Elliptical orbit of revolution of earth Well known Kepler laws state that earth revolve around sun in an elliptical path with sun at one of the focii.  My question is rather simple. Why so?   I mean for an equilibrium of earth that is it is not accelerated towards or away from sun its gravitational force must be balanced by centrifugal force (pseudo force as frame corresponding to earth)   But following an elliptical path it distance from sun won't be same and hence the gravitational force and hence how is this?   I suspect may be it is due to presence of other celestial bodies but that seems too vague and escaping from the truth   Also maximum of derivations in gravitation are done by assuming circular path of earth around sun. (atleast at my level)   Please give me the real physics behind it?
How did planets have an elliptical orbit in the first place? I know that planets speed up when getting closer to the sun, but they speed up because they have an elliptical orbit, and they have an elliptical orbit because they speed up. Why did they have an elliptical orbit in the first place?
How to prevent iMessage syncing without access to device I foolishly logged into someone's iPad with my Apple ID. This person is now receiving my full communications on iMessage. I know I can remove my account from that iPad but I don't have access to it. How can I stop the device from getting my iMessages without physical access? UTF-8 -> ASCII in C language I'm looking to build a collection of fantasy miniatures, preferably pewter - but I don't want to buy them one at a time from my local hobby store... Much too expensive, and they don't often carry anything I'm interested in buying, which makes it a long term venture as well. So I'm looking for ideas on how to obtain many miniatures at once, preferably for cheap. D&amp;D Miniatures aren't a good source for me as they're collectibles, and the prices on those are also prohibitive.  By the way - they don't have to be pewter, that's just my preference. =) Why is $\alpha \rightarrow \forall x(\alpha)$ not generally correct in first-order logic? Why is $\alpha \rightarrow \forall x(\alpha)$ not generally correct in first-order logic?  i.e., when there are free occurrences of $x$ in $\alpha$, and, on the same point, why is the formula scheme correct when there are no free occurrences of $x$ in $\alpha$? My passport is expiring; can I still travel? How to extend WIFI from ethernet Here's my current setup.   Bonded "Zone" DSL modem/router on main level serving laptop #1 via Ethernet and laptop #2 via WIFI.  WIFI does not serve basement level well, so I have Ethernet running to basement where it is divided by a switch with one Ethernet going to laptop #3 and another Ethernet going to entertainment system, which houses a Sony Playstation 3. The PS3 has gone on the fritz and is now only good for playing discs, so I recently added a Google Chromecast to the TV. The Chromecast, of course is WIFI only, and is only receiving a weak signal. Plus I need to have a decent WIFI signal to my phone, which is the interface device for the Chromecast. So what I would like to do is to use the Ethernet that was serving the PS3 and broadcast WIFI from it. What device can I plug the Ethernet into that will do this for me? And if you have a recommendation, are there any special setup instructions? Orange squares appearing on render? Placing listing and figure side by side in memoir Show $\sum\limits_{n=0}^{\infty}{2n \choose n}x^n=(1-4x)^{-1/2}$ How do you prove that $\sum\limits_{n=0}^{\infty}{2n \choose n}x^n=(1-4x)^{-1/2}$? I tried to identify the sum as a binomial series, but the $4$ and the $-1/2$ puzzle me. (This series arises in studying the first passage time of a simple random walk.) If I downvote every competing answer, will I get flagged for vote abuse? ML estimate of exponential distribution (with censored data) In Survival Analysis, you assume the survival time of a r.v. $X_i$ to be exponentially distributed. Considering now that I have $x_1,\dots,x_n$ "outcomes" of i.i.d r.v.'s $X_i$. Only some proportion of these outcomes are in fact "fully realized", i.e. the remaining observations are still "alive".   If I wanted to perform a ML estimate for the rate parameter $\lambda$ of the distribution, how can I utilize the non-realized observations in a coherent/appropriate manner? I believe they still contain useful information for the estimation.   Could someone guide me to literature on this topic? I am sure it exists. I am however having trouble finding good keywords/search terms for the topic. Dryer Outlet - 4 prong to 3 prong Our new dryer has 3 prongs vs. 4. We are changing to the new 3 prong dryer outlet, but want to make sure we are grounding. The wires coming from the wall our white, red &amp; black - the the copper wire. Do I need to ground it?? Thank you! Molly How do I get an XBOX 360 controller working? I have a Microsoft XBOX 360 gamepad with the wireless adapter and I was wondering what I would have to install to use them with Ubuntu I do know that when using this on Windows I have to manually install the drivers for the wireless receiver (if that is relevant.) Ring of $\mathbb{Z}_2$-valued functions Let $R =\{f:\{1,2,3,4,\cdots ,10\}\to \mathbb{Z}_2 \}$ be the set of  all $\mathbb{Z}_2$ -valued functions on the set $\{1,2,3......10\}$  of the first ten positive integer. Then $R$ is a commutative ring with point-wise addition and multiplication of functions. Which of the following is true?     1) $R$ has a unique maximal ideal.      2) Every prime ideal of $R$ is also maximal.      3 ) The number of proper ideals of $R$ is $511$.      4 ) Every element of $R$ is idempotent.   R is finite commutative ring so  every prime ideal  is maximlal ideal ,so I think option  2 is true   .But for the other options   I am  helpless  . How would I prove that for all elements of a set {n | n ∈ ℕ ∧ n &gt; 7} (all natural numbers greater than 7), there are multiples of 3 and 5 which, when added up, are equal to that element of the set?  A := {n | n ∈ ℕ ∧ n &gt; 7} ∀ n ∈ A: n = x*3 + y*5   I do understand why this is true:   8 = 1*3 + 1*5 9 = 3*3 + 0*5 ...  15 = 0*3 + 3*5   and this pattern repeats once 16 is reached, as 8 can be replaced with 1*3 + 1*5, so I'd basically have to add 1 to x and y for every time 8 fits in n.  I am however not sure how I can formulate this mathematically correct.  Thanks in advance, CrushedPixel Selecting Unique Elements From a List in C# Do free falling observers see gravitational blueshift? Observers at rest in gravitational fields will see infalling light signals as blueshifted.  Do inertial observers in free fall in a gravitational field see the same shift?  If someone is standing on a cliff at rest in the gravitational field and then steps off, do they instantly see a change in the blueshift as a result of being in free fall in an inertial reference frame? Getting image dimensions without reading the entire file Can the Artificer Artillerist's tiny-sized Eldritch Cannon that is not held in hand still ride or be carried elsewhere on the body? Problem with long chapter title and arsclassica