Newton's Law of Gravitation states:     $$F=\frac{GM_1M_2}{r^2}$$   How did he recognize that there is a force between two masses?
I am having trouble comprehending how anyone could come up with this formula:  $$F = \frac{GMm}{d^2}.$$   Could someone walk me through this?
What is the English equivalent of gatasan? How do I know when to use "the" versus "a" versus "∅" as an article on a noun? With proper nouns, we don't use the except for river names, newspaper names, etc.  I want to know why we use the with White House. I mean, under which rule can we categorize it? What could other similar examples for that rule be? With Glade Designer that lets you set up Gtk-Ui's you can check the option that windows are not shown in the launcher. If I take a look at the ui-file generated by Glade, it says &lt;property name="skip_taskbar_hint"&gt;True&lt;/property&gt;. In gtk code this hint is  window.set_property('skip-taskbar-hint', True). However I believe that this option is not exclusively Gtk-specific, and want to apply this one on my PyQt4-app. The Ubuntu window manager must be able to receive that hint, otherwise I would see the window of a gtk-application i use (stickynotes-indicator). So there MUST be a way of doing this in Qt or any other language, right?  Does anybody know such an option? Python or Qt syntax, doesn't matter! How do I troubleshoot the "Error, press shutter release button again" message on my Nikon? The LCD on my Nikon D3000 is displaying the following error message:     Error. Press shutter release button again.   I have pressed the shutter release button but the camera still does not work. eGPU Vega 56 (Blackmagic) Mac + cycles problem Hello I just got the AMD Radeon RX Vega 56 (blackmagic eGPU Pro) yesterday  plugged it in to my brand new Mac mini (Mojave), it shows up in the menubar and as an alternative as a render engine,. My question is, can I use this eGPU for cycles renders? (Blender 2.80)  Very grateful for your responses. Yesterday, one of our computers dropped to grub shell or honestly, I am unsure what shell it was when we turned on the machine.  It showed that it can't mount the root filesystem or something in this sense, because of inconsistencies.  I ran, I believe:  fsck -fy /dev/sda2   Rebooted and the problem was gone.  Here comes the question part:  I already have in her root's crontab:   @reboot /home/ruzena/Development/bash/fs-check.sh    while the script contains:  #!/bin/bash touch /forcefsck   Thinking about it, I don't know, why I created script file for such a short command, but anyways...  Further, in the file:  /etc/default/rcS   I have defined:   FSCKFIX=yes    So I don't get it. How could the situation even arise?    What should I do to force the root filesystem check (and optionally a fix) at boot?  Or are these two things the maximum, that I can do?  OS: Linux Mint 18.x Cinnamon 64-bit.  fstab:  cat /etc/fstab | grep ext4   shows:   UUID=a121371e-eb12-43a0-a5ae-11af58ad09f4    /    ext4    errors=remount-ro    0    1    grub:   fsck.mode=force    was already added to the grub configuration. Badge Name is Blue? Now some random badges on the Profile page for the mobile web is now blue! This is seemingly weird as the default and now permanent color for Badge name text is white. Here's the problem here:     Ahhhh! Now it has invaded the desktop/computer version too! Now seemingly, every version has badges with blue text. Android app has the same issues too! Can the badge color be fixed from blue to white on the mobile version please? Question: Best way to derive an ellipse formula when given bunch of points (say 60 points which when connected draws an ellipse)?  Background: Using R Momocs library function  which returns confidence ellipse coordinates. Would be nice to abstract those points into a formula.  You can see my ellipse points in the image below;    Any suggestions much appreciated, Thanks If $X$ is a Banach space, and $T:X \to X$ is a bounded linear operator with norm &lt; $1$, then $I-T$ has a bounded inverse defined by $(I-T)^{-1} = \sum_{n=0}^\infty T^n$.   Thinking in terms of a converse, if $T$ is any bounded linear operator defined on $X$, then does the existence of a bounded inverse $S=(I-T)^{-1}$ imply that $S$ can be represented as $S=\sum_{n=0}^\infty T^n$? How to receive sms from our android app? Can the program counter on Intel CPUs can be read directly (that is without 'tricks') in kernel mode or some other mode? Sequences or 'chains' of adjoint functors Suppose we have (some categories and some functors such that) $F_1$ is left adjoint to $G_1$, $G_1$ left adjoint to $F_2$, $F_2$ left adjoint to $G_2$. Will $F_1$ then be equal to $F_2$ (and $G_1$ to $G_2$)?  Or can there exist arbitrarily long 'chains' of adjoint functors that do not trivialize? Set of continuity points of a real function I have a question about subsets $$ A \subseteq \mathbb R $$ for which there exists a function $$f : \mathbb R \to \mathbb R$$ such that the set of continuity points of $f$ is $A$. Can I characterize this kind of sets? In a topological,measurable or in some way? For example, does there exist a function continuous on $\mathbb Q$ and discontinuous on the irrationals? Few days back while attending a thesis defense, one Professor was asking the defender why does he think, he deserves the degree. I was wondering since then, is there really any general answer for that? or the answer should be given describing my own work and then emphasis them how it is important for research field?  I asked the question here to know your opinion about it and to list down what could be the possible answers to this question. Cannot translate vertice/edge will duplicate Is there a way to "auto login" in PuTTY with a password? Is there a way to configure a password for a stored session in ?  I know there is the capability to specify an "auto-login username" (under Connection/Data), but is there a way to do the same with the password? How does Latex compilers integrate packages into its existing core functions? I am trying to solve this exercise from Royden's 3rd edition.     The question is as follows: Let $f$ be a real-valued function defined for all real numbers. Show that the set of points at which $f$ is continuous is a $G_{\delta}$.    Let $$A_n = \{y : \text{there is a }~\delta_y \gt 0 : |f(s)-f(t)|\lt 1/n ~ \text{whenever}~ s,t \in (y-\delta, y+\delta)\}\;.$$     Then by the definition of open sets, $A_n$ is open.     To complete the proof, I need help in showing that $f$ is continuous at say $x$ if and only if $x\in \cap A_n$.     If $f$ is continuous at $x$, the there is a $\delta \gt 0$ such that $|f(x) - f(a)| \lt 1/n$ whenever, $x\in (a-\delta, a+\delta)$. so $x \in A_n$ son it must be in $\cap A_n$.  Thanks. Android reading from .txt File created in src folder Planck's Law in terms of wavelength