Using the small angle formula to determine distances or linear sizes

Using the small angle formula to determine distances or linear sizes

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Using the small angle formula to determine distances or linear sizes Astronomers express angular diameters in seconds of arc (arc seconds). They also always use the same units for the distance to an object and the linear diameter of that object (although the units may vary). The formula is: ** (Images not to scale) Object Small nebula Horsehead nebula Hyades Pleiades Globular Cluster M 71 Angular diameter (seconds of arc) 20 1 pc 900 (15 arc min) 430 (7.2 arc min) Linear diameter (units must be given) 20 pc Distance (units must be given) 1000 pc 500 pc 48 pc 130 pc 42,380 pc
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Unformatted text preview: **There are 360 degrees in a circle. There are also 2 pi radians in a circle. This works out so that 1 radian = 360 / 2 pi = 57.3 degrees (about). How many arc seconds are in a circle? 1 degree = 60 minutes of arc, and 1 minute of arc = 60 seconds of arc. So, 1 degree = 3600 seconds of arc (arc seconds). Thus, there are 360 * 3600 = 1,296,000 arc seconds per 360 degrees. Since this also equals 2 pi radians, we divide 1,296,000 by 2 pi ? to get the number of arc seconds per radian. This works out to be: 1 radian = 206,265 arc seconds (206,264.8 to be exact)....
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