Re: [Utah-astronomy] Predicting the brightness of a satellite at distance x, how to
I made a simple magnitude model of the LCROSS-EDUC brightness at various observer-booster distances out to 400,000 km. The results of the model are shown graphically in two figures: Magnitude by distance http://members.csolutions.net/fisherka/astronote/observed/LCROSS/20090118Cen... y axis = Centaur estimated apparent magnitude; x axis = observer satellite distance km Minimum aperture by distance http://members.csolutions.net/fisherka/astronote/observed/LCROSS/20090118Cen... y axis = minimum aperture inches; x axis = observer satellite distance km The simple model has based on two Centaur booster records in the CalSky and Heaven's Above satellite databases that describe the apparent magnitude at perigee (100% illumination) and at a standard distance of 1000km (50% illumination): Object USSPACE-CMD Id Int’l ID MStar 3 Cent Rocket 25725 1999-023B USA 136 Cent Rocket 25035 1997-068B The MStar 3 Cent Rocket is a currently observable satellite. Heaven's Above has more that 150 observations for this object, the last being on 17 Jan. 2009. The simple magnitude model is based on differential magnitudes and a simple telescopic limiting magnitude equation: m2 - m1 = 5 * log10(d2/d1) Distance modulus formula m2 = 5 * log10(d2/d1) + m1 Distance modulus formula solved for m2 m2=1.8 + 5*log10(D_mm) where m2 is Telescopic Limiting Magnitude. Steavenson-Sigdwick simple telescopic limiting magnitude (TLM) D_mm = 10^(m2-1.8)/5) where m2 is Telescopic Limiting Magnitude. Steavenson-Sigdwick TLM solved for minimum aperture to observe a magnitude. A spreadsheet of supporting computations can be found at: http://members.csolutions.net/fisherka/astronote/observed/LCROSS/20090118EUD... Comments and criticisms of the above are welcomed and appreciated. I am looking for confirmation by more experienced observers that the approach is sound and that there are no basic thinking errors in it. Thanks, Kurt
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