Light Curves

 

The aim of this work was to use my finder camera to produce calibrated light curves for satellite passes. The finder camera has a 135mm f2.8 lens and uses a 1004XA board camera with a 1/3" BW Sony EXviewHAD chip. Tis chip has a 0.003 LUX rating and can capture stars down to about magnitude7.0. The field dimensions are 125.4'x94.0' making it easy to keep the satellite in view during tracking

Camera Calibration

To calibrate the camera I wrote a calibration tool for the AutoTrack program which finds stars of any desired magnitude from the bright star catalogue and points the LX200 at them. The user then clicks on the star and the program calculates a brightness. The brightness is the sum of all pixels in a box round the star after subtracting the sky background (mean plus 3.5 standard deviations). 

An example result from December 2006. The program found stars in roughly half magnitude intervals ,all either spectral type A or B. I t calculates a regression line as well but the result is reproduced here by XL. 

The theoretical gradient is -2.5 if the camera and capture card are perfectly linear in response. 

 

The camera model is therefore

magnitude = M0 - k log10(brightness)

M0 is the magnitude for unit brightness
k is the gradient which is theoretically -2.5 from the definition of the magnitude scale. 

Lacrosse 2 Result

A light curve for Lacrosse 2. Despite the large field of view the satellite wandered outside the magnitude calibration box around closest approach hence the spikes to around magnitude 5. 

Modelling the Magnitude

The estimated magnitude is a curve fit to the measured magnitude. The basic equation for the curve is 

magnitude = A + B*log10(range/1000)+C*log10(I)+D*log(max(1,Fmax-F))

where

A is the magnitude at 1000km, fully illuminated and not flaring
B is the theoretically +5 for an inverse square law
I is the illuminated fraction obtained from the phase angle phi using  I=(1+cos(phi))/2. This equation is true for a spherical object.
F is the flare angle and Fmax is the maximum flare angle or cut-off above which no flare is seen

The curve fit for Lacrosse 2 above has A=2.34, B=5 and C=-1.56. Due to the bad data in the middle I fixed A and C manually although my program has a least squares capability for all parameters. D is not used here because no flare occurred. 

 

Here is a screen shot from the light curve program. The graph is rudimentary but the results can be saved to a CSV file for use in XL.

 

 

 

 

 

 

 

 

 

ERS 2 Dimensions
Overall height: 11.8 m
Solar generator: 11.7 x 2.4 m
SAR antenna: 10 x 1 m
Total mass: 2516 kg

ERS 1 Dimensions
Mass 2400kg
Dimensions 12x12x2.5m 

 

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