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Unformatted text preview: Astronomical Distance Determination For relatively nearby sources, one can measure distances by “surveying”  by measuring the very small angles that a star’s position is displaced relative to very distant objects because of the orbit of the Earth around the sun. For more distant objects one uses either “standard candles” or a theoretical model . Obtaining Distances by Parallax note: angles are exaggerated * * * * * * * * Jan Jun This displacement is twice the parallax angle History of Parallax • The first Parallax of the star 61 Cygni was measured by F. Bessel in 1838. • Since that time, parallax has been considered the most direct and accurate way to measure the distances to stars. Another way to measure angles: Radians: There are radians in a circle, hence one radian is 360 o / = 57.296… o The merit of this unit is that when p is measured in radians AU = d p 2 π 2 π d = AU p s s s s s s P d AU For simplicity assume a star 90 o above the ecliptic θ s r d AU p s = r θ AU = d p 1 radian = 360/2F = 57.296… o But astronomers actually report the angle p in seconds of arc. 1 radian is 360 o /2 π = 5 7 .2 9 6 ο and each degree is 3600 arc seconds. So 1 radian = 206265 arc seconds. Thus for p measured in seconds of arc (call it p ’’), d = 206265 ΑΥ π 220d220d δ = 1παρσεχ π 220d220d This defines the parsec, a common astronomical measure of length. It is equal to 206,265 AU’s or 3.0856 x 10 18 cm. It is also 3.26 light years. A little thought will show that this also works for stars whose position is inclined at any angle to the ecliptic. What p measures then is the semimajor axis of the “parallactic ellipse”. 1 AU seen from one parsec away would subtend an angle of 1 arc second AU p (in radians) d = Examples: If the parallax angle of a star is 1 arc second, it is 1 parsec = 3.26 light years away If the parallax angle is 0.5 arc sec it is 2 parsecs away If the parallax angle is 2 arc sec (no such star) it is 0.5 parsec away etc. Note for quite nearby stars one has to correct for the “proper motion”, the continuing drift in the location of the star because it does not orbit the Milky Way at precisely the sun’s speed and direction. This can be subtracted out. To what accuracy would one have to measure angles to get distances to 1000 pc? Hipparcos (the satellite) (1989  1993) Measured the position of 118,218 stars to a positional error of about a milliarc second (about your size on the moon as viewed from earth) Check out http://www.rssd.esa.int/Hipparcos/ and click on “web site tour” then on the five bullets  closest stars, brightest stars, fastest stars, HRdiagrams and Movies Distances measured to 10% accuracy for about 10,000 stars to a distance of 1000 pc (those that can be seen optically) Some comments Historically one used other forms of parallax – secular, statistical, moving cluster, etc., that since Hipparchos are not so important anymore....
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 Spring '11
 aaa
 Astronomical, cepheid variables, Cepheids

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