Office of the Secretary of Defense: 027_Satellite_Flaring_Paper

All-domain Anomaly Resolution Office (AARO)
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where ℎ is satellite height above the Earth’s surface, 𝑅𝐸 is the Earth’s radius. As the zenith angle
is complementary angle of the look angle, 𝜀, the substitution 𝑧 = 𝜋
2 − 𝜀 has been made in Equation
(1).
Equation (1) is a transcendental equation, meaning that it must be solved numerically to find  as
a function of 𝑎, the sun’s altitude. Using the mathematical software package MATLAB®, a plot
was generated and is shown in Figure 10 for various Starlink satellite constellations, each of which
have varying orbital altitudes between about 540km and 570km.
Figure 11 illustrates the geometry for a nominal Starlink orbital altitude of 550km. Simple
trigonometry is used to determine that θr ≅ θi ≅ 67° and the angle A ≡ |a| + ε ≅ 46°. For
perfect specular reflection and a satellite bus with its bottom surface that is aligned exactly
perpendicular to its orbit, A = 46° and ε = 0. In other words, the satellite and resultant flare are
directly at the horizon. Realistically, no surface is a perfect specular reflector and any small
deviations from exactly perpendicular will reflect light off-axis resulting in ε ≠ 0. Assuming the
light cone is reflected as much as ± 2° off axis, Starlink flares are then generally visible when the
Sun’s altitude is roughly between -38° and -46° as illustrated in Figure 10. This is determined from
the inset in Figure 10, which shows that flares are visible somewhere between the horizon and
about 10° above the horizon for up to 2° off axis reflection, as indicated by the dashed green lines.
Figure 10: Plot of the Elevation Look Angle from the horizon to the satellite flare window as a
function of the Sun’s altitude below the horizon. Green lines indicate best set of Elevation Look
Angles for observing Starlink flares is up to about 10° above the horizon assuming off-axis
reflections up to 2°.027Page determined to be Unclassified
Reviewed by Chief of Staff, AARO
IAW FY24 NDAA, Section 1841(a)(1)(C)
Date: 2/14/2025