Measuring Size in HOU

symbol used
type of "size"
(units)
s
measured diameter
(pixels)
plate scale:
conversion of measured diameter to angular diameter in arcseconds
q
angular diameter
(seconds of arc)
unit conversion
for
angular diameter
(from arcseconds to radians)
 
(radians)
small angle formula:
conversion of 
angular diameter (in radians) to linear  diameter 
D
linear diameter
(or true diameter)
(m, km, c-yr)


    plate scale:  how to find it (for a given image)

    1) a) it's given in the image header (in Image Info under Data Tools)
        b) it's given in the HOU activity
        c) it's given in another HOU activity that was produced with the same telescope/CCD combination

    2) figure it out because you recognize some object (Jupiter, Sun) in the image whose
        angular size you know (because you can look it up) and  whose measured diameter
        you can measure on the image (in pixels)

    3) calculate it from first principles (HOU wouldn't really expect you to do this!), but you can
        calculate it if you know the CCD linear size and the telescope's focal length


    conversion of angular units

    the 4 units of angular diameter (or angular size) that are encountered in HOU activities are:

    degrees
    arcseconds (also ")
    arcminutes (also ')
    radians

    1 degree  =  60 arcminutes ( = 60 ' )  =  3600 arcseconds ( = 3600 " )

    a full circle  =  360 degrees  =  2 p  radians

    combining the above 2 lines,   1 radian  =  206,265 arcseconds

    radians is probably the only unit that will need some introduction:
    see Supplementary Activity 6 in the Measuring Size book


small angle formula  (valid only if      is smaller than 15 degrees)

    D  =   x  d

    where  d = distance to the object
               q = angular diameter of the object in radians
               D = linear diameter of the object

    D will be in the same units that  d  is in.  If  d  is in kilometers, D  is in kilometers; 
    if  d  is in light years, D will be in light years.