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. K

    Binary Operation, Abstract Algebra

    Define a binary operation on Z, the set of integers by the equation m * n = m + n + mn. Which of the following statemnts is / are true about the binary structure of Z with * 1) * is not associative 2) There is no element e belonging to Z such that for every z belonging to Z, z*e = e*z = z 3)...
  2. T

    Planetary orbits in a Binary Star system.

    http://spaceflightnow.com/news/n0210/11planet/ This is the only discovered planetary orbit around a close binary star that I know about. I have some general questions about planetary orbits around or within close binary systems or even the further apart binary star formations or triples...
  3. T

    Programming Binary Addition with a Turing Machine

    hello, One can wonder what is the relation between the title of this thread and the subject of quantum mechanics, well, i was reading in a book about quantum computation and information and it was talking about computer science in some chapter where it shows a basic understanding of Turing...
  4. K

    Is there a test for binary numbers divisible by 2^n - 1?

    Dear All, I have to test if a binary number is divisible to 2^n - 1 where n is even. Is there a test available for binary numbers like to test a divisibility by 3. Thanks in advance...
  5. B

    Printing a Binary Tree: Solving the Space Issue

    Hi, would you mind helping me in solving this problem? Because I stuck now. The problem is to print a space in a binary tree (not binary search tree) my current program can only output without appropriate spacing so if input is : 4 7 8 9 2 0 3 1 5 the output will become 4 7 8 9 2 0 3 1...
  6. K

    Number theory: Binary Quadratic Forms

    P.S. I'm not sure where to post this question, in particular I can't find a number theory forum on the coursework section for textbook problems. Please move this thread to the appropriate forum if this is not where it should belong to. Thanks!
  7. F

    What does momentum conservation reveal about period and mass of binary systems?

    Homework Statement A binary star consists of two stars that are orbiting a common centre. The only force acting on the stars is the gravitational force of attraction in a direction along the line joining the stars. a) Explain carefully why the total momentum of the binary is constant...
  8. B

    Strain gauges - converting to parrallel binary word

    Homework Statement I want to convert the output of a strain gauge into an equivalent parellel binary word Homework Equations i need to list the process blocks in correct sequence and starting at the strain gauge The Attempt at a Solution Strain gauge- convert ohms to volts-...
  9. bcrowell

    Very close binary, strongest steady source of gravitational waves

    This paper http://arxiv.org/abs/1003.0658 nails down the interpretation of a binary white dwarf system with an orbital period of only 5.4 minutes, versus 8 hours for the celebrated Hulse-Taylor binary neutron star system. This would probably be the strongest source in the sky of steady...
  10. I

    Commutative monoids have binary products

    Homework Statement Hello, I'd like to prove that the category cmon of commutative monoids has binary products. The Attempt at a Solution actually I'm aware that i have to use cartesian products given monoids (M, \bulletm, e^{}_{m}) and (N, \bulletn, e^{}_{n}) it follows that...
  11. S

    Binary in Real Analysis & Sets?

    Hi, I have a few questions because I'm watching a lecture on real analysis & I'm a little bit unsure of a few things. I have them in point form for your convenience in answering. http://www.youtube.com/watch?v=lMHR6d0leKA&NR=1 1. (from 2.30 in the video - no need to watch) A & B are sets &...
  12. U

    N-ary relation as a combination of binary relations

    Hello, I am looking for a formal way to represent an n-ary relation as a combination of binary relations and logical connectives. Suppose we have a set A, a set B = \{b: b\subseteq A^2\} of binary relations over A, and a set of logical connectives C = \{\neg, \wedge, \vee\}. We define a set...
  13. W

    Eclipsing binary stars question

    Homework Statement Figure 1 showed the light curve for an exlipsing binary system. This system consists of 2 stars. Star is is the larrger of the stars, and has a surface temp of T1=5000 K. Star 2 has a surface temp of T2=10000K. The ratio of their radii is R1/R2=4. Fnormal is the flux...
  14. N

    Simple Binary Subtraction: Learn How to Calculate with Step-by-Step Guide

    Hi Friends, I'm scratching my head for not able to figure out this problem of binary (fraction) subraction. 0.1101 - 0.00000011 = 0.11001101 Can someone please help me with steps how do i get the answer as sshown above . I tried as shown below and I am getting a different answer...
  15. V

    RCHow can a digital circuit perform sine wave integration using TTL chips?

    I need to design a digital circuit using TTL chips (adders, registers, etc.) to perform integration on binary values. The binary values are converted from analog signals such as a sine wave, constant, square pulse, and saw tooth. I can achieve the process for constants and positive signals...
  16. B

    Closure under * for subset H of commutative elements in set S

    Homework Statement suppose that * is an associative binary operation on a set S. Let H = {a elementof S | a*x = x*a forall x elementof S}. Show that H is closed under *. Homework Equations The Attempt at a Solution i don't really know where to begin. I know i need to show forall...
  17. P

    Binary transitions, power consumption

    I'm studying the ethernet devices and the transmission system over cable wire and I'm interested especially on the power consumpiot due to the binary transitions from 0 to 1 and viceversa in the transistors. It is possible to estimate how many WATTS (i thinks nW) are necessary to the device to...
  18. E

    Finding magnitude of part of binary system

    3. A very cool, faint white dwarf is identified as such from its spectrum and is known to have an apparent visual magnitude, mv = 16.73. A series of observations over several years yields a parallax measurement of 171±2 mas (milli-arcseconds). (i) How far away is the white dwarf, and what...
  19. L

    Converting Between Binary, Hex, Octal, and Decimal

    I'm taking a microcontrollers course and need to know how to convert between base 2, 8, 16, and 10. I understand how each base works, however I'm finding it hard to convert between them. What are some good methods to use when converting bases?
  20. F

    358 in binary single floating point using excess 4

    i need to express 358 in binary single floating point format using excess 4 notation...i can do it easily using the 32-bit standard representation with the excess 127 exponent. i know that 358 is 101100110 therefore i assume floating point would be 1.01100110 with an exponent of 8. i know excess...
  21. F

    Why is 1000 = -8 in signed 4-bit binary?

    I was wondering why 1000 in signed 4-bit binary notation is equal to -8 in decimal. From my understanding, the 1 simply states that sign (1 being negative and 0 being positive) it has no real decimal value. I have read that it is not possible to correctly take the 2's complement of -8 so I...
  22. Astronuc

    What Caused the Ejection of Mu Columbae and AE Aurigae from Orion?

    I was listening to the regional NPR station yesterday and hear a brief discussion of two binary systems. http://stardate.org/radio/program.php?f=detail&id=2009-12-26 Is this common? Is it plausible? I presume that some how the velocity of Mu Columbae and the other star traveling 'north'...
  23. S

    Binary Star system common period

    Homework Statement The questions are about binary star system. Homework Equations Why the two stars in a binary star system are always diametrically opposite positions? Why the two stars have common period? Why the inner star is more massive? The Attempt at a Solution For the...
  24. W

    Segmentation of a binary image

    Hello PF users, This is my first time on these forums. I'm not sure this is exactly the right place for this question, but as I couldn't find an image processing sub forum I'm posting it here in the hopes someone can help me! Homework Statement I have a binary image (see below)...
  25. V

    Find Apparent Magnitude of Binary Star System w/o Distance

    Please could you let me know how to find out apparent magnitude of a star when you know the apparent magnitude of the binary star system? p.s. the distance between the observer and the system is'nt given. I have the luminosities of both the stars as well as absolute magnitudes of both the stars.
  26. U

    What are all the possible 5-digit binary code combinations?

    Hi all. I recently am thinking of developing a compression software with extreme speed and compression. The simple principle behind the working of this software is that the software is converting the program into binary code. Then, five sets of 0s and 1s are converted into alphanumeric...
  27. K

    Mass of invisible binary companion

    Hey guys, got this question that's been giving me some trouble. The spectral lines in a low-mass main sequence star are observed to show sinusoidal velocity variations with an amplitude of 500km/s and a period of ten hours. Calculate the lower mass limit of the unseen binary companion...
  28. K

    Astrophysics: Finding the mass of a hidden star in a binary system

    Homework Statement The spectral lines in a low mass main sequence star show sinusodal velocity variations with an amplitude of 500 km/s and a time period of 10 hours calculate a lower limit to the mass of the unseen binary companion Homework Equations M1 + M2 =...
  29. K

    Another question involving the masses of two stars in a binary syste

    Homework Statement The Spectral lines in a double-lined spectroscopic binary exhibit sinusodal motion with ampliutudes of 15 and 35 km/s in a period of 80hrs. assuming that we view the system close to edge on, calculate the individual masses in solar masses. What would you look for...
  30. K

    Determining the masses of 2 stars in a binary system.

    Homework Statement A binary star is resolved on the sky, the orbit is circular, it has a period of 30 years and the semi-minor and semi-major axes are observed to be 0.5 and 4 arcseconds respectively. If the distance to the system is 10pc, what are the masses of the stars? give an answer in...
  31. James889

    Question about binary counter with jk flip-flops

    Hi, Let's say i want to make a binary counter using jk-flip-flops that counts 1,3,5,7,1... Then i'd use the excitation table for the jk-flip-flop to determine the next state. The next step would be to use karnaugh-maps to minimize the j and k columns. My question is: Do i need to...
  32. B

    Binary Hypothesis Test Homework: Formulate Likelihood Ratio Test

    Homework Statement This was a midterm question that took some people a rapid time to solve, hence I can only imagine either I was needlessly long winded or something else occurred. Hypothesis 1: S = 2 + \omega Hypothesis 2: S = -2 + \omega \omega \sim \mathcal{N}(0,\sigma^2_{w})Homework...
  33. H

    Transitive Closure of Binary Relation T on A={0,1,2,3}

    Homework Statement T is a binary relation defined on A = {0, 1, 2, 3}. Let T = {(0,2), (1,0), (2,3), (3,1)} Find T^t, the transitive closure of T.The Attempt at a Solution I'm going to skip using commas cause it takes to long 02 23 = 03 31 10 = 30 23 31 = 21 10 02 = 12 12 23 = 13 02 21 = 01...
  34. M

    Is binary divisibility by 3 determined by even and odd bit count?

    Well i found this sentence: "If the number of even bits minus the number of odd bits is a multiple of 3 (e.g. -3,0,3,6, etc) then the number is divisible by three." Can anyone tell me the proof of this? Thanks
  35. Z

    How Are the Masses of Binary Stars Calculated?

    Homework Statement (a) 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, telescopic observations repeated...
  36. I

    Binary relations: weak order, strict partial order, equivalence

    Homework Statement I'm totally lost about this. I know the properties of binary relations (or at least I think I know them, what it means to be transitive, complete etc). This exercise asks me to show that P and I are strictly partial and equivalent respectively when P and I are defined...
  37. F

    Binary star system distance between stars

    Homework Statement A binary star system has a period of 90 days. It consists of two equally massed stars each with a mass of twice that of the sun, that rotate like a dumbbell about the center of mass at the midpoint between them. How far apart are these stars? Homework Equations F =...
  38. K

    Binary Number Theory-like problem

    Homework Statement I have a function f: \mathbb Z_p \times \mathbb Z_p \to \mathbb Z_p for some prime p. I am given (r_1, r_2) \in \mathbb Z_p \times \mathbb Z_p\setminus_{\left\{0,0\right\} } , and told that f(a_1, a_2) = f(b_1,b_2) \Leftrightarrow (a_1,a_2)-(b_1,b_2) = m (r_1,r_2)...
  39. N

    Binary to hex conversion proof

    Hello PF members! I am interested in proving that the conversion of binary to hex is valid. Example: 1000100100110111 Breaking into 'quartets' 1000 1001 0011 0111 Now using the fact that 24 = 0...15 1000 = 8, 1001 = 9, 0011 = 3, 0111 = 7. So 10001001001101112=893716 I can...
  40. L

    Binary star system ratio of force

    Homework Statement 2 stars rotating around the common centre of mass have masses m and 3m. What is the ratio of the force due to each star at the common centre of mass. Homework Equations None The Attempt at a Solution I tried to find the centre of mass and applied Newtons law of...
  41. C

    Binary Star Analysis: Mass Calculation from 10pc, 33yr Period, i=90°

    Homework Statement We observe a binary system in which the two stars are 1 and 2 arc sec, respectively, from the center of mass. The system is 10pc from us. The period is 33 yr. What are the masses of the two stars, assuming that i=90 degrees? Homework Equations The Attempt at a...
  42. X

    How do I convert signed decimal to binary

    1. Convert the following numbers to 32-bit two's complement binary numbers. -22 , -100 Can someone explain this to me? I thought I just convert the +22, which is 10110 and add it to all the 1's. Like, 111111...10110 and positive would be 00000000...10110. But that's not how it...
  43. C

    Using 2x 74LS47 to input binary 0-15

    is it possible to connect 2x 7447 IC's and 2x 7 segment and input binary 0-15?
  44. G

    In a binary mixture, when is one flow negligable?

    I am looking for a non dimensional parameter that will tell me if I can neglect the flow of one of the gases and just consider the mass and momentum conservation equations for the background species. This is not a homework question. For example: If there is a pipe dumping a contaminant into...
  45. C

    Proving Binary Tree Properties: 2^(h-1) Leaf Nodes & 2^(h-1) - 1 Internal Nodes

    2 questions that came up in a past paper. A binary tree which is both full and complete and has h levels contains a total of 2^(h-1) leaf nodes. Prove that this is the case for all h > 0. Show that with h levels the number of internal nodes is 2^(h−1) − 1 proof by induction apparently...
  46. J

    Testing Group Properties on Q with Binary Operation *

    Group properties: 1. \forall a, b, c \in G, (a * b) * c = a * (b * c). (associativity) 2. \exists e \in G such that \forall x \in G, e * x = x * e = x. (identity) 3. \forall a \in G, \exists a' \in G such that, a * a' = a' * a = e (inverse) Instruction: Determine whether the...
  47. J

    Group (Associativity of Binary Operators)

    Statement: One of the key elements in being in what people call group is that elements must be associative. So this means if we take any three elements from what we propose to be a group, they should be associative, a*(b*C) = (a*b)*c Question: Suppose we do have a group with elements a, b, c...
  48. M

    Help with Binary Relations Homework

    Hello :smile: I was wondering if I could get some help with work on Binary Relations. We've done very little of this in class, and hours of Googling has provided little help. So I was hoping that someone could look over my attempts at the questions and let me know if I've gone wrong...
  49. Q

    Binary converter (supports IEEE754)

    Here is a good tool for checking your solution when converting a number from decimal to binary or from binary to decimal. It supports integer numbers (8, 16 and 32 bits) for both unsigned and signed numbers. It also includes a converter for single precision and double precision numbers...
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