Double Star Observation SAO118981(=XZ17514,=ZC1692) in Apr.28 2007
Apr.29 2007
1.Abstract
Masayuki Ishida (Moriyama ,Shiga) sent me a .CSV file of his observation of a doublestar SAO118981. And I also observed same event at IkedaTown, Nagano Pref.. I analyzed these observations using Limovie. The result of astrometry and photometry are as follows.
Table 1. Result of analysis 


Observation 
Catalog 
Separation (arcsec) 
0.80 
0.8 
Position Angle (degree) 
136 
130 
If the magnitude of the pair is 6.94 then .. 

First star(mag) 
7.0 
6.9 
Second star(mag) 
9.8 
9.9 
2. Limovie plot (overview luminous change)
Figure 1. Moriyama, Shiga
Figure 2. Ikeda, Nagano
3. Predictions and calculating parameters for analysis
31 Prediction
Table 2 Prediction derived from LOW
for Konohama, Shiga
For Ikeda, Nagano
Table 3 Prediction derived from Win OCCULT.
For Moriyama, Shiga
For Ikeda, Nagano
32 Caluclate Linar velocity
for Konohama obs. 
for Ikeda, Nagano 
Va : Velocity as angle (“/sec)， CCT : Contact Angle， RV : Radial Velocity Ds : Moon distance Then moon velocity V (m/sec) is calculated as follows. RV = cos(CCT)* Va Va = RV / abs(cos(CCT)) = 0.218 / abs(cos(+51)) = 0.3464 ("/sec) V = Ds*π*Va/(180*3600) Ds = 404564(km) V = 404564(*0.3464*pi()/(180*3600) = 679 m/sec

Va : Velocity as angle (“/sec)， CCT : Contact Angle， RV : Radial Velocity Ds : Moon distance Then moon velocity V (m/sec) is calculated as follows. RV = cos(CCT)* Va Va = RV / abs(cos(CCT)) = 0.151 / abs(cos(+64)) = 0.3445 ("/sec) V = Ds*π*Va/(180*3600) Ds = 404576(km) V = 404576(*0.3445*pi()/(180*3600) = 676 m/sec 
4. Diffraction Analysis
41. Moriyama, Shiga.
Figure 3.Disappearance of main component
Figure 4. Disappearance of companion
First star : No.282 Frame 11 millisecond +/ 2 millisecond
Time of TIVi (centre of frame) is No.282=10h42m12.23s then event time is 10h42m12.22s
Hence, the event time is 10h52m10.190sSecond star : No.343 Frame 13 millisecond +/ 10 millisecond
Time of TIVi (centre of frame) is No.343=10h42m14.27s then event time is 10h42m14.26s
Time Difference = 61 Frames – 2 millisecond = 61 / 29.97 – 0.002 second = 2.035 – 0.002 = 2.033 second
42. Ikeda, Nagano
Figure 5. Disappearance
Fugure 6. Appearance
First
omponent : No.645.5 Frame 21 millisecond +/ 5 millisecond
Time
of KIWIOSD are .. at field start :10h52m10.194s, at field end :
10h52m10.227s. Then centre of field is 10h52m10.211s .
Hence, the event time is 10h52m10.190s
Second component : No.711.0 Frame +0 millisecond +/ 57 millisecond
Time of KIWIOSD are .. at field start :10h52m12.363s, at field end : 10h52m12.396s. Then centre of field is 10h52m12.380s .
Hence, the event time is 10h52m12.380s
Time Difference = 2.190 second
5. Astrometry
Fig.7 Position of component and lunar limb 
Case of b2>b1 From Fig、6 b1=a*sin A (1) b2=a*sin(A+P1P2) (2) C=P1P2 b2=a*sin(A+C) =a*(sinA*cosC+cosA*sinC) =a*sinA*cosC+a*cosA*sinC (3) From (1) a = b1/sinA (4) put into (3) b2 = (b1/sinA)*sinA*cosC +(b1/sinA)*cosA*sinC b2 = b1*cosC+b1*(1/tanA)*sinC b2 = b1*cosC+b1*sinC/tanA b2 = b1(cosC+sinC/tanA) b2/b1 = cosC + sinC/tanA b2/b1  cosC = sinC/tanA (b2/b1  cosC)/sinC = 1/tanA tanA = sinC/(b2/b1  cosC) (5) put A into (4) and obtain separation a. Hence Position Angle P is P=90(p1+A) (6)
In the case of b1>b2 then a=b2/sinA (4) tanA = sinC/(b1/b2  cosC) –(5) P=90+p2A (6) 
P1=82 , P2=68 then C is
C=26 = 14
b1=0.218*2.190=0.4774
b2=0.151*2.033=0.3070
this case is b1>b2 then
tan A = sin14 / (0.4811/0.3070 – cos 14) = 0.4137
A = 22.48
P=90+6822=136
a=b2/sinA=0.3070/0.3823=0.8030
then
Separation = 0.80 (arcsec)
Position Angle = 136 (degree)
These values are well corresponding to the description of catalog .
6. Magnitude of stars
from Konohama obs. 
from Ikeda Nagano 
Lunimous of pair : 1381.9 Step : average(119.7,113.0) = 116.4 Background : 17.0 Luminous of first star = 1381.9116.4=1265.5 Luminous of second star=116.417.0=99.4 Lunious of pair = 1381.9 – 17 = 1364.9 from the canalog the pair is 6.92 .. (Tycho2) from the formula m1m2 = 2.5 log(b2b1) = 2.5 log() The difference in magnitude of the two star is .. m1m2 = 2.5 log(b2/b1) = 2.5 * log(1265.5/99.4) =2.76 if the magnitude of the pair is 6.94 then the magnitude of first star is .. m16.94=2.5*log(1364.9/1265.5)=0.08 m1=7.02 then the magnitude of second star is 9.78 
Lunimous of pair : 306.0 Step : average(14.0,16.5) = 15.3 Background : 1.9 Luminous of first star = 306.015.3=290.7 Luminous of second star=15.31.9=13.4 Lunious of pair = 306.0 – 1.9 = 304.1 from the canalog the pair is 6.92 .. (Tycho2) from the formula m1m2 = 2.5 log(b2b1) = 2.5 log() The difference in magnitude of the two star is .. m1m2 = 2.5 log(b2/b1) = 2.5 * log(290.7/13.4) =3.34 if the magnitude of the pair is 6.94 then the magnitude of first star is .. m16.94=2.5*log(304.1/290.7)=0.05 m1=6.99 then the magnitude of second star is 10.33 
In the observation at Ikeda, the gain of camera was set in a small value to avoid the off axis rays reflected at inside the optical tube. And it is considered that the value of pixels are not large enough to estimate the magnitude. Therefore, I will report the value calculated from Konohama observatory as star's magnitude.