Absolute magnitudes

Rainer Kracht (0412188960-0001@t-online.de)
Wed, 29 Nov 95 00:47 +0100

Absolute Magnitudes from Russell's Satobs

Ted Molczan wrote in seesat 1069:

>Some day, I would like to replace or augment the dimensions with true
>standard magnitudes, determined through observation. Russell Eberst's
>observations are a treasure trove of magnitude data. The main task
>will be to reconstruct the circumstances of the observations, i.e. range
>and solar phase angle. Once that is done, it should be relatively easy
>to determine means and standard deviations of magnitude.

It is simple to reconstruct the solar phase angle of an 
observation. One has just to compute the position of the sun for 
the time of the observation and then the angular distance of the 
satellite from the sun (elongation). The phase angle is then 180 
deg - elongation, since the sun is much farther away than the 

Due to the high accuracy of Russell's observation one can get very 
good range estimates through calculating circular orbits from 
pairs of his observations, if the orbit of the satellite is nearly 
circular (thus eliminating the need to search for suitable two 
line elsets for each of his observations).

About one year ago I have used two line elsets of 91-17A and a 
satellite prediction program to reconstruct the circumstances of 
26 observations of 91-17A from 1994 May 26 to 1994 Sep 09 and 
derived an absolute magnitude of 3.7 for Lacrosse 2.

I have now tested the new method with Russell's observations of 
Lacrosse 1 (1988-106B, 19671) and Lacrosse 2 (1991-17A, 21147) 
from 1991 April 26 to 1995 October 09. These satellites should 
show similar absolute magnitudes (of about mag 3.7) and phase 

Result from 487 observations of 88-106B by RDE:

m = (2.97 1 0.06) + (0.0072 1 0.0008) * phase + 5 * LOG10(range/1000)
Absolute magnitude (1000 km, 90 deg) is 3.62.

Result from 472 observations of 91-017A by RDE:

m = (3.10 1 0.08) + (0.0062 1 0.0008) * phase + 5 * LOG10(range/1000)
Absolute magnitude (1000 km, 90 deg) is 3.66.

Both results correspond very well giving an absolute magnitude of 
3.64 and a phase coefficient of about 0.0067 for the Lacrosse 

Rainer Kracht