Value chain · CLM-1163
In plain terms
Between the spring conference paper and the autumn final report, Boeing's figure for how bright a satellite would glow at night fell twelve-and-a-half-fold, from ten times Venus to about Venus, and the report does not say why; the factor is almost exactly what a 4-pi slip in the diffuse-reflection formula would give.
The claim as recorded
The final Boeing brightness report's Table 5 prints the diffuse night-time irradiance of an SPS in GEO as 8 x 10^-7 W/m2 and of the OTV/staging base in LEO as 2.4 x 10^-5, where the same table in the April 1980 proceedings paper (SRC-449 PDF 489) prints 1 x 10^-5 and 3 x 10^-4, every other row being identical; both differences are a factor of 12.5, which is 4 pi to half a per cent, and the final report's equation (1), H_d = K r_d a H_sun G / (2 pi R^2) with its case D2 inputs (K 0.8, r_d 0.05, 58 km2, 1,400 W/m2, 5.2 deg, 35,700 km), reproduces its own 8 x 10^-7; by the report's magnitude formula 8 x 10^-7 is -3.6 ("comparable to Venus") and 1 x 10^-5 would be -6.3, so the April paper's "an order of magnitude more light than Venus at its brightest" and the October report's "comparable to the stellar magnitude of Venus at its brightest" are consistent with one calculation before and after a 4-pi change in the diffuse normalisation, which the report does not mention; a changed input (reflectance or area) giving the same factor in both rows is not excluded.
Evidence behind this: T3-two printings of one contractor table six months apart, both read at the render, with the final report's equation recomputed here; the factor between them is the audit stream's arithmetic (2026-09-20 read), the report states no change.
Scope and limits
THE 4-PI IDENTIFICATION IS THE AUDIT STREAM'S ARITHMETIC (2026-09-20 READ): two rows moved by one factor, the factor equals 4 pi, and the final equation reproduces the final table; the report never states that a normalisation changed, and a changed input (reflectance or area) producing the same factor in both rows is not excluded. Not an ON-027 case (12.5, not a power of ten) and not asserted as an error in either printing. The specular rows, which carry the brightest cases, did not change.
What it assumes
The proceedings' table was computed with the same inputs (area, reflectance, geometry) as the final report's; the report does not say and the proceedings paper prints no equation with its table.
Where it comes from
PDF 68 / printed 65, Table 5 (crop read): Diffuse 1 OTV/SB in LEO 2.4 x 10^-5; Diffuse 2 SPS in GEO 8 x 10^-7; Diffuse 3 4 x 10^-6; Diffuse 4 2 x 10^-7 and 5 x 10^-8; Specular rows 1.2, 19, 0.1, 2, 0.03, 0.0003, 0.01, 0.19, 0.01, 0.002, 56, 0.4 W/m2. SRC-449 PDF 489 / printed 468 (render read): Diffuse 1 3 x 10^-4; Diffuse 2 1 x 10^-5; Diffuse 3 4 x 10^-6; Diffuse 4 2 x 10^-7 and 5 x 10^-8; the same specular values. PDF 49 / printed 46: "it will be assumed that the total area of the SPS (58 km2 from Case S2) is a diffuse source with rd= 0.05" and "R = 35,700 km resulting in an irradiance of 8 x l0- 7 W/m2" (normalised, the page's l for 1); "Thus a = l .62 km and the diffuse irradiance is 2.4 x lo- 5 W/m2" (normalised, case D1). PDF 46 / printed 43 (render read): equation (1) as transcribed in the claim, H_sun 1.4 x 10^3 W/m2 "is the solar constant at earth" (raw), r_d "is the diffuse reflectivity, and" (raw), G = 2 cos theta_r cos theta_i "for Lambertian surfaces" (raw). PDF 69 / printed 66 (render read): "diffuse reflection from SPS in GEO (02) has an apparent magnitude of -3.6, and specular reflection from the SPS antenna in GEO (S3) has a magnitude of -13.8, comparable to the full moon" (normalised); PDF 67 / printed 64: "the SPS in GEO is ccmparable to the stellar magnitude of Venus at its brightest" (normalised). CLM-1074 for the April paper's "the SPS in GEO casts an order of magnitude more light than Venus at its brightest" (SRC-449 PDF 487). Recomputed: 3e-4 / 2.4e-5 = 12.5; 1e-5 / 8e-7 = 12.5; 4 pi = 12.566; equation (1): 0.8 x 0.05 x 5.8e7 x 1400 x (2 cos^2 5.2 deg = 1.984) / (2 pi x (3.57e7)^2 = 8.01e15) = 8.0e-7; m(8e-7) = -26.7 - 2.5 log10(5.71e-10) = -26.7 + 23.1 = -3.6; m(1e-5) = -26.7 + 20.4 = -6.3; m(0.01) = -26.7 + 12.9 = -13.8; magnitude difference 2.5 log10(12.5) = 2.7, "an order of magnitude" in light is 2.5 magnitudes.
Basis: W/m2 diffuse ground irradiance; apparent magnitude m = -26.7 - 2.5 log10(H / 1400)
Cite this
energyaperture.com/c/clm-1163
CLM-1163, Energy Aperture, as of 1980-10.
Connected records
Other published records linked to this one. A list, not a judgement.
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- Also from SRC-530
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