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. T

    C/C++ Its all about C++ Binary Trees

    I'm trying to write an address book that is based on a binary tree. I'm devloping in Visual C++ (I blew up my Ubuntu with the new dist), starting with the basics: #ifndef binarySearchTree_h #define binarySearchTree_h #include <string> #include <iostream> using namespace std...
  2. C

    Varibles/Eclipsing Binary systems

    Hey, What are the most common eclipsing binary stars and variable stars to observe with periods of a few hours? Im observing from Ireland. Thanks
  3. radou

    Group Definition: Closure Not Required?

    In the definition of a group on mathworld, http://mathworld.wolfram.com/Group.html" , implies closure, so, isn't it unnecessary to talk about the property closure in the definition of a group?
  4. C

    Complete preorders (and other binary relations)

    Is there a commonly-used name for a complete preorder (a transitive and total relation, Sloan's A000670 and A011782 for labeled and unlabeled, respectively) within set theory? (Not a total order, mind you -- it need not be antisymmetric.) I've heard the term "weak order", but that's from the...
  5. P

    Need help reading and writing from binary file

    I'm writing a large amount of data to a binary file. Trouble is, I don't know how much until the program finishes executing. Given this, I'd like to rewind back to the beginning of the binary file and write an element indicating how many records I wrote to the binary file - this way I can...
  6. Oxymoron

    Representing Sets as Binary Trees

    I'm using the definition of a full binary tree which is a graph where there is exactly one path between any two vertices, there is a root, and where every vertex has either two children or none at all. If I had the following graph: * that is, just the root, then could I construct the...
  7. S

    How Can I Use a Binary Spatial Data Grid for Vegetation Mapping?

    Hi, Just working on an environmental project about vegetation mapping. I've got a regular grid of points with percentage of plants for each points. I've intepolated the different percentage values to produce distribution maps for each plant. Anyway, now i wonder what i can do if instead of...
  8. G

    How Do You Debug a Parent Method in a Red-Black Tree?

    Hello, I am having some trouble with my red and black tree. I made up a parent method which finds the node before the node and then sets an iterator to that node. The code is below: private RBNode parent(Comparable x, RBNode i) { RBNode tmp = new RBNode(null,null,null); if(i==null ||...
  9. P

    Is Our Sun Part of a Binary Star System?

    http://www.spacedaily.com/reports/Evidence_Mounts_For_Companion_Star_To_Our_Sun.html the above article seems to suggest that we are part of a binary star system. I thought (or rather assumed) that astronomers would have done a thorough scan of our neighborhood by now - so why hasn't anyone...
  10. J

    Seeking 64-bit Linux Compiler for Fortran 95 Binary

    hi, I was wondering if anyone was running 64-bit linux. In particular, I need someone to compile a 64-bit fortran95 binary for me.
  11. J

    Non-Negative Integer Binary Concatenation: Is This an Irrational Number?

    I am interested in the following number which is obtained by concatenting the binary representations of the non-negative integers: .011011100101110111... i.e. dot 0 1 10 11 100 101 110 111 ... This is a little bigger than .43 and I assume it irrational since no pattern of bits repeats...
  12. C

    Calculating Mass of Stars in a Binary System

    Q: Suppose that a binary star system consists of two stars of equal mass. They are observed to be separated by 340 million kilometers and take 5.0 Earth years to orbit about a point midway between them. What is the mass of each? I figured out that: mass=4pi^2(radius)^2/Gravitational...
  13. N

    Gravitational Forces of binary star

    I have this problem: The question says: A binary star system has two stars, each with the same mass as our sun, separated by 1x10^12m. A comet is very far away and essentially at rest. Slowly but surely, gravity pulls the comet toward the stars. Suppose the comet travels along a straight line...
  14. G01

    Distance between Binary Star Systems

    A binary star system has a period of T=90 days. Each star is 2X the mass of the sun. They rotate like a dumbell around the center of mass. what is the distance d between them? OK first, Mass of sun = 1.99 X 10^{30} kg Lets concentrate on one of the stars rotating around the center of mass...
  15. S

    Digital circuit: multiplying 2 binary numbers

    "Design a digital circuit that multiplies two binary numbers by the repeated addition method (to mult. 5x4, the digi system evaluates the product by adding the multiplicand fours times: 5+5+5+5=20). Let the multiplicand be in register BR, the multiplier in reg AR, the product in reg PR. An adder...
  16. B

    Why does the professor stop converting at the fourth digit?

    I am sorry to bother you people again and I don't really know if this is the right place to put it. my great professor shows us in pdf format that 0.83(decimal)=0.1101(binary) because 0.83 x 2 = 1.66 carry 1 0.66 x 2 = 1.32 carry 1 0.32 x 2 = 0.64 carry 0 0.64 x 2 = 1.28...
  17. M

    Binary to decimal confusion signed numbers

    binary to decimal confusion! signed numbers! OKay this makes no sense to me... THe directions say: The following binary numbers have a sign in the leftmost postion and if negative, are in 2's complement form. Perofrm the indciated airthmeic operations and verify the answers. So i have...
  18. M

    Binary adding/subtracting, am i doing this right?

    Hello everyone, I'm alittle confused, we have an exam tomarrow and i want to make sure I'm doing this right. I'm suppose to do the following: Perform the indicated subtraction with the following unsigned binary numbers by taking the 2's compliment of the subtrahend. so for one of them...
  19. I

    Multiplication in R=\mathbb{Z}_5 \times \mathbb{Z}_5: Operations and Definitions

    How is multiplication in R=\mathbb{Z}_5 \times \mathbb{Z}_5 defined? if (a,b) and (c,d) is in R, what's (a,b)(c,d)? (ac,bd)?
  20. B

    Proof of gcd and lcm properties for prime factorizations

    If n has k digits in its binary numeral, show that there are at most 2^k/2 numbers n. Can there be exactly 2^k/2? I tried to understand this question with an example so I took n=36 which has the binary number 100100; k=6 but 2^k/2n gives 2^3 36 but 8 is not less than or equal to 6? Any help...
  21. J

    Astrophysics - Can there be a contact binary from white dwarfs

    Question: A typical white dwarf has a mass of 1 solar mass and a radius of 10 thousand km. A typical neutron star has a mass of 1.5 solar masses and a radius of 30km. Given that there's a natural speed limit in Nature, namely the speed of light, is it possible to have a contact binary...
  22. M

    Is the LuniSolar theory a legitimate scientific theory?

    Any thoughts on this, fellas? I have not read the book nor viewed the documentary (narrated by James Earl Jones) but I have read a few articles, and, well, precision is a complex sport, so I am intrigued with the notion...I am no astronomer though, only have a layman's fascination...
  23. F

    Request for help - math problem using binary code

    Hello I have math question that I am struggling with that apparently can be solved using code (or reasoning - I tried that and mine didn't work. GO figure :confused: ). Can anyone help me out? Here is the question: A coffee club with 8 membres meet every MOnday Wednesday and Friday...
  24. M

    Decimal to binary, Decimal to Octal confusion

    Hello everyone, I realize this is really basic stuff and mainly pointless considering calculators can do it for you but I'm still wondering on why this isn't working out right. I'm in a digital design class and he showed us a method for converting decimal to binary and it seemed easy and seemed...
  25. B

    Let R be a binary relation on a set X

    i have a statement: Let R be a binary relation on a set X. R is reflexive if (x, x) belongs to R for each x belongs to X. what is a binary relation? what does the (x, x) mean? how can x be both the input and output? and finally...i see the book i have has IdX where X is a subscript. and...
  26. W

    Stability of Binary System with Anti-Particle Circulation in Quantum Physics

    Hi, I have a question about anti-particle. In the modern physics, we "know" (I don't think we really know it) the reason, why the shell electron did not collapse into its ion core, because of quantum theory. But is it possible a electron "circulate" a positron without annihilation. Is there...
  27. E

    What is exactly the definition of a complete binary tree?

    Hi Ho! ^_^ Actually, what is the definition of a complete binary tree? I have searched the Internet and come up with several definition. This problem is confusing enough. According to http://planetmath.org/encyclopedia/CompleteBinaryTree.html , "A complete binary tree is a binary tree...
  28. M

    Binary Sequence: What Comes Next?

    Not sure if this has been done... I sort of discovered this sequence myself, but who knows... 01000101010001000100010101000101... What comes next?
  29. B

    Proof of Binary Quadratic Forms and Modulo Squares with Hint

    show that if a number n is represented by a quadratic form f of discriminant d then 4an is a square mod |d|. I have no clue how to even start this proof. I tried using the jacobi symbol.. but it's not gettin me anywhere. Could someone give me a hint.. :confused:
  30. E

    Efficient 4-Bit Binary Subtractor Design Using Half-Adders and Full-Adders"

    Hello folks : the task is to design a circuit which subtracts 4 bit binary number a3,a2,a1,a0 and b3...b0. the MSB is a sign bit. Assume that you are given half-adders and full-adders, i.e. you don't have to design the logic of the half-adder or full adder chip. the two numbers are fed...
  31. N

    Proving the Number of Nodes in a Full Binary Tree

    I need to prove that for any full binary tree with N\geq1 leaves, that it has 2N-1 nodes. I can see this when looking at a tree, but I can't figure out how to prove this.
  32. Clausius2

    Binary Gas Mixture Physical Properties & Local Viscosity, Diffusitivity

    I am searching for the physical properties of a binary gaseous mixture. In particular, I would want to know the local viscosity \mu and local mass diffusitivity D of any binary mixture of gases, as a function of the local mass fraction of each other. I have not found nothing in Google...
  33. L

    Binary Stars: Moment of Inertia & Angular Momentum

    two stars, A and B, are in circular orbit of radii r1 and r2, respectively, about their common center of mass. each star has the same period of revolution T. Determine expressions for the following two quantities in terms of the stars' masses, radii and T. 1- the moment of inertia of the...
  34. D

    What is the concept of concentrated mass?

    A little confused, could someone explain what it means when it is said that "the point in a body or a system of bodies, at which the total mass of the body or system may be regarded as concentrated".(definition of Center of mass) What does it mean concentrated? I'm trying to understand the...
  35. M

    Exploring Binary Planetary Systems

    <Hmm. I just realized that this post would be better suited for the "Celestial Mechanics" forum. Would you mind moving this post, since it appears that I am unable to do so myself without posting twice?> To begin with, does anyone know of the confirmed existence of or believe in the...
  36. F

    Java Java AVL Tree Library: Simplifying Binary Search Trees for Student Storage

    Is there a library in java I can use to make AVL trees. See we have this project where we have to store students in a Binary search tree and then have access to their stuff... anyway is there a structure I can just import to be able to use it... or do I have to implement my own generic tree?[
  37. V

    Binary pulsars and general relativity

    hi just wondering if anyone knows some interesting things about binary pulsars in relation to general relativity. i have to give a short presentation on the topic and need some ideas on what to talk about thanks in advance
  38. C

    Exploring Binary and Hexadecimal Numbers: Examples and Explanation

    Hello all I need help understanding binary and hexadecimal numbers. What exactly are they? Could you give me some examples? Thanks
  39. D

    Convert octal to hex, w/out converting to Binary

    I have been trying to convert a from octal to hex and hex to octal without using binary. I believe the method is called repeated divison. Example of problem I am trying to solve, Convert 173 octal(123 dec) to hex 173 oct / 16 oct = 10 oct remainder 13 oct...
  40. X

    Convert Decimal to Binary - Get Help Here

    hi! does anybody know how to convert a fraction(deciaml) to Binary? for example how can we convert 0.16 to Binary? thx for helping
  41. P

    Create 8-bit Binary Decoder Circuit w/3 Mechanical Switches

    How difficult would it be to create a circuit that uses 3 mechanical switches as inputs to light up 8 LEDs for the binary combinations? This is for my electric circuits class. I've done one for Logic class, but I was able to use Logic gates and some other extra equipment. So any hints on...
  42. C

    Proof Involving Binary Operators

    I am trying to prove that A union (B intersection C) = (A union B) intersection (A union C). In other words, proving one of DeMorgan's Laws. I have gotten this far, and not sure if I'm right thus far: Let x belong to A union (B intersection C). Then x is in either A or in (B intersection C)...
  43. N

    How many binary strings of length 10 contains exactly two 01?

    Hi all! I'm in serious need of some help. The question: How many binary strings of length 10 contains exactly two "01"? My idea was to weld together 4 bits to 2 "01". That way, there's \frac{8!}{2!} strings with at least 2 "01". But there are a bunch of strings with more than 2 "01" in...
  44. Labguy

    Will Gravitational Wave Detectors Challenge Current Theories on Binary Stars?

    Some "new" relaeases of interest also here in General Astronomy. Merits discussion in this forum too, I think. Go to PF post: https://www.physicsforums.com/showthread.php?s=&threadid=12315
  45. V

    BINARY LAW of BACKGROUND RADIATION

    The idea of this work has appeared in 2002. At mathematical simulation of processes of mechanical resonance in classical objects of the ring form we have confronted with inexplicable effect. The computer program "drew" the graph of the smooth function with periodically iterating peaks. This...
  46. wolram

    Kuiper Belt Binary Pairs: Existence Confirmed?

    i remember a referance to, binary pairs in the kuiper belt, i can not remember if a mass for the objects was given or orbital distance, my memory may be fading or wrong, can someone comfirm or dispute the existence of these objects?
  47. S

    Calculating the Period of Binary Stars

    Hello. Two binary stars (m1 and m2) orbit each other around their center of mass. They orbit in circles of radii r1 and r2. I am to show that the period is given by T2=4pi2(r1+r2)3/(G(m1+m2)) The mutual force between m1 and m2 is F=Gm1m2/(r1+r2)2 Considering m1, the acceleration of m1 is...
  48. L

    Calculating Mass of Equal-Mass Binary Star System

    suppose that a binary star system consists of two stars of equal mass. they are observed to be separated by 360 million km and to take 5.0 Earth years to orbit about a point midway between them. what is the mass of each? P. 135 "Physics: Principles With Applications" Fourth Edition. Giancoli...
  49. A

    Is a*b = |ab| a Group Operation?

    [SOLVED] Binary Operations I believe I understand the critera to see of something is a "group" 1.It must be binary 2.It must be associative 3.Must contain a Identity 4.Must have a inverse My question is the how to read a problem. For example: All real numbers minus zero under the...
  50. M

    Question on binary stars & binary stars

    Hi. What a great forum, so many interesting things I am facing a problem with the working out for my last question in my practice paper, for my mid-year examinations. i don't know how to write the notation here, so i have just attatched a screenshot, i hope u don't mind. i just have...
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