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- When you look up at the night sky on a good night in a good location you can count 4,000 points of light. Surprisingly, 65% of those points are actually binary stars, or multiple star systems.
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- Over 1,000 exoplanets have been discovered to date. Astronomers estimate that 200 million planets exist in the Milky Way galaxy. Tens of millions of these are likely circum-binary planets. What's a circum-binary planet.?
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- How can planets exist if they are being tugged by two or more suns?
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- The two suns could be orbiting each other relatively close together. Planets could be orbiting the pair in a far larger orbit.
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- Or, the two suns could be widely separated orbiting a center of mass. Planets in this configuration would have more complex orbits. Could they even exist in such a solar system?
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- If the two stars have orbits in hundreds of years then there solar system of planets are likely unaffected by the other sun.
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- If the two stars have closer orbits then there gravity could likely destabilize the planets orbit. Planets would either be swallowed up or ejected out into the galaxy.
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- However, there is a middle ground where planets could orbit two stars and still have stable orbits. These are called circum-binary planets. Do they exist?
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- The math for orbits gets extremely complicated for a 3-body system.
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- The trick is to find these eclipsing binary stars. These stars pass in front of each other once per orbit. Astronomers can see this if we happen to be in the right line of sight. By measuring the light curve as the light dims during the eclipses astronomers can learn the size and shape of the stars, and, the geometry of their orbits. They can measure the star’s diameter and mass.
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- In a binary system the planet will cross the star early and sometimes late of a predictable orbit. The transits will not be periodic. Once this data is well understood the binary stars orbit can be deciphered. Circum-binary planets can be confirmed. So far out of 1,000 exoplanets found 7 are Confirmed circum-binaries.
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- Over 2,000 eclipsing binary star systems have been discovered by the Kepler space telescope. In 2011 Kepler – 16b was the first transiting circum-binary planet discovered. Named “ Tatooine“ from Star Wars movie.
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- These discoveries are made by the dip in brightness that is periodic. The primary eclipse and the secondary eclipse are repeated very accurately in their light curve. Measuring how much the light curve is early or late confirms the orbit about a center of mass.
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- Measurements made on the eclipsing planets can yield the same calculations. These data are all moeled in a computer suntil the model matches observations. Once the model is perfected conclusion are made ast o the binary orbits and the masses of stars and planets in the system. Amazing!
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- As stars orbit each other one can eclipse the other. The light dims during the eclipse. In a 2-body system the light intensity dips in a perfectly periodic and regular manner. In a 3-body system with a planet or planets involved the light curves get more complex
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- In a 3- body system the center of mass of the 2-body systems orbits around the center of mass of the 3-body system. At times the 2 stars will be further away at other times the 2 stars will be closer together. This distance change will make a slight delay in the observed eclipse timing. If the distance is shorter the eclipse will occur slightly earlier. T
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- By only observing a single star we observe a point of light. We can analyze the light spectrum to learn surface temperature and age of the star. But, if we have a binary system of 2 or more stars orbiting a common center of gravity we can calculate masses, periods, luminosity, and, frequency of radiation. If they eclipse each other we can calculate diameter, volume, density, and accumulate an astronomical wealth of information.
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- To illustrate the math used in to be learned from eclipsing binaries. The orbit of one star is eclipsing with a semi-major axis of 4 astronomical units, and, its complete orbit takes 2.5 years. Kepler's third law states that the sum of the masses equals the radius cubed divided by the period squared
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------------------------ Masses = (radius)^3 / ( period)^2
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---------------------- ( M1 + M2) = a^3 / p^2
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----------------------- ( M1 + M2) = (4)^3 / (2.5)^2
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---------------------- ( M1 + M2) = 10.5 Solar Mass
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- This is the sum of the two masses. The formula works when the period is in years and the radius is in astronomical units. If the stars are eclipsing it may be possible to determine the relative sizes of the two orbits around a center of mass and the ratio of the two masses, M1 / M2.
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- The second way to learn amasses eclipsing binaries is created light curve of the apparent brightness as a blocking star dims the total light that we see. Newton's version of' Kepler’s 3rd law relates the masses to the orbital system in the general case using metric units:
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------------------------------- ( M1 + M2) = (4*pi^2 / G) * a^3 / p^2
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- The orbital velocities are determined measuring the Doppler shift that occurs when the star moving toward us versus the star moving away from us shifts the light spectrum observed.
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------------------------- velocity = distance traveled in one orbit / period of one orbit.
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---------------------------- v = 2*pi*a / p
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- The ratio of M1 / M2 can be calculated knowing the relative velocities of the 2 stars around a common center of mass is inversely proportional to their relative masses.
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------------------------ p = period = 2 years = 6.3*10^7 seconds
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------------------------ a = semi-major axis of an ellipse, or, radius of a circle.
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------------------------ a = P*v / 2*pi
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------------------------ a = ( 6.3*10^7) * ( 10^6 meters / second) / 2*pi
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------------------------ a = 10^12 meters
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------------------------ (4*pi^2 / G) = 5.92*10^11
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----------------------- ( M1 + M2) = (5.92*10^11) * a^3 / p^2
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- The sum of the masses in kilograms = the ratio of 600,000,000,000 * the cube of the radius to the square of the period.
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---------------------- ( M1 + M2) = (5.92*10^11) * (10^12)^3 / (6.3*10^7)^2
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---------------------- ( M1 + M2) = 1.5*10^32 kilograms
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- Measuring the Doppler shift of the spectral lines shows that one star has twice the spectral shift of the other star:
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---------------------- Star 1 = 0.5 * 10^32 kilograms
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----------------------- Star 2 = 1.0 * 10^32 kilograms
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----------------------- Solar Mass = 2 * 10^30 kilograms / Ms
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----------------------- Star 1 = 25 Ms
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----------------------- Star 1 = 50 Ms
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- Two stars are better than one, if you do the math.
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(1) Request review # 1528 “ Measuring Binary Stars”
(2) Request review # 1384 “ Spiral Sprinkler not a Galaxy”
(3) Request review # 1118 “ Why are 2 stars better than one?”
(4) Request review # 1063 “ Binary Stars”
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RSVP, with comments, suggestions, corrections. Index of reviews available ---
--- Some reviews are at: -------------------- http://jdetrick.blogspot.com -----
---- email request for copies to: ------- jamesdetrick@comcast.net ---------
---- https://plus.google.com/u/0/ , “Jim Detrick” ----- www.facebook.com ---
---- www.twitter.com , --- 707-536-3272 ---- Wednesday, January 15, 2014 ---
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