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. BastianQuinn

    Ring Suspension Between Binary Masses

    I'm having trouble conceptualizing the variables involved with this system, and I was wondering if some expertise might make the problem much simpler than I believe it to be. Two massive spherical bodies (Osmium, minimum radius 900km, 5.08m/s^2 surface gravity) orbit each other with a solid or...
  2. S

    MHB Equivalences and Partitions and Properties of binary relations

    If someone could explain some of the steps needed to work out these 2 questions it would be much appreciated!
  3. B

    Binary classification: error probability minimization

    Typically in problems involving binary classification (i.e. radar detection, medical testing), one will try to find a binary classification scheme that minimizes the total probability of error. For example, consider a radar detection system where a signal is corrupted with noise, so that if the...
  4. Duderonimous

    Subtraction using 8-bit binary 1's complement

    Homework Statement Perform the indicated subtraction using 8-bit binary in 1's complement: (22-59)10 (-11-64)10 Homework Equations i. Convert the numbers from decimal to binary ii. Take the ones complement of binary representation of any negative numbers iii. Add the two numbers together add...
  5. Steven Ellet

    Converting Program X to Binary: How to Achieve Optimal Efficiency?

    If I have program X how do I get it in binary form?
  6. caffeinemachine

    MHB Finding an Infinite Binary Sequence with Average Frequency of 1's = p

    The following question came up when me and a friend of mine were discussing some basic things about probability:Let $p$ be a real number in $[0,1]$. Does there exist a sequence $(x_1, x_2, x_3, \ldots)$ with each $x_i$ being either $0$ or $1$, such that $$ \lim_{n\to \infty} \frac{f(n)}{n} =p...
  7. E

    Metric matrix for binary star system?

    What does the metric matrix look like for a binary star system? Does each follow its usual geodesic about the other? It seems like the solution would have to be different somehow than that for a tiny planet circling a big sun.
  8. NaughtyBear

    Programming Question (Python) - Boolean Binary Search

    So I am in my Intro to CS course and they are going over Binary searches via an algorithm to search for simple things. The code goes as this: Set first to 0 Set last to length-1 Set found to FALSE WHILE (first <= last AND NOT found) Set middle to (first+last)/2 IF...
  9. B

    Tight binding s-orbital for 2D binary compound

    Hi guys! I'm new to the forum, i hope you can help me with this trouble! it really is important =D i have a 2D binary compound AB (made of one of the 100 family of planes of a rocksalt structure) and i am asked to "consider a single s-orbital on each atom (atomic energies Ea,Eb) and nearest...
  10. 2

    Confused about binary star systems?

    I was thinking about the motion of two stars in a binary star system, but there is something I cannot quite figure out. Suppose you have a binary star system with two stars masses m1 and m2 with m2>m1 so that m2 is closer to the centre of mass of the system. Then when the two stars are as far...
  11. C

    MHB How Can Binary Integer Programming Optimize Subject Distribution in Schools?

    I am about to do a paper about distributing subjects to students with the constraints on: number of subjects that the student need, number of students whom these subjects will be distributed to, and the number of students that every subject can handle (for example, 50 for math 1 and so on)...
  12. W

    What happens in the center of mass of binary star system ?

    Good night! Please, what happens to an object (eg a spaceship) placed exactly in the center of mass of a binary star system (composed by two similar stars)? Would it be compressed by a huge gravitational mass (something like the mass of both stars)? Would it be stretched and torn? Or would it...
  13. M

    Binary Star Inclination Angle probability distribution

    Can someone explain why the probability of the inclination angle of a binary system being less than i_0 is 1-cos(i_0) i.e. why the fractional distribution of binary stars is df = sini * di, where i is the inclination angle? Where does the sin i come from? Why is not not uniformly distributed...
  14. L

    Binary Stars and Apparent Magnitudes

    Homework Statement A binary star system at a distance of 85pc consists of two stars of equal luminosity that are so close together that they are observed in a telescope as a single image. If the apparent magnitude of the two stars combined is 10.7 what would be the apparent magnitude of just...
  15. ChrisVer

    Book recommendation on Binary systems

    I am looking for books that explain the binary (stars or black holes or whatever) systems in a good (introductory if possible) and/or extensive way... Thanks :)
  16. Silicon Waffle

    C/C++ [C++] Reading a binary file into a byte array

    I have to read a binary file into a byte array and chop it wherever I like. I'd like to use a vector of char to do this. But reading some resources from known people, I find they tend to use char* or char []. Using a vector of chars seems easier for retrieval of any block of bytes. Which means...
  17. Henry R

    MHB How to Build a Binary Search Tree with Given Data?

    Draw a Binary Search Trees (BST) produced when data containing 30,40,50,60,10,20,55,15 is inserted one by one. Thanks.
  18. N

    How programming interacts with transistors

    Forgive the broadness of the question. I know this is a huge concept which entire books have been written about. I am an amateur computer programmer entering my first object-oriented class soon and want to get some things out of the way. When I write lines of code how does the computer know what...
  19. evinda

    MHB Deleting Leaf Nodes from an Ordered Binary Tree

    Hi! (Nerd) Given a tree, I want to write an algorithm, that deletes from each node, from the corresponding ordered binary tree, the rightmost child, that is a leaf. That's what I have tried: Algorithm(NODE *P){ if (P==NULL) return error; if (P->RC!=NULL) P=P->RC; if (P->LC!=NULL)...
  20. evinda

    MHB Computing Binary Tree Sums without Globals/Statics

    Hi! (Wave) I want to write an algorithm, that counts the sum of the keys of the nodes of a binary tree, without the use of globals and statics. That's what I have tried: S(NODE *P){ if (P==NULL) return 0; int m=P->data+S(P->left); int n=m+S(P->right); return n; Could you tell me if it...
  21. evinda

    MHB Finding Depth of Perfect & Complete Binary Trees

    Hi! (Wave) How can we find the depth of a perfect binary tree and how of a complete one? (Thinking) Since a perfect binary tree is a full binary tree, at which the leaves have the same depth, I thought that we can find the depth, by just looking at the leftmost nodes, like that...
  22. evinda

    MHB Checking if a Binary Tree is Full: A Hint

    Hello! (Smile) I want to write an algorithm, that checks if a binary tree is full or not. Could you give me a hint how I could do this? (Thinking)
  23. evinda

    MHB Drawing Binary Tree: Exploring Pre-Order & In-Order Traversal

    Hi! (Smile) I am looking at the following exercise: It is given a binary tree with 8 nodes and keys 2,4,6,8,10,12,14,16.The in-order tree traversal gives this order: 2,4,6,8,10,12,14,16. The pre-order traversal gives the order: 10,8,2,6,4,16,14,12. Draw the tree. Explain how you drawed it...
  24. evinda

    MHB Divide Binary Search Tree at Key k: Algorithm & Analysis

    Hello! (Wave) Given a binary search tree $B$, I want to write an algorithm, that divides $B$ into two new trees $B_1, B_2$, so that the first one contains all the keys of $B$ that are smaller than $k$ and the second one contains all the keys of $B$ that are greater than $k$. Hint : Execute a...
  25. TheSodesa

    Problem related to the center of mass of a binary star.

    So here's my problem: The distance between two stars is constant(d = 4,3 * 1010m), and they have a common center of mass. Ms = mass of our star, ma = 0,82 * Ms and mb = 2,2 * Ms. What I'm supposed to do is calculate the period of orbit of both stars, which is the same for them both, since the...
  26. evinda

    MHB Analyzing Time Complexity and Memory of Binary Search Algorithm

    Hello! (Wave) I want to show that the $T(n)$ of the following algorithm is equal to $O(\log n)$. How can we do it, now that we have if, else conditions? (Thinking) int BinarySearch(int A[1…n], int y, int low, int high) { if (high < low) { return -1; //not found } mid = low + (high -...
  27. I

    MHB How Do You Correctly Subtract Using 1's and 2's Complement in Binary?

    (Wave) i have to subtract binary numbers using the method where you take the 1's complement and then the 2's complement. but I am doing something wrong. say for example 11-1. take 1's complement of 1 which is 0 and then take the 2's complement by adding 1 so 0+1=1 and now you go back and add...
  28. Lolligirl

    MHB Designing an NFA that accepts binary strings divisible by 5 or 6

    Hello everyone! I'm trying to make a transition diagram for an NFA that accepts strings that are either divisible by 5 or by 6. Here's the specific question: Question: Present a transition diagram for an NFA that recognizes the set of binary strings that starts with a 1 and, when interpreted as...
  29. R

    Will the future quantum computers use binary, ternary or quaternary?

    Hello. Our current computers use bits, so they use the binary numeral system. But I heard that the future quantum computers will use qubits instead of simple bits. Since in the word "qubit" there is the word "bi" I first thought that this meant that quantum computers would use binary (base...
  30. C

    Converting .11111 to binary w/o converting to fraction

    Homework Statement Imagine any recurring decimal in base 10, call it X. examples: .1111111111... .2222222222... .23232323... my question is - can you convert it to binary without rewriting X in fractional form. I know how to do it in fractional form. I know how to convert it to fractional form...
  31. gfd43tg

    Binary Search Tree Homework - Setup BST & Write Functions

    Homework Statement Binary search trees In these problems you will set up a binary search tree and write some associated functions that make the search tree useful. Loading the data file students.mat (downloaded with this assignment) places a cell array called Students in the workspace...
  32. T

    MATLAB MATLAB : How to find the line of best fit through a binary image?

    I have found the 2D Fourier transform of a figure and then changed it to a binary image (attached). I want to find the line of best fit through the longest "axis"? of this figure. What would be the simplest way to accomplish this?
  33. A

    MHB Proving Binary Relations: R & S

    Hi, I'm currently stuck on a few questions regarding binary relations as I'm unsure on how to prove their properties. R is defined on N by aRb if and only if a <= b and b <= a+5 Is R reflexive, symmetric, antisymmetric, transitive? S is defined on Z (union) {x + 1/2 : x is an element of all...
  34. Q

    Polarity of the Binary Halogen Acids

    Does the polarity of the binary halogen acids increase or decrease down the group? I have one argument for decrease based solely on electronegativity considerations. I have one argument for increase based on orbital overlap and electron density. Taking electron density in an orbital to be...
  35. U

    M_p^3 = \frac{V_s^3}{2\pi G} PM_s^2Solve Binary Star Mass Homework Equation

    Homework Statement How do I show that for a binary star system, if one star has mass ##M_s##, speed ##V_s##, period ##P##, the mass of the other star is given by: ##M_P^3 \approx \frac{V_s^3}{2\pi G} PM_s^2##? Homework Equations The Attempt at a Solution \frac{GM_pM_s}{(a_p+a_s)^2} =...
  36. J

    Creating an 8 Bit x 4 Bit Binary Multiplier in Multisim

    hi all, new here, so sorry, but how do i make a binary multiplier in multisim? is there a specific chip... or...? i need to make an 8 bit x 4 bit multiplier
  37. K

    Binary star period calculation

    The problem is attached, and the official answer is given. The step in the answer does not make a lot of sense to me. How does the luminosity L converted directly into distance d, and why is the solar distance is used? And where does the dm=0.75 come from. It's just not making sense to me...
  38. A

    MHB Understanding Binary Relations: Reflexive, Symmetric, Antisymmetric & Transitive

    Hi, I'm having trouble understanding how to determine whether or not a binary relation is reflexive, symmetric, antisymmetric or transitive. I understand the definitions of what a relation means to be reflexive, symmetric, antisymmetric or transitive but applying these definitions is where I...
  39. B

    MHB Digraph of a Binary Positional Tree

    Hello- I think I understand how to draw a digraph of the given binary positional tree in my work. Could someone please tell me if I've got it correct, or if I'm not even close?
  40. G

    Graphs of electric field due to binary charge configuration

    sir in the graphs of electric field due to binary charge configuration why some curves are below x-axis and some are above x axis
  41. P

    Which Proof Should I Use for Binary Relations and Proofs Homework?

    Homework Statement The Attempt at a Solution I know what the question means and all, and I know a lot of different proofs. But I really don't know which proof to use for this question. I tried starting up a proof, but I don't exactly know how. Would a proof by contradiction work for a)?
  42. E

    Attempting to get this interative binary tree insert to work.

    Homework Statement Binary Tree/ Insertion scheme Homework Equations N/A The Attempt at a Solution bool treeNodeADT::_insert(int item) { if(this->isRootted==false){ this->root=new node; this->root->data=item; this->root->right=0...
  43. P

    Calculating Binary Star Masses

    Hello, I wasn't sure whether I should post this is the homework section since it's technically a textbook problem, but I figured I'd get better responses here. The problem is as follows: Sirius is a visual binary with a period of 49.94 years. Its measured parallax is .37931"## \pm...
  44. H

    Habitable Binary Worlds, and their characteristics

    I'm working on a SF story that takes place on Binary Planets orbiting a single star. I've worked out their mean distance from each other (702,904.853 km) from their star (167,323,260 km or 1.1 AU) and their orbits around the common barycenter(48 days), and the parent star(432 days). For...
  45. H

    At what distance would binary planets not be tidally locked?

    Working on a story idea that involves binary worlds. To keep the math simple I'm assuming the planets to be Earth sized, and mass, orbiting a star identical to the sun. I managed to find someone to help with the first equations and discovered that based on the time it takes them to orbit each...
  46. jk22

    Understanding Probability and Equality in Binary Choices

    Suppose we have 2n binary choices. Then the probability of having the same number of results is : C(2n,n)/2^(2n) ? I don't know if this is true, since for the case n=1million, we have a probability as high as 1/2000, which seems quite important ?
  47. P

    Right inverse, left inverse, binary operations

    Homework Statement If * is a binary operation on a set B, and the domain of definition is B^2, if * is associative and the neutral element is p. If r and l are elements of b we can say that r is a left inverse of l under * iff r * l = p, and l is a right inverse of r iff l * r = p. Show that if...
  48. Mechatron

    What is the significance of translating binary code?

    Can you help me to translate this binary code? 01001001 00100000 01001100 01001111 01010110 01000101 00100000 01011001 01001111 01010101
  49. Dembadon

    Responding with Why? to a binary question

    Responding with "Why?" to a binary question First, an example: Me: "Do you have to work tonight?" Wife: "Why?" Me: "Does your work schedule depend on my reason for asking?" Wife: *playfully punches me in the arm* "No, I don't have to work tonight, smartass." Me: :biggrin: Does this type of...
  50. V

    Binary Language or Alternatives

    Do artificial intelligence projects usually revolve around using some sort of binary language or are there alternative mathematical languages and is there combinations of mathematical languages being investigated? I always thought that the prime numbers 3 and 5 have some potential that 2 doesn't...
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