17: Visual Binary Stars
- Page ID
- 6902
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\(\newcommand{\avec}{\mathbf a}\) \(\newcommand{\bvec}{\mathbf b}\) \(\newcommand{\cvec}{\mathbf c}\) \(\newcommand{\dvec}{\mathbf d}\) \(\newcommand{\dtil}{\widetilde{\mathbf d}}\) \(\newcommand{\evec}{\mathbf e}\) \(\newcommand{\fvec}{\mathbf f}\) \(\newcommand{\nvec}{\mathbf n}\) \(\newcommand{\pvec}{\mathbf p}\) \(\newcommand{\qvec}{\mathbf q}\) \(\newcommand{\svec}{\mathbf s}\) \(\newcommand{\tvec}{\mathbf t}\) \(\newcommand{\uvec}{\mathbf u}\) \(\newcommand{\vvec}{\mathbf v}\) \(\newcommand{\wvec}{\mathbf w}\) \(\newcommand{\xvec}{\mathbf x}\) \(\newcommand{\yvec}{\mathbf y}\) \(\newcommand{\zvec}{\mathbf z}\) \(\newcommand{\rvec}{\mathbf r}\) \(\newcommand{\mvec}{\mathbf m}\) \(\newcommand{\zerovec}{\mathbf 0}\) \(\newcommand{\onevec}{\mathbf 1}\) \(\newcommand{\real}{\mathbb R}\) \(\newcommand{\twovec}[2]{\left[\begin{array}{r}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\ctwovec}[2]{\left[\begin{array}{c}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\threevec}[3]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\cthreevec}[3]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\fourvec}[4]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\cfourvec}[4]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\fivevec}[5]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\cfivevec}[5]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\mattwo}[4]{\left[\begin{array}{rr}#1 \amp #2 \\ #3 \amp #4 \\ \end{array}\right]}\) \(\newcommand{\laspan}[1]{\text{Span}\{#1\}}\) \(\newcommand{\bcal}{\cal B}\) \(\newcommand{\ccal}{\cal C}\) \(\newcommand{\scal}{\cal S}\) \(\newcommand{\wcal}{\cal W}\) \(\newcommand{\ecal}{\cal E}\) \(\newcommand{\coords}[2]{\left\{#1\right\}_{#2}}\) \(\newcommand{\gray}[1]{\color{gray}{#1}}\) \(\newcommand{\lgray}[1]{\color{lightgray}{#1}}\) \(\newcommand{\rank}{\operatorname{rank}}\) \(\newcommand{\row}{\text{Row}}\) \(\newcommand{\col}{\text{Col}}\) \(\renewcommand{\row}{\text{Row}}\) \(\newcommand{\nul}{\text{Nul}}\) \(\newcommand{\var}{\text{Var}}\) \(\newcommand{\corr}{\text{corr}}\) \(\newcommand{\len}[1]{\left|#1\right|}\) \(\newcommand{\bbar}{\overline{\bvec}}\) \(\newcommand{\bhat}{\widehat{\bvec}}\) \(\newcommand{\bperp}{\bvec^\perp}\) \(\newcommand{\xhat}{\widehat{\xvec}}\) \(\newcommand{\vhat}{\widehat{\vvec}}\) \(\newcommand{\uhat}{\widehat{\uvec}}\) \(\newcommand{\what}{\widehat{\wvec}}\) \(\newcommand{\Sighat}{\widehat{\Sigma}}\) \(\newcommand{\lt}{<}\) \(\newcommand{\gt}{>}\) \(\newcommand{\amp}{&}\) \(\definecolor{fillinmathshade}{gray}{0.9}\)A visual binary is a gravitationally bound system that can be resolved into two stars. These stars are estimated, via Kepler's 3rd law, to have periods ranging from a number of years to thousands of years. A visual binary consists of two stars, usually of a different brightness.
- 17.1: Introduction to Visual Binary Stars
- This page covers the methods for observing and measuring binary stars, detailing the use of telescopes and micrometers to assess angular separation and position angles. It distinguishes between optical pairs and gravitationally-bound systems, addressing measurement challenges related to brightness and motion. Furthermore, the page explains the differences between apparent and true orbits, emphasizing the importance of precise long-term observations for accurate determinations.
- 17.2: Determination of the Apparent Orbit
- This page outlines the method for determining parameters of an apparent elliptical orbit, focusing on the semi-major axis, eccentricity, orientation, and center coordinates. It mandates five position observations for ellipse fitting and stresses adherence to Kepler’s second law. A technique for plotting position versus time to detect errors is also suggested. The ultimate goal is to obtain an accurate ellipse that reflects orbital motion, paving the way to deducing true orbital elements.
- 17.3: The Elements of the True Orbit
- This page explains how to determine the orbit of a secondary star in a binary system, focusing on elements like semi-major axis, eccentricity, and inclination, alongside their measurement. It notes the ambiguity in inclination signs and the importance of visual and spectroscopic binaries for understanding star masses, despite challenges in measuring distant systems. Additionally, it discusses the directionality of orbits based on position angle changes.
- 17.4: Determination of the Elements of the True Orbit
- This page explores methods to determine the true orbit of celestial bodies, starting from their apparent orbit in conic form. It covers coordinate systems, calculating eccentricity, and identifying significant orbital parameters. Additionally, it focuses on the Equation of the auxiliary ellipse, determining axis lengths from known coordinates, and discusses the line of nodes in relation to the major axis, highlighting projection effects on orbit shapes.
Thumbnail: Algol B orbits Algol A. This animation was assembled from 55 images of the CHARA interferometer in the near-infrared H-band, sorted according to orbital phase. (CC BY-SA 3.0; Dr. Fabien Baron, Dept. of Astronomy, University of Michigan, Ann Arbor, MI 48109-1090, labels indicating phase added by Stigmatella aurantiaca).