What is Binary: Definition and 603 Discussions

A binary star is a star system consisting of two stars orbiting around their common barycenter. Systems of two or more stars are called multiple star systems. These systems, especially when more distant, often appear to the unaided eye as a single point of light, and are then revealed as multiple by other means.
The term double star is often used synonymously with binary star; however, double star can also mean optical double star. Optical doubles are so called because the two stars appear close together in the sky as seen from the Earth; they are almost on the same line of sight. Nevertheless, their "doubleness" depends only on this optical effect; the stars themselves are distant from one another and share no physical connection. A double star can be revealed as optical by means of differences in their parallax measurements, proper motions, or radial velocities. Most known double stars have not been studied adequately to determine whether they are optical doubles or doubles physically bound through gravitation into a multiple star system.
Binary star systems are very important in astrophysics because calculations of their orbits allow the masses of their component stars to be directly determined, which in turn allows other stellar parameters, such as radius and density, to be indirectly estimated. This also determines an empirical mass-luminosity relationship (MLR) from which the masses of single stars can be estimated.
Binary stars are often resolved as separate stars, in which case they are called visual binaries. Many visual binaries have long orbital periods of several centuries or millennia and therefore have orbits which are uncertain or poorly known. They may also be detected by indirect techniques, such as spectroscopy (spectroscopic binaries) or astrometry (astrometric binaries). If a binary star happens to orbit in a plane along our line of sight, its components will eclipse and transit each other; these pairs are called eclipsing binaries, or, together with other binaries that change brightness as they orbit, photometric binaries.
If components in binary star systems are close enough they can gravitationally distort their mutual outer stellar atmospheres. In some cases, these close binary systems can exchange mass, which may bring their evolution to stages that single stars cannot attain. Examples of binaries are Sirius, and Cygnus X-1 (Cygnus X-1 being a well-known black hole). Binary stars are also common as the nuclei of many planetary nebulae, and are the progenitors of both novae and type Ia supernovae.

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  1. E

    Find inverse function of binary entropy

    Homework Statement Find the inverse function f^{-1} of the binary entropy f (given below) on the domain of definition [0;1/2[ (i.e. where f is continuous strictly increasing). The function f is given by: f(x)=-x\log(x)-(1-x)\log(1-x) (where \log is the logarithm base 2) Homework...
  2. B

    Doing binary arithmetic in Windows Calculator and

    I was doing some conversions from binary to decimal and vice versa today using Windows Calculator and I noticed the following, if I multiply B11111111 and B11111111 I get the following: B1111111000000001. Uhhh...great! What's going on here? It looks like it's rolling over the 8 LSB when it...
  3. Q

    Binary Stars and Their Planets

    I have a question regarding binary or multiple star systems and their [hypothetical] orbiting planets. I am curious if it is common (or even possible) for one or more of the orbiting planets to constantly switch the star they are orbiting, as in a figure eight shape. Can the stars "trade the...
  4. R

    Obtain Binary String: X + Y - Z | Binary Addition and Subtraction Rules

    Obtain Binary String ? Homework Statement Given That X=10111 ,Y=101; Z=1001, obtain binary strings that represent P Q where P=X+Y and Q=P-Z; state clearly each rule you apply . Homework Equations The Attempt at a Solution Hey up to the extent which i know i did this as a...
  5. R

    Representing Sets in binary string?

    Homework Statement X={4,8,12,16} Y={2,6,10,12} K=X U Y(union) They asked to represent X and Y on K using binary String >i don't know how to do this please help .What is meant by Binary String ? Homework Equations The Attempt at a Solution
  6. S

    Calculating Center of Mass in Binary Systems

    What is the correct formula for center of mass of a binary system? I had seen that it is R=\frac{m_{1}r_{1}+m_{2}r_{2}}{m_{1}+m_{2}} If that is the right equations what exactly does r one and two stand for? I had also seen a much more complicated formula. Side note: This is not...
  7. T

    Synchronous non-sequential binary counter

    I am required to design a synchronous binary counter using jk flip-flops giving the count sequence: 0, 8,9,4,7,2,1,0 I have derived the excitation table using 4 jk flip-flops, however when using karnaugh maps to minimise or trying to use the unminimised function in a circuit I am unable to...
  8. M

    Please help - Binary Relations driving me utterly insane

    Homework Statement If R and S are two equivalence relations on the same set A, we define R ◦ S = {(x, z ) ∈ A × A : there exists y ∈ A such that (x, y) ∈ R and (y, z ) ∈ S }. Show that the following conditions are equivalent: (i) R ◦ S is a symmetric relation on A ; (ii) R ◦ S is a...
  9. F

    Orbital period variation in binary system

    Homework Statement Using the conservation of angular momentum and Kelper's third law, show that the relative change in orbital period produced by mass transfer is given by 1/P * dP/dt = 3 dM1/dt * (M1 - M2)/(M1M2) Homework Equations L = mu * sqrt(GMa) P^2 = (4*PI^2)/(G(M1+M2)) * a^3...
  10. M

    Semimajor axis of binary system help

    Default semimajor axis of binary system help hi, I'm not sure if I am posting in the right place but I could really do with some help figuring out the semi major axis of a binary star system. I have been give the mean distance of each star from the center of mass (star A = 3.96 AU star B =...
  11. hxtasy

    Need a cheap binary AM transmitting circuit

    Need a cheap "binary" AM transmitting circuit I'm posting this in a forum because I'm not really sure what to search for online. I need a circuit that transmits a one or a zero, basically I have a sensor and i want it to turn something on or off remotely. I was thinking about using an AM...
  12. S

    C/C++ Find Nearest Record in Binary Search Tree | C++ Implementation

    Hi everyone, i have a binary search tree proble, please help me.. * Find record with key x in the tree. If not found, return the two nearest records in the tree (in alphabetical order) * Return values: * FOUND: Return the address of the node in the tree which contains key x, set n1 =...
  13. K

    Hexa to Decimal Conversion, Binary to Decimal Conversion?

    Homework Statement 1) How to convert 101010.0101B to decimal? 2) and Hexa number 17DB.C to Binary. 3) and lastly, -101 (decimal) to the 2's complement form. Homework Equations The Attempt at a Solution for the first one, clearly my problem lies at .0101B. I thought it's...
  14. Y

    Problem about binary star system

    Problem about "binary star system" Homework Statement About half of the visible "stars" are actually binary star systems, two stars that orbit each other with no other objects nearby. Consider the motion of the center of mass of a binary star system. For a particular binary star system...
  15. F

    Comp Sci How Can I Modify a C++ BST Implementation to Check for Duplicate Values?

    Homework Statement I am working on an assignment in which I have to add a method to my BST class which checks if a binary tree object is in fact a Binary Search tree. So (1) A left child must be smaller than the parent (2) A right child must be larger than the...
  16. V

    Calculate the Masses of two binary stars

    Homework Statement I am trying to understand the following example question in my course book, The answer is actually given but i don't understand how they got to it, i would like someone to give me an idea how this has been worked out In the Sirius Binary system the orbital period is 50...
  17. S

    Adding Binary Fractions: A Simple Guide to Calculating and Understanding Results

    10.00 + 00.11 = 10.11 ...am i right? how about if.. 0.1 + 0.1 = ? is it equal to 1.0 ? thx for helping =)
  18. Z

    Inverse (LS) problem for binary data

    As per topic. Is there any well established method for solving linear systems for binary data? pardon if this is in wrong cathegory, english is not my first language and I'm not that well aware of the english terms. i.e. the classical g = M*f problem, where g is measured data and we want...
  19. K

    Newton's 3rd Law applied to binary stars

    Below is a question I recently got wrong, and the (automated) feedback. Since the stars are in a stable configuration, I realize that the forces must be equal, but I thought that the differing gravitational forces were balanced by the centripetal forces of the orbit (the smaller star being...
  20. M

    How can Binary Relations on a Set with 3 Elements be Symmetric and Reflexive?

    Homework Statement Let A = {a, b, c} be a set with 3 elements. (a) How many binary relations are there on A? (b) How many binary relations on A are reflexive? (c) How many relations on A are symmetric? (d) How many binary relations on A are both symmetric and reflexive? Homework...
  21. R

    Binary Stars: Equal Mass, 350 Million km Separation, 5.4 Earth Years Orbit".

    Suppose that a binary-star system consists of two stars of equal mass. They are observed to be separated by 350 million {\rm km} and take 5.4 Earth years to orbit about a point midway between them. I got 1.1x10^29 as my answer, but it is incorrect. Can anyone help me out?
  22. J

    Converting Equations to Binary & Irrational Numbers

    ... can we convert this equation to binary notation? Also another one, would an irrational number be irrational in any number format?
  23. S

    Odd-Numbered Binary Inputs & XOR Gates

    Hi i am a theoretical physicist and am trying to understand electronics. (not a very bright idea) basically my question is how can we use 2 input xor gates to give a high output when an odd number of bits are high in a four bit binary. also what would such a circuit look like.
  24. H

    Abstract algebra / binary operation

    Homework Statement a. In each case a binary operation * is given on a set M. Decide whether it is commutative or associative, whether an identity exists, and find the units. M=N(natrual); m*n = max(m,n) b. If M is a moniod and u in M, let sigma: M -> M be defined by sigma(a) = ua for all a...
  25. I

    C++ Binary Search Help - Find #23

    I have to write a C++ binary search code where it generates the first 100 odd numbers and the search is used to the find the # 23 any help? I am ompletely lost
  26. O

    Determining Thermal Coefficient of Binary Solvent Mixture

    Hello, Currently, I am working on a science project involving the creation of silica aerogels through the process of freeze-drying. As a result, i need to experiment with mixtures of solvents with low thermal expansion coefficients (so the crystallization of the solvents will not damage the...
  27. S

    Fortran 90 (need to read in binary data files into arrays)

    Hello, I am currently doing a 3rd year undergrad project on forward radio meteor scatter the problem involves the following: I have over 80Gbs worth of 10 second data blocks of recorded radio input. They are stored as date stamped .bin files in binary format, each of order 1700kb or...
  28. C

    Binary Decimals - Dual Expansion

    Hi, I'm trying to prove that there's a bijection between the open interval (0,1) and the set of all sequences whose elements are 0 or 1 in order to show cardinality continuum. So let C={a1, a2, a3,...|ai is either 0 or 1} which is the set of all sequences of 0's and 1's and let...
  29. G

    Astrophysics - Apparent Magnitude of stars in a close binary system

    Homework Statement 2 solar type stars are in a close binary system. Each indivual star has an apparent brightness of m = 10 mag. Determine the apparent magnitudes of the combined system of the 2 stars assuming they cannot be resolved as individual objects. Determine the minimum brightness...
  30. T

    Commutative Binary Operations on Sets of 2 and 3 Elements

    Homework Statement How many different commutative binary operations can be defined on a set of 2 elements? On a set of 3 elements? The Attempt at a Solution I do not understand the question. Seems like an infinite number.
  31. J

    Solve Binary Operations Question: Prove Isomorphism

    So I have really been struggling with this question. The original question said: The map \varphi:Z->Z defined by \varphi(n)=n+1 for n in Z is one to one and onto Z. For (Z, . ) onto (Z,*) (i am using . for usual multiplication) define * and show that * makes phi into an isomorphism. I know that...
  32. I

    Binary operations, subsets and closure

    Homework Statement 1) Let S be a set and p: SxS->S be a binary operation. If T is a subset of S, then T is closed under p if p: TxT->T. As an example let S = integers and T be even Integers, and p be ordinary addition. Under which operations +,-,*,/ is the set Q closed? Under which...
  33. P

    Calculating Pi in Binary: How Many Decimals Do I Need?

    My first topic here. Here goes I've written a small program that first calculates pi in decimal and then changes it into binary. But as you know there's no accurate binary presentation even for 0.1 so I just can't change the whole 20000 decimal representation of pi into binary. I there for...
  34. T

    Java Binary Tree java help please, with getRight and getLeft subtree.

    I can't figure out how to get these 2 methods to work. In my assignment description it says public BinTree getLTree() Get a reference to the left subtree. If this is not possible to do then throw an IllegalArgumentException. NOTE This routine returns a BinTree, not a Tnode. You...
  35. M

    Using the definition of the binary product

    Prove or find counterexamples: If A x B = empty set then A = empty set or B = empty set.
  36. T

    What is a bilateral binary rotation?

    I may be posting to the wrong forum, if so, please advise. I'm reading a book on rotational symmetry and its relationship to quantum mechanics. The author is talking about rotations of a unit sphere, in particular binary rotations, i.e. rotations of 180 degrees. He says "If a rotation [he...
  37. U

    Why Is 2r Used in Calculating the Masses in Plaskett's Binary System?

    hey i've been having trouble understanding a part in this question. i'll just map out the basics to the question: 2 stars with a velocity of 220km/s are orbiting at equal distance. the masses of the stars are equal. period = 14.4 days it asks to find the mass of each star. i understand that...
  38. T

    Where can i find binary tree recursion manual

    where can i find a tutorial on binary tree recursion i searched in google: http://www.google.co.il/search?hl=iw&sa=X&oi=spell&resnum=0&ct=result&cd=1&q=binary+tree+recursion&spell=1 and there is no tutorials for this kind of stuff ??
  39. S

    Binary Operation: Find Identity Element & Inverse

    Homework Statement A binary operation is defined by: the set of 2 x 2 matrices with real entries under matrix multiplication. Find the identity element and the inverse. Homework Equations identity element: a\oe=e\oa=a inverse: a\ob=b\oa=e The Attempt at a Solution I think...
  40. H

    Calculating the motion of binary stars

    This is more of general question, but i am working on a project that involves binary stars. Basically, i am capturing data through a telescope, and i was wondering if i had all the parameters, how could i project, or calculate the motion of a binary star in terms of speed and direction. Any...
  41. thenewmans

    Binary cycle power plants – One small part I don’t get

    I don’t get how a http://www1.eere.energy.gov/geothermal/powerplants.html#binarycycle" keeps the fluid flowing in one direction. My guess is it has something to do (1) with the condenser and (2) with a pump thrown in. The problem with a pump is that it must use up as much energy as the heat puts...
  42. A

    Is a Full Binary Tree's Internal Path Length Equal to Its External Path Length?

    The internal path length of a full binary tree is the sum, taken over all internal nodes of the tree, of the depth of each node. Likewise, the external path length is the sum, taken over all leaves of the tree, of the depth of each leaf. Consider a full binary tree with n internal nodes...
  43. Y

    Binary Tree Algorithms: Generating Random Trees

    Does anybody know where i can get info on generating random binary trees? I've been checking a lot of publications and have come across the yule process and uniform method. The trees they are being applied to, however, are speciation trees and most of the stuff is incomprehensible to me. Can...
  44. U

    # of different binary ops. on a set S

    Bear with me, Haow mainy difffferent biiinary operarations can be dephined on the set S when it has 1,2,3 or n elementz? Sorry I typed so wierd, I don't want anybody finding this answer. Can I confirm with you guys/gals in here that the answer is (hopefully) 1 elem = 1, 2 elem = 2^4...
  45. E

    How Can I Convert Binary to Decimal?

    I'm trying to figure out how to convert from decimal to binary. I've read a few explanations but I still don't understand. Could someone please help? The method I've read about invloved dividing the number you want to convert, by 2 each time, and looking at the remainder.
  46. M

    Fortran Problems reading binary file in FORTRAN

    I am having problems reading a binary file in FORTRAN. I know that the file was generated by the code below: open(7,file='hctd1_kxx.dat',form='unformatted') ... write(7) iscl write(7) inode,npoints write(7) (kxm(i)*(10**(prop(i))),i=1,npoints) close(7)...
  47. G

    Converting Binary to Decimal: Calculating 2/3

    Homework Statement Calculate the binary equivalent of 2/3 out to eight places. Then convert from binary to decimal. How close is the result to 2/3? The attempt at a solution I new to this and I am still trying to figure this stuff out so if someone could walk me through this that...
  48. P

    How Do We Calculate the Mass of Binary Stars Like Centauri A and B?

    Homework Statement Centauri A and Centauri B are binary stars with a separation of 3.45x10^12m and a period of 2.52x10^9s Assuming the two stars are equally massive (which is approximately the case), determine their mass. Homework Equations ( m1 + m2 ) P^2 = ( d1 + d2 )^3 = R^3...
  49. N

    Convert octal to hex, w/out converting to Binary

    I am trying trying to convert a from octal to hex and hex to octal without using binary/dec transform using repeated divison... Logically I thought I could use the hex base in octal for repeat division which is 20 oct Example of problem I am trying to solve, Convert 326 octal to hex (ans...
  50. G

    Binary Star System Data - Get Answers Here!

    Where can I get some data for Binary Star system? Thanks in Advance
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