print 'public method' ...     def __myPrivateMethod(self): ...             print 'this is private!!' ...  >>> obj = MyClass()   What I did there is create a class with a public method and a private method and instantiate it.  Next, I call its public method.  >>> obj.myPublicMethod() public method   Next, I try and call its private method.  >>> obj.__myPrivateMethod() Traceback (most recent call last):   File "", line 1, in  AttributeError: MyClass instance has no attribute '__myPrivateMethod'   Everything looks good here; we're unable to call it. It is, in fact, 'private'. Well, actually it isn't. Running dir() on the object reveals a new magical method that python creates magically for all of your 'private' methods.  >>> dir(obj) ['_MyClass__myPrivateMethod', '__doc__', '__module__', 'myPublicMethod']   This new method's name is always an underscore, followed by the class name, followed by the method name.  >>> obj._MyClass__myPrivateMethod() this is private!!   So much for encapsulation, eh?  In any case, I'd always heard Python doesn't support encapsulation, so why even try? What gives? Gendry was born in the Crownlands and should therefore be referred to as Gendry Waters. However, he refers to himself as Gendry Rivers.   Did showrunners forget or is Gendry ignorant of the customs? How do I send a file with FileZilla from the command line? I have a batch file that builds an application, and then I want to upload it to an FTP server from the command line.   Considering I do the upload manually with , is there a command line for it to upload files?  I am limited to Windows. How do I set a default host for nginx? I'm trying to figure out how to set a default host for my nginx installation. I found this article in the nginx Wiki:    Unfortunately, this doesn’t work. After restarting I get this:  Restarting nginx: nginx: [emerg] unknown directive "http" in /etc/nginx/sites-enabled/catchall:1 nginx: configuration file /etc/nginx/nginx.conf test failed   After removing the http directive I get this:  Restarting nginx: nginx: [emerg] unknown log format "main" in /etc/nginx/sites-enabled/catchall:7 nginx: configuration file /etc/nginx/nginx.conf test failed   I’m on Ubuntu 10.04.3 where I’m using the official nginx PPA. Version 1.0.9 of nginx is running.