Since bodies like planets moving around sun perform uniform circular motion where gravitation provides the necessary centripetal force,  so the orbits should be circular   for the gravitational force to be central but as we know the paths are not perfectly circular but elliptical. Why this is so?
This might be a completely wrong question, but this is bothering me since many days ago. Given the mass (Sun) curves the space around it, gravitation is the result of such curved space (Correct me if I am wrong, source: A Documentary film). Given any point on a circle with center same as center of the mass, curvature in the space should be equal (Intuition).   Planets rotate around the Sun because of the curve in the space they should follow a circular path and the distance between planet and Sun should be at a distance.  Given the fact that earth has a elliptical orbit around the sun, and the distance between Earth and Sun varies according to position of the earth. Why do we have a elliptical orbit not a circular orbit.
How to get the list of IP addresses in a LAN? How to get reflections from 3D to show up on real images Cannot create custom config entity fails because ID is blank This is homework. I've tried my best to find the best answer that I could understand and could be accepted by my lecturer.   I've searched my lecture notes, wiki and google to find some good explanation defining solar irradiance. But somehow I still don't understand how I should 'define solar irradiance'. Can someone give me a few good sentences explaining solar irradiance. What are the changes, if any, in a photovoltaic cell (in terms of short-circuit current and open-circuit voltage) if the irradiance is reduced by 50%? How can I search within a manpage? Prove that, for any $n+1$ integers $a_{1},a_{2},....,a_{n+1}$, there exist two of the integers $a_{i}$ and $a_{j}$ with $i \neq j$, such that $a_{i} - a_{j}$ is divisible by $n$.  Please help me about this problem,I know there is lots of answers can find from Google, but I am not really understand them. I hope someone can give me more details explanation. I would really appreciate your help. I'm currently typing a mathematical document which counts many sum symbols. I frequently use the align environment to render equations, although the default behaviour of this environment is to render the equations in displaystyle, which in my opinion wastes vertical space. I therefore have added \textstyle at the beginning of each line of math in this environment, but I'm looking for a more convenient solution.   So is there an environment that is similar to align with the exception it displays textstyle math by default ? Thank you. How do suggested edits work? Here's :        At the moment, the latest entry there is October 13, which would be mistaken to mean October last year (2012), but it actually is October 2010. This applies to all the filters in the activity tab. Do professors care about their rating on websites such as RateMyProfessor or Koofers? I am wondering if a professor is already an Associate Professor, do they still care about their reputation in the eyes of the department considering tenureship is already granted? Reset CSS display property to default value Why does reversing serial upvoting not reverse the Mortarboard badge? user has serial up-voting reversed, but he still have badge Mortarboard.   Is it correct behavior of badges? I suppose it should be reversed too.  And will this 200 daily reputation (2012-03-20) score for the Epic, and Legendary badges? Examples of the Pigeonhole Principle As most of you might know, the Pigeonhole Principle basically  that      If $n$ items are put into $m$ containers, with $n&gt;m$, then at least one container must contain more than one item   It always surprises me how this trivial - and at the same time powerful - idea might be the key in order to solve extremely complicated math olympiad-problems...  Quick and beautiful solutions are characteristic of pigeonhole problems, which are often a three-part process   Recognize that the problem requires the Pigeonhole Principle Figure out what the pigeons and what the pigeonholes might be After applying the pigeonhole principle, there is often more work to be done   I'll illustrate this with an example I've always liked...     (Example-)Problem: Given a $n\times n$ square, prove that if $5$ points are placed randomly inside the square, then two of them are at most $\frac{n}{\sqrt2}$ units apart.   Step 1: This problem can be solved with the Pigeonhole Principle  Step 2: We divide the $n\times n$ square into four $\frac{n}{2}\times\frac{n}{2}$ squares (pigeonholes). Consequently, at least two points (pigeons) are inside the same $\frac{n}{2}\times\frac{n}{2}$ square.  Step 3: The maximal distance between two points in an $\frac{n}{2}\times\frac{n}{2}$ square is the diagonal, which has the length $\frac{n}{\sqrt2}\qquad\square$  Another problem which can be solved with the Pigeonprinciple is the following:     IMO $1972/1$           Prove that from a set of ten distinct two-digit numbers (in the decimal system), it is possible to select two disjoint subsets whose members have the same sum.      At this point, you might have noticed how useful the Pigeonhole Principle can be, if you know how to recognize and use it.     Question: I would like to work on this amazing principle with my students for a week and was, therefore, gathering problems related to the Pigeonhole Principle with beautiful solutions.   Could you suggest some more? Ubuntu won't boot because of lvmetad I've followed this tutorial to install Ubuntu 15.10:    After restarting my computer I got to the grub menu and chose Ubuntu. Shortly after that I got this error:  /run/lvm/lvmetad.socket: connect failed: No such file or directory WARNING: Failed to connect to lvmetad. Falling back to internal scanning.   These messages keep adding up on a black screen every second. After a while,  I get access to the initramfs ash console.  what am I doing wrong? Is "remove" a reserved keyword in Google Chrome? I have written an essay last year, as a personal exercise. I now have a course at uni on the topic and could basically just hand in this essay now, the topic fits perfectly. I have also never submitted this essay to any other course or so.  Could I just hand in this essay, or would I violate some rules with that? Is this maybe already self-plagiarism? Instead of relying on my host to send an email, I was thinking of sending the email messages using my Gmail account. The emails are personalized emails to the bands I play on my show.   Is it possible to do it? Is it required for panel data to use dummy variables? I am doing research considering seven countries and I have panel data. My question is: do I need to include dummy variables every time I use panel data in regression, or is enough to do it as a fixed effect in Stata, without dummy variables? What's a word like "disregard" or "bypass" that means "hides"? Prime factors + number of Divisors I know that one way to find the number of divisors is to find the prime factors of that number and add one to all of the powers and then multiply them together so for example  $$555 = 3^1 \cdot 5^1 \cdot 37^1$$  therefore the number of divisors = $(1+1)(1+1)(1+1) = 2 \cdot 2 \cdot 2 = 8$  What I do not know (and can't seem to find when I look) is WHY this relationship exists or a formula which shows its proof.  Has anyone seen such a formula?