Calibration constant of Filar Micrometer
                                         March 2003
                                   By Kazumi Funakoshi  
1.Introduction
 The filar micrometer is a device used for measuring the angular separation between double
stars or the angular size of planets,etc. Although you may say that the analog device like a filar
micrometer is old-fashon in the age of digital device like a highly sensitive CCD camera, I feel
a interesting to measuring by analog device.
 I get the filar micrometer eyepiece for microscope. Therefore, it is a little improvement in
order to use for telescope. One is connection to telescope. other is light up the scale.
Please show here.
 (I can see the scale and 7th magnitude star by light up the scale)


2.Explanation of filar micrometer eyepiece

 Figure1 LOMO's EFM-16X Filar Micrometer Eyepiece
    weight is 210g, size is 85x 55 x 35 mm.
    
Figure2 shows Stationary Scale and Movable Scale (L). To measure the separation between two
stars, we first rotate the device so that the scale lines are perpendicular to the imaginary line
connection of the two star(A and B). Next, we move the telescope so that one star(A) just on the
one of stationary scale. Next,we ratate the screw of micrometer untill other star(B).
Then, we read the value of micrometer.
To obtain the angular separation,we mulitple this value to micrometer's calibration constant.



Figure 2 Stationary Scale:8mm/8div and Movable Scale:1mm/100div

3.Filar micrometer's calibration constant
I test filar micrometer eyepiece in order to get the calibration constant.
Followings are measurement results (telescope power is about 200X);

Object: Magnitude Separation micrometer's division Seconds per micrometer's division
δ Ori:2.2  6.8    52.5"       115div      →0.456"/div
β Mon:4.7  5.2    7.2"         18div     →0.40"/div
σ Ori:3.8  6.7    42.9"        94div      →0.456"/div
γ Ari:4.6  4.7     7.7"        18div      →0.428"/div

(1)Mean value
  calibration constant=mean value of seconds per micrometer's division
             =0.435"/div.

(2)Least square value
  Figure.3 shows relation between micrometer's division and second.
 Line shows least square:y=0.4503X,Square of correlation R is 0.9992.
 Accordingly, calibration constant from Least square method is 0.45"/div.

Figure 3 relation between micrometer's division and second

4.Some measurements of celestial body
(1)Saturn's body
   Measurement result is 42div. Therefore, size of saturn's body is 0.435"/div.*42div=18.3"
   or 0.45"/div.*42div=18.9"
   According to the astronomical yearbook, size of Saturn at March 2,2003 is 18.8".
   →%error is 2.7% or 0.5%.
(2)Jupiter's body
   Measurement result is 100div. Therefore, size of saturn's body is 0.435"/div.*100div=43.5"
   or 0.45"/div.*100div=45.0"
   According to the astronomical yearbook, size of Jupiter at March 12,2003 is 43.4".
   →%error is 0.2% or 3.7%.
(3)Moon's crater
    Figure 4 shows calculation method of Moon's crater size.
   
   Figure4 Calculation of Moon's crater size
  <Theophilus crater >
   Measurement result of Theophilus crater is 123div.
   Distance between earth and moon at March 9,2003 is (404429-6378-1738)=396313km
   Therefore,the size of Theophilus crater is
    396313*2*tan((PI*123*0.435/(180*60*60))/2)=102.8km
   According to the book, size of Theophilus crator is 100km.
   →%error is 2.8%.
  <Gassendi crater >
   Measurement result of Gassendi crater is 143div.
   Distance between earth and moon at March 14,2003 is (383458-6378-1738)=375342km
   Therefore,the size of Gassendi crater is
    375342*2*tan((PI*143*0.435/(180*60*60))/2)=113.2km
   According to the book, size of Theophilus crater is 112km.
   →%error is 1.1%.
  <Bianchini crater and Sinus Iridum >
   Measurement result of Bianchini crater is 49div. Entrance of Sinus Iridum is 266div
   as shown Figure 5.
   
   Figure 5.

   Distance between earth and moon at March 14,2003 is (383458-6378-1738)=375342km
   Therefore,the size of Bianchini crater is
    375342*2*tan((PI*49*0.435/(180*60*60))/2)=38.8km
   According to the book, size of Theophilus crater is 38km.
   →%error is 2.1%.
   Entrance of Sinus Iridum is 375342*2*tan((PI*266*0.435/(180*60*60))/2)=210.6km



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