ASTR 1101 Chapter : Small Angle Formula And Method
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D = d / 206265 ( in arc-seconds) " 1 = 3600 arc-seconds: if you hold up a dime just under 2 meters from your eye, # it will almost exactly cover up the full moon. I measure the diameter of dimes to be 18 mm (0. 018 m). Step zero: realize that you are dealing with a small angle" problem! Step one: draw out the triangle and label the angle and distances! d=2m! Step two: write out the small angle formula [d= d], solve for what you ! are looking for [ =d/d], plug in the numbers, and do the math:! = d/d = 0. 02m / 2m =1/100 =0. 01 rad! Step three: importantly for small-angle problems, the answer you get ! from =d/d is in the units of radians. Often, it is convenient to convert ! radians to degrees. Step four: we are told that the dime has the same angular size as the !
