Still, I don't understand how come the satellites won't fall into earth. I know the general explanation to this question is that the satellite's horizontal velocity is too fast that makes the gravity impossible to pull it to the earth.  This, for me, sounds like the gravitational force need to take a few moments to sense the existence of this object and then pull it downward, just right at the moment the earth notice the object and begin to pull it for its position, it had already moved to another place.   Well, I think since the vertical velocity id independent of horizontal velocity, therefore, no matter how fast the horizontal speed is, it will not prevent the gravity to pull it straight down to the earth, isn't it?   can someone point out what's wrong with my understanding here?
Why doesn't the Moon fall onto the Earth? For that matter, why doesn't anything rotating a larger body ever fall onto the larger body?
Colorize symbols with lstdefinelanguage in latex Why does part of my model disappear when I zoom in on it in the 3D Viewport? Outlier Detection on skewed Distributions Under a classical definition of an outlier as a data point outide the 1.5* IQR from the upper or lower quartile, there is an assumption of a non-skewed distribution. For skewed distributions (Exponential, Poisson, Geometric, etc) is the best way to detect an outlier by analyzing a transform of the original function?  For example, distributions loosely governed by an exponential distribution, could be transformed with a log function - at which point is it acceptable to look for outliers based on the same IQR definition? The covid19 death data for US shows strong periodic trends. It does not make sense to me that people die periodically.   What could be the reason to having such data? I thought it might be the reporting artifacts, for example, people always update data at Monday, but the period seems to be 3-4 days. If I change the password for the root user is that going to automatically change the password for the user account?   I found this link for root:    How do I change the user account password? The Nazgul are afraid of fire, but can they be harmed by it? When Aragorn and the Hobbits are on Weathertop, just after seeing the Nazgul below them and prior to inflicting Frodo's knife wound, Aragorn says the following:     Sauron can put fire to his evil uses, as he can all things, but these   Riders do not love it, and fear those who wield it. Fire is our friend   in the wilderness.   Is there any mention as to whether fire can actually cause harm to the Nazgul and if not, is there a specific reason for their fear of it? What is the right way to get the current users profile in an apex class?  When I tried to print the following in visualforce page,  i am able to get the profile name  &lt;apex:outputText value="{!$Profile.Name}"/&gt;    But when i tried to print in the Apex class using System.debug(Profile.Name), I couldn't. How to change the "User License" type for customer portal users using a script? Using separation of variables to solve the wave equation I'm trying to teach myself separation of variables and have been following some notes for the wave equation, but there's one part which really confuses me and I'm not exactly sure how it makes the step.  For the wave equation   $$u_{tt} - c^2 u_{xx} = 0$$   with length $l$ and fixed ends, $u(0,t)=u(l,t)=0$ we seek a solution in the form $$u(x,t)=v(x)q(t)$$  and substituting this into the equation gives $$\frac{1}{q(t)}\frac{d^2 q}{dt^2}=c^2 \frac{1}{v(x)}\frac{d^2 v}{dx^2}=-\omega ^2$$   and I understand all of this so far. But when solving the equation  $$q''+\omega ^2 q = 0$$ the general solution is $$q(t)=A \cos(\omega t +\alpha)$$ where $A$ and $\alpha$ are constants - which is the part which I'm not exactly sure on how it gets to.   Could someone explain this step to me? Thanks! What is the default 'backup' user for? I am setting up multiple-machine backup plan and I was hoping to use a user called 'backup' on each machine as the backup destination.   My problem is, there is already a user called 'backup' on my machine.  What is it for, and can I hijack it for my own purposes?  root@frodo:~# useradd backup useradd: user 'backup' already exists the relationship between maximizing the likelihood and minimizing the cross-entropy How can I make an application automatically start when I have logged in? How to check that a cubic polynomial is irreducible? Disabled mac os SIP but still can't delete default apps I'm using mac os 11.2.1 Big Sur. My question concerns using the Terminal utility to delete Apple default apps protected by SIP. I have disabled System Integrity Protection and confirmed that it is off by typing: csrutil  Terminal duly returns &quot;disabled&quot; to confirm that SIP is definitely off. I then attempted to delete various Apple default apps, as follows: sudo rm -rf FaceTime.app/  sudo rm -rf TV.app/  sudo rm -rf Mail.app/  But nothing seems to happen. The apps are still in my Applications folder and launch normally. If I try to delete them manually, I get a beep and the deletion is rejected just as if SIP were still enabled. Can someone suggest a better way to remove Mail? Is is possible to convert a .vdi file into a .iso that can be burned to a cd or dvd and make it like an installer. Or Is it possible to convert virtual machines to physical environments? Assume two black holes in the most common size range, spiraling into each other until they merge. The event releases significant amounts of energy via gravitational waves, which warp the space-time.  If the distortion is powerful enough, it would get noticed in daily life, or perhaps even detected by the proprioceptors in the human body.  How close, as an order of magnitude estimate, would you have to be to the merger to perceive it like that, without any instrument? Generate four random words from a list for XKCD-like passwords For start, we know how can we output random lines from a txt file:   perl -MList::Util -e 'print List::Util::shuffle &lt;&gt;' words.txt   But we need a general solution (perl is usually installed on every unix-like OS) to output 4 random words from a txt file, how can we do it?    $ cat words.txt ... alpha beta gamma delta epsilon ... $   The "..." represents many other words.   Example output (without newline between them, but one unix newline is needed at the end, spaces should separate them):  $ perl SOMEMAGIC words.txt gamma alpha delta beta $   Using only perl, the shortest possible solution (oneliner).   It will be used as human memorable password generator:    Since afaik perl is enough good to be named "random generator".   Example common english wordlist with 32768 unique lines: Viewing computer screen through 3D glasses, why the asymmetry? I am looking for a way to replace a string in a file with a string that contains a slash by using sed.  connect="192.168.100.61/foo" srcText="foo.bar=XPLACEHOLDERX" echo $srcText | sed "s/XPLACEHOLDERX/$connect"   The result is:  sed: -e Expression #1, Character 32: Unknown option for `s' Multi-Question Questions: How Best to Handle Them? Sometimes I come across a question on SO that is actually a number of questions all in one. If these &quot;sub-questions&quot; are closely related, it's not a problem. But if they are only weakly related (or not at all) it gets ugly. I'm now (ironically or hypocritically) going to ask a few questions of my own for the community to respond to:  Do you consider a question made up of a number of weakly-related sub-questions &quot;inappropriate&quot;? Why or why not? How many is too many sub-questions? What do you think is the best way to deal with such questions?  As an example,  I had some discussion about with another user. I will add a more complete version of my response in an answer below, but in short I felt that this question should be closed and many of the questions asked separately.