# Rung 2 - The entire main sequence of a cluster is used in...

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Rung 2: Geometric Methods On the next rung of the distance scale ladder, you can convert trigonometric parallax measurements into distances to the nearby stars using their angular shift throughout the year and the numerical value of the Astronomical Unit. Distances to nearby clusters like the Hyades or the Pleiades are found via trigonometric parallax or the moving clusters method (another geometric method). The cluster's main sequence is calibrated in terms of absolute magnitude (luminosity). Geometric methods are used to find distances out to about 100 parsecs (or several hundred parsecs with Hipparcos' data). Rung 3: Main Sequence Fitting and Spectroscopic Parallax On the next rung outward the spectral type of star is determined from its spectral lines and the apparent brightness of the star is measured. The calibrated color-magnitude diagram is used to get its luminosity and then its distance from the inverse square law of light brightness.
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Unformatted text preview: The entire main sequence of a cluster is used in the same way to find the distance to the cluster. You first plot the cluster's main-sequence on a color-magnitude diagram with apparent magnitudes, not absolute magnitude. You find how far the unknown main sequence needs to be shifted vertically along the magnitude axis to match the calibrated main sequence. The amount of the shift depends on the distance. The age of the cluster affects the main sequence. An older cluster has only fainter stars left on the main sequence. Also, stars on the main sequence brighten slightly at a constant temperature as they age so they move slightly vertically on the main sequence. You must model the main sequence evolution to get back to the Zero-Age Main Sequence. This method assumes that all Zero-Age main sequence stars of a given temperature (and, hence, mass) start at the same luminosity. These methods can be used to find distances out to 50 kiloparsecs....
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## This note was uploaded on 12/15/2011 for the course AST AST1002 taught by Professor Emilyhoward during the Fall '10 term at Broward College.

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