Binary Star Zip
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| from __future__ import division |
| from visual import * |
| from visual.graph import * |
| #Andre Londono |
| #UC Berkeley |
| #Binary star system for Physics 77 |
| scene = display(width = 800, height = 800) |
| scene.autoscale =0 |
| scene.range=7e11 |
| #Create objects to be modeled/ define geometric attributes |
| star1 = sphere(radius = 7e9,color = color.white, pos=vector(1.5e11,0,0) ) |
| star2 = sphere(radius = 7e10, color = color.blue,pos=vector(-1.5e11,0,0)) |
| #mywindow1 = gdisplay(xtitle = 'time(s)',ytitle = 'Energy (J)', title = 'Total energy of star 1') |
| #f1 = gcurve(gdisplay = mywindow1, color = color.cyan) |
| #f2 = gcurve(gdisplay = mywindow1, color = color.red) |
| #Define physical attributes of objects |
| G = 6.7e-11 |
| star1.m = 2.0e30 |
| star2.m = 10.0e30 |
| #star2.m = 2.0e30 |
| #Specify initial conditions |
| star1.p = star1.m*vector(0, 5e4,0) |
| #star1.p = star1.m*vector(0, 5e3, 0) |
| star2.p= -star1.p |
| planet1 = sphere(pos = (-300, 10, 0), radius = 30, color = color.red, make_trail=true) |
| star2.Fnet = vector(0,0,0) |
| star1.Fnet = vector(0,0,0) |
| #Visualize momentum/force vectors with arrows |
| #Determine scale through approximation of magnitude of vector to scale arrow into scene |
| scale = 2e10/1e27 |
| star1.FnetVector= arrow(pos = star1.pos, axis = star1.Fnet*scale, color = color.white) |
| star2.FnetVector = arrow(pos = star2.pos, axis = star2.Fnet*scale, color = color.blue) |
| momentumScale = 2e11/star1.p.mag |
| star1.momentumVector = arrow(pos = star1.pos, axis = star1.p*momentumScale, color = color.white) |
| star2.momentumVector = arrow(pos = star2.pos, axis = star2.p*momentumScale, color = color.blue) |
| trail1 = curve(color = star1.color) |
| trail2 = curve(color = star2.color) |
| t = 0 |
| dt = 1.0e5 |
| while true: |
| rate(100) |
| dvector = star1.pos-star2.pos |
| dmagnitude = mag(dvector) |
| dDir = dvector/dmagnitude |
| #calculate gravitational force between stars |
| Fgrav1 = G*star1.m*star2.m / dmagnitude**2.0 |
| star2.Fnet = Fgrav1*dDir |
| star1.Fnet = -star2.Fnet |
| #update momentum/position |
| star2.p = star2.p + star2.Fnet*dt |
| star2.pos = star2.pos+star2.p/star2.m*dt |
| star1.p = star1.p + star1.Fnet*dt |
| star1.pos = star1.pos+star1.p/star1.m*dt |
| #append positions to curve object |
| trail1.append(pos = star1.pos) |
| trail2.append(pos = star2.pos) |
| star1.momentumVector.pos=star1.pos |
| star1.momentumVector.axis=star1.p*momentumScale |
| star2.momentumVector.pos=star2.pos |
| star2.momentumVector.axis=star2.p*momentumScale |
| star1.FnetVector.pos=star1.pos |
| star1.FnetVector.axis=star1.Fnet*scale |
| star2.FnetVector.pos=star2.pos |
| star2.FnetVector.axis=star2.Fnet*scale |
| t = t+dt |
| #graphs |
| # star1KE = .5*star1.m*mag(star1.p)**2 |
| # star1GPE = G*(star2.m*star1.m)/(mag(star2.pos-earth.pos) |
| #t = t + dt |
| # f1.plot(pos = (t, star1KE)) |
| # f2.plot(pos = (t, star1GPE)) |
Learning Goals: Students will learn how the changing light from an eclipsing binary star system can reveal information about the individual stars and their orbits.
Suggested Observations: time-delay series of images of a known eclipsing binary star system timed during subsequent minima (the dimmest point in the lightcurve) e.g.: AB And, BU Vul, XZ And
Challenge:
Binary Star Zip Code
Find the period and relative luminosities of the components of an eclipsing binary star system. Observe an eclipsing binary and make a measurement of its period.
Part 1: Occulting Stars
Binary Star Photos
Part 3: Period of an Eclipsing Binary
Resources: Worksheet
Terminology:binary star, lightcurve, minimum
Demos from UNL: Eclipsing Binary
Tutorials: Importing Images into MaxIm, Photometry in Maxim
Background:
A binary star is a star system consisting of two stars orbiting around their common center of mass. The brighter star is called the primary and the other is its companion star, or secondary. Research between the early 19th century and today suggests that many stars are part of either binary star systems or star systems with more than two stars, called multiple star systems. The term double star may be used synonymously with binary star, but more generally, a double star may be either a binary star or an optical double star which consists of two stars with no physical connection but which appear close together in the sky as seen from the Earth. A double star may be determined to be optical if its components have sufficiently different proper motions or radial velocities, or if parallax measurements reveal its two components to be at sufficiently different distances from the Earth. Most known double stars have not yet been determined to be either bound binary star systems or optical doubles.
Binary Star Pair
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 Star Zip Line
Binary stars are often detected optically, 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, as they are detected by their changes in brightness during eclipses and transits, photometric binaries.