How to prove ? How did Kepler proved it? Is it possible to prove the third law without applying Newton's universal law of gravitation?
Is there a simple way to explain how Kepler's third law follows from the inverse square law that of gravity  (and laws of motion)  For example for Kepler's second law we can say it's because Gravity is a central force  What is it about the law of gravity which ultimately gives rise to Kepler's third law?
Any nice, stable ways to keep a window 'Always on top' on the Mac? Is is possible that a software issue could be causing spotty USB-C connections on 2017 MacBook Pro? I have a 2017 MacBook Pro. It has 2 USB-C ports on the left side and I use an Aukey hub to provide more ports (4 USB, 1 HDMI, 1 USB-C) and always to connect two monitors.   I connect one monitor through the hub with the HDMI port and another directly to the MBP with a USB-C adapter. Sometimes when I connect the hub to the Mac and the 2nd monitor to the Mac, it works as it should with no problem...but more than half the time I have to connect, disconnect, jiggle, jangle, switch ports, reconnect HDMI, etc. and hopefully they will both work. OFTEN, I can only get one monitor to fire up.  Is there any kind of software fix or reset that might solve this issue? Any other thoughts welcome. Thanks. At 12 o'clock, the hour hand and minute hand of the clock can be swapped, and the clock still gives the same time, but at 6 o'clock, it can not be swapped. So in what cases when we swap the hour and the minute hand position does a clock still give a valid time? How is it possible for the Root Name Servers to handle all DNS requests? I was reading about DNS some days ago and learned how the requests are processed. If you surf to www.example.com, then a request will go to the Root Name Servers to see who owns that .com address, then another request will go to another, more local, DNS server to see who owns the example.com address and so on.  How is it technically possible that the 13 Root Name Servers can handle all requests done by earth's billions of Internet users simultaneosly without beeing ddos:ed? The score for the 4 questions are 111, 1218, 261 and 5 respectively, but they display 2 digits per line. This is an obvious bug in design. How are Anonymous inner classes used in Java? What is the use of anonymous classes in Java? Can we say that usage of anonymous class is one of the advantages of Java? If the universe is expanding, what is it expanding into? Calculating $\lim_{n\to\infty}\sqrt[n]{2^n-n^2}$ Loading D3.js data from a simple JSON string No file output after rendering? I usually am able to render successfully to the c:\tmp folder, but when I came into work today, I rendered out the image on my work laptop, and everything seems to work, but I'm not getting an output to the tmp directory.  Does anyone know how to make this work? I have two passports/nationalities. How do I use them when I travel? I am a citizen of two different countries, and have two passports.  How should I use my passports when traveling? Why does comparing strings using either '==' or 'is' sometimes produce a different result? Is there a way to solve this integral?  $$\int \frac{dx}{\sqrt{-ax^2 + bx +c}}, \;\;\;\;\; \forall\; a,b,c \in (0,+\infty) \;in\;R$$  I have tried it by changing of variable and by parts, but no result. I don't know what else to do.  Thanks in advance. GNOME 3.26 - Clicking one window brings another in the foreground (Ubuntu 17.10) I'm on Ubuntu 17.10 with GNOME 3.26.  Often I have windows tiled on the left and right side of the screen. A typical setup is to have a browser and text editor on the left, a PDF reader and terminal on the right.  Something I've seen happen very often: I'm reading the PDF on the right, having the window in focus. The text editor on the left. When I click on the text editor to write something, it brings forward another window on the right (say the file browser), covering the PDF reader.  This seems to have something to do with the Alt-Tab view history.  My question is: Is it possible to remove the automatic bring-to-front of windows? I don't understand why unrelated windows are brought to the front when I click on another application. I have a question on Holder space.Is the space $C^2(\mathbb{R}^n)$ embedded in $C^{1,\alpha}(\mathbb{R}^n)$? I think in the bounded domain case, this should be true. But what if in the case where the domain is not bounded? Thanks for any hint! Suppressing addition of blank page before figure when wrapping long JPEG image Does Overhand Chop override the damage bonus from wielding a two handed weapon? I was showing a GM friend of mine a build I was making that uses the Two-Handed Fighter Archetype and we are both unsure of how it interacts with the damage bonus you get from two-handed weapons (which is 1-1/2 times your STR.) It reads:     Overhand Chop (Ex): At 3rd level, when a two-handed fighter makes a single attack (with the attack action or a charge) with a two-handed weapon, he adds double his Strength bonus on damage rolls. This ability replaces armor training 1.   So, does Overhand Chop turn the 1-1/2 times multiplier from two-handed weapons into a 2 times multiplier, or do the two add up? Or, do they interact in some other way?   This assumes a Medium sized character with 20 STR and a greatsword with 3 levels. How do moving charges produce magnetic fields? Answer didn't load temporary Does a car use friction to move?