Thanks to Mike Waterman for posting his report of the observation of the Apollo 12 3rd stage (69099B, #04226) back in 1969. You must keep some excellent records! > I observed the Apollo 12 3rd stage (69099B = #04226) and its fuel > dump on 19691114 from 2042 to 2056UT. > ... At 2043 the rocket was flashing max mag 8, period 2.5s. > The range was 29000 km. I do not have RA/dec at 2043, but it > would only move a few degrees until 2057 when RA=20:09 > Dec=8.6 (epoch 1950). > Site = COSPAR 2428 = 51.3136N -0.7417E. (Not that it's important to this analysis, but is that .7417 east, or .7417 west? Negative longitudes usually imply western longitudes.) > The sun would then be about RA=1522 Dec=-19, about 76 degrees away. > Using Robert Matson's formula, Phase factor = 0.65 Yes -- I concur. > Standard mag = 8 + 15 - 2.5*log10(29000^2/0.65) = 8+15-22.8 = 0.2 . Also correct. Mike McCants has informed me that the 7.4 x 2.4m Cosmos boosters are in fact quite dark, so it's possible that the Saturn IV-B is many times brighter. One can estimate the theoretical maximum brightness for a white lambertian cylinder with the dimensions of the Saturn IV-B, in order to put an upper limit on the brightness. The exoatmospheric solar constant is 1353 W/m^2, though this figure varies some with time of year due to the earth's elliptical orbit. Only about 13% of this energy is in the spectral range of 5000-6000 angstroms (the peak region of the visual response curve). The inband energy percentage increases a bit when you include the full 4000-7000 angstrom visual band. When you convolve the solar spectrum with the photopic visual response curve, you get about 384 watts/m^2. A magnitude 0 object corresponds to an illuminance of ~2.65 x 10^-6 lumens per meter-squared, and there are 350 lumens/watt for the solar spectrum across the visual band. So: (2.65e-6 lm/m^2) / (350 lm/W) = 7.57e-9 W/m^2 for a zero magnitude object (e.g. Vega). Unfortunately, I have found conflicting references for the conversion factor between watts/meter^2, lumens, and visual magnitude, so there is some uncertainty in the above value. For example, I found one reference which gave an exoatmospheric illuminance of 2.089 x 10^-6 for a magnitude-0 object, a difference of about 0.26 magnitudes from the figure above. But let's turn to the booster. Viewed broadside, it has a projected area of 117.5 square-meters, so at full-phase it collects (384 W/m^2)*(117.5 m^2) = 45100 watts. I won't get into the calculus here, but a lambertian reflecting cylinder has pi/4 times the brightness of a lambertian reflecting plane with the same projected area. The intensity of the booster is: (pi/4)*45100 watts / (pi steradians) = 11275 W/sr. At a range of 1000 km, this results in an irradiance of 1.13e-8 W/m^2, which corresponds to a visual magnitude of -0.43 using the above conversion formula. The "standard magnitude" for the booster would be 1.24 magnitudes dimmer (a factor of pi in brightness) or +0.81. This is ~0.6 magnitudes dimmer than what Mike Waterman measured in 1969. Considering the many possible error sources, this is pretty good agreement. So, I must agree with Mike McCants' remarks - the Cosmos rocket bodies are VERY dark, and thus a poor choice for comparison with the Saturn IV-B. Indeed, even if the standard magnitude of these Cosmos rockets is brightened from +5.5 to 5.0 (to correct for the factor of pi vs. factor of two conversion from 100% phase), their albedo works out to about 14%. So, allowing for some decrease in albedo after 30 years in a space environment, 69099B and 2000 SG344 may indeed be one and the same. To bring a 0.81 standard magnitude down to the observed +2 requires a reflectivity of about 33%; to get it to +1.8 implies a reflectivity of 40%. Include some uncertainty in the CCD measurement of the magnitude of 2000 SG344, and the derived reflectivity could take on a wide range of reasonable values. So alas, this analysis shows that the Saturn rocket can neither be confirmed or ruled-out as the identity of 2000 SG344. I say hit it with radar -- the magnitude and variation in signal return over time should be able to differentiate a perfect cylinder from a rock. Final words from Mike Waterman: > Footnote: shiny spheres have no phase factor. > Shiny cylinders will have some phase factor, but I believe > the effect will be less than the formula above. Specular spheres indeed have no phase factor. But shiny spheres and shiny cylinders are always dimmer than their lambertian counterparts of the same reflectivity. Best, Rob ----------------------------------------------------------------- Unsubscribe from SeeSat-L by sending a message with 'unsubscribe' in the SUBJECT to SeeSat-L-request@lists.satellite.eu.org http://www2.satellite.eu.org/seesat/seesatindex.html
This archive was generated by hypermail 2b29 : Tue Nov 14 2000 - 14:50:18 PST