Starlink v1.0: Photometric Analysis

• Starlink v1.0 is the initial deployment of SpaceX’s LEO mega-constellation with distinct photometric properties and brightness profiles.
• The satellites show phase-dependent brightness variations and light curve morphologies, including specular flares that affect ground-based astronomical observations.
• Mitigation designs like dark coatings and deployable visors reduce satellite brightness by 40-60%, providing practical solutions to minimize contamination in astronomical surveys.

SpaceX’s Starlink Version 1 spacecraft, constituting the initial operational deployment of the Starlink low earth orbit (LEO) mega-constellation, exhibit photometric and geometric properties that have direct implications for satellite visibility, ground-based astronomical surveys, and mitigation strategies. Empirical studies using large datasets of multi-band photometry and visual magnitude measurements establish the quantitative basis for characterizing the brightness, phase-angle response, color indices, and the engineering-driven design evolution of Starlink v1.0 and its derivatives.

1. Photometric Properties and Brightness Distributions

The intrinsic brightness of Starlink v1.0 satellites is defined with reference to absolute magnitudes reduced to a standard distance (1,000 km). A comprehensive multi-color observational campaign using the Xinglong 50 cm telescope yielded the following median photometric statistics for v1.0, based on 814 light curves (24,276 data points) (Zhi et al., 2024):

Filter	Median M (mag)	σ (mag)
Clear	5.97	0.62
g	5.85	0.45
r	5.71	0.44
i	5.67	0.33

The observed median r-band absolute magnitude of $M_r \approx 5.7$ at 1,000 km corresponds to apparent $r \approx 4$–$6$ at typical LEO altitudes (e.g., 550 km), surpassing the SATCON1 recommendation for satellite apparent magnitude ($m > 7$) required to avoid significant contamination of survey images.

The characteristic magnitude $m^*$, representing the average apparent magnitude of a satellite observed at zenith at the end of astronomical twilight (solar phase angle $\alpha^*=72^\circ$, altitude 550 km), is more luminous for the Original v1.0 design ($m^*\approx 4.7$), with fainter values for subsequent mitigation variants (Mallama et al., 2022).

2. Illumination Geometry and Phase Function

Starlink v1.0 satellite brightness is determined predominantly by the solar phase angle (SPA), defined as the vertex angle Sun–satellite–observer:

$$\varphi(t) = \arccos \left( \frac{ (\mathbf{r}_\odot - \mathbf{r}_\text{sat}) \cdot (\mathbf{r}_\text{obs} - \mathbf{r}_\text{sat}) }{ |\mathbf{r}_\odot - \mathbf{r}_\text{sat}| \; |\mathbf{r}_\text{obs} - \mathbf{r}_\text{sat}| } \right)$$

After correcting for range $d(t)$ and instrumental/atmospheric factors, the calibrated magnitude is:

$$m_\text{cal} = m_\text{inst} - kA - m_d - Z - k_c C_\text{std}$$

where $A(\zeta)$ is the airmass, and $$m_d = 2.5 \log_{10} \left[(1{,}000\,\text{km})^2/d(t)^2\right]$$ adjusts for non-standard distance (Zhi et al., 2024).

The phase-angle dependence of brightness ($m(\varphi)$) in the r-band for $0^\circ \leq \varphi \leq 90^\circ$ is well described by a 6th-order polynomial fit:

$$m(\varphi) = a_0 + a_1\varphi + a_2\varphi^2 + a_3\varphi^3 + a_4\varphi^4 + a_5\varphi^5 + a_6\varphi^6$$

For the broader visual band, a quadratic phase function $\Phi(\alpha) = a_0 + a_1\alpha + a_2\alpha^2$ is also effective. Original v1.0 satellites display a relatively flat phase curve over a wide angular range with only modest brightening at low SPA due to pronounced specular glints off highly reflective aluminum surfaces (Mallama et al., 2022).

3. Light Curve Morphologies and Sources of Variability

Analysis of individual light curves reveals a smooth, monotonic brightening trend as $\varphi \to 0^\circ$, with sporadic, brief specular “flares” at the smallest phase angles. Over the interval $\varphi \in [5^\circ, 90^\circ]$, a typical peak-to-peak amplitude $\sim 2$ mag is observed; the standard deviation at fixed phase angle is $0.4$–$0.6$ mag, attributed to small but stochastic variations in spacecraft attitude (flat-panel orientation) and surface reflectivity heterogeneities (Zhi et al., 2024).

Folded phase-angle–magnitude curves confirm this structure, with measured $m_r \approx 7$ mag at $\varphi \approx 90^\circ$ rising to $m_r \approx 4.5$ at $\varphi \approx 5^\circ$, consistent with the model fits.

4. Comparative Evolution: Mitigation Designs and Brightness Suppression

To address adverse impacts on astronomy, Starlink implemented sequential hardware modifications: DarkSat adopted dark surface coatings, VisorSat incorporated deployable sun visors, and Starlink v1.5 refined the visor concept. The effectiveness of these interventions is measured by the magnitude difference $\Delta m(\varphi)$ relative to v1.0, and the corresponding fractional brightness reduction:

$$\Delta m(\varphi) = m(\varphi) - m_0(\varphi) = -2.5\log_{10}\left[\frac{F(\varphi)}{F_0(\varphi)}\right]$$

$R(\varphi) = [1 - 10^{-\Delta m/2.5}] \times 100\%$

Median scattered-light reductions (for $\varphi < 90^\circ$) are:

Variant	Median Reduction	Mechanism
DarkSat	≈60%	Low-albedo (matte) coatings
VisorSat	55.1%	Deployable visors
Starlink v1.5	40.4%	Improved visor geometry & materials

Visored variants show largest suppression at intermediate SPA, with lingering residual specular flares remaining at low phase angles due to incomplete coverage and persistent metallic surfaces (Zhi et al., 2024, Mallama et al., 2022).

5. Color Index Distribution and Photometric Identification

Simultaneous $g$, $r$, and $i$ photometry permits calculation of color indices ($g$–$r$, $r$–$i$) for matched phase angle and epoch. Starlink v1.0 forms a tight cluster in ($g$–$r$, $r$–$i$) double-color space, with a centroid of $(0.35 \pm 0.05,\,0.15 \pm 0.05)$ mag. This clustering is more robust than correlations with phase angle or single-band magnitude, facilitating unambiguous identification of v1.0 buses among heterogeneous satellite populations (Zhi et al., 2024).

6. Consequences for Ground-based Astronomical Observations

The photometric properties of Starlink v1.0 and its early successors have significant impacts on wide-field, time-domain, and deep-field astronomical surveys. The bright streaks produced—when apparent $r$-band magnitude typically lies in the 4–6 range—are above the SATCON1 mitigation target ($m > 7$), necessitating the adoption of both hardware (e.g., visors, coatings) and observational protocols (e.g., avoidance scheduling, real-time crossing prediction) to mitigate contamination. Image-processing masks are critical to deal with trails spanning $\sim3''$ FWHM in out-of-focus detector planes, and satellite-generated scattered light increases the local background by $\sim 10\%$.

Predictive models exploiting the deterministic phase dependence $m(\varphi)$ can optimize observation windows but are insufficient to eliminate contamination by specular glints and trailing artifacts (Zhi et al., 2024).

Mitigation interventions reduce mean trail brightness by 40–60%, but cannot fully suppress flare events. The design trajectory indicates an ongoing requirement for both engineering controls and coordinated orbital/attitude management (e.g., advanced TLE release and phase-aware pointing) to converge on magnitude thresholds compatible with next-generation surveys such as LSST/Rubin (Mallama et al., 2022).

7. Numerical Phase Function and Characteristic Magnitude Summary

The phase functions for the Original, VisorSat, and Post-VisorSat models are fit quadratically as:

$\Phi(\alpha) = a_0 + a_1\alpha + a_2\alpha^2$

with coefficients (Table 1 in (Mallama et al., 2022)):

Model	$a_0$	$a_1$	$a_2$	$m^*$ (zenith, twilight)
Original	4.774	0.02496	$-0.0001023$	4.7
VisorSat	3.493	0.09481	$-0.0005412$	6.2
Post-VisorSat	3.944	0.06893	$-0.0004089$	5.5

The Original phase function is relatively flat; VisorSat introduces pronounced minima at moderate $\alpha$, and Post-VisorSat achieves an intermediate response.

Consequently, the absolute and phase-normalized photometric characterization of Starlink v1.0 underpins mitigation policy and the engineering evolution of the Starlink constellation. These data-driven models provide a quantitative foundation for future mega-constellation impact assessments and response strategies (Zhi et al., 2024, Mallama et al., 2022).