When Combined brightness for satellite trains is turned on, every member of an unresolved formation (e.g. a freshly-launched Starlink train) is drawn at the train’s combined apparent magnitude instead of its individual brightness — matching what a naked-eye observer actually sees. The math below explains why that combined magnitude is much brighter than any one member: brightness adds linearly, while astronomical magnitudes are logarithmic.

What “unresolved” means

Two light sources are unresolved when their angular separation is smaller than the observer’s resolving power, so the eye merges them into a single point or streak of light rather than seeing distinct dots.

• Naked-eye resolution under good conditions is about 1 arcminute (1/60 of a degree, or ~0.017°). Atmospheric turbulence, daylight, fatigue, and inexperience all degrade this in practice.
• What 1 arcminute means at orbital distances: at a slant range of ~550 km (a Starlink passing nearly overhead), 1 arcminute corresponds to a physical separation of about 160 m on the satellite; at ~1000 km, about 290 m; at ~1500 km (low on the horizon), about 440 m.
• Why fresh-launch Starlink trains look like a single streak: immediately after deployment the satellites are spaced only about 0.022° (~1.3 arcminutes) apart — barely above the naked-eye limit — so witnesses see one glowing “cigar of light” rather than a chain of discrete dots. Days later, as the satellites drift apart to operational spacing, they become individually resolvable and this effect disappears.

Internally, CuriousPilot treats satellites as one cluster when their pairwise angular separation is within 0.1° (6 arcminutes) and the resulting group is cigar-shaped (length at least 5× the width). The threshold is intentionally looser than ideal naked-eye resolution to accommodate real-world viewing conditions (atmospheric turbulence, twilight glare, untrained observers) under which the practical resolving power is several arcminutes rather than one.

Basic magnitude addition

Suppose:

• Each satellite has apparent magnitude x.
• There are N satellites contributing light.
• The satellites are unresolved — close enough in the sky (see above) that their light blends into a single perceived point or streak.

The flux from one satellite is proportional to:

F₁ ∝ 10^−0.4x

The total flux from N identical satellites is:

F_tot = N · F₁

The combined magnitude is therefore:

m_tot = −2.5 · log₁₀(F_tot) + C

which gives:

m_tot = x − 2.5 · log₁₀(N)

This is the standard result for combining equal-brightness sources.

Example: 48 satellites

For N = 48:

2.5 · log₁₀(48) ≈ 4.20

so:

m_tot ≈ x − 4.20

Thus 48 unresolved magnitude-4 satellites would appear roughly as a magnitude −0.2 object.

If the satellites are not equally bright

More generally, if the satellites have individual magnitudes m_i:

F_tot = ∑_i=1..N 10^{−0.4 · m_i}

and the combined magnitude is:

m_tot = −2.5 · log₁₀( ∑_i=1..N 10^{−0.4 · m_i} )

This is the formula used for a realistic Starlink train because illumination and orientation vary from satellite to satellite.

Important caveat: specular reflections (“flares”)

The calculation above assumes the satellites act as independent incoherent light sources and that their reported magnitudes already describe the brightness seen by the observer.

Specular reflections complicate things:

• A satellite flare can be several magnitudes brighter than its average brightness.
• If only one satellite is producing a strong glint toward the observer, that one satellite may dominate the total flux.
• The train’s brightness then becomes approximately the brightness of the brightest glint plus the summed contribution of the others.

For example, if one satellite is magnitude −2 during a flare and the other 47 are magnitude 4, the combined magnitude is not simply (−2 + 4.2). Instead you sum the fluxes:

F_tot = 10^0.8 + 47 × 10^−1.6 ≈ 6.31 + 1.18 ≈ 7.49

giving m_tot ≈ −2.19. The flare contributes most of the light, and the total magnitude is only slightly brighter than −2.

Another caveat: surface brightness vs. integrated magnitude

If the train is visibly elongated (“cigar-shaped”) rather than point-like, the integrated magnitude is still:

m_tot = x − 2.5 · log₁₀(N)

but its light is spread over a larger angular area. The object may appear less conspicuous to the eye than a point source of the same integrated magnitude because the surface brightness is lower. Astronomers distinguish between:

• Integrated magnitude — total light received.
• Surface brightness — light per unit angular area.

For visual detection from aircraft or the ground, both quantities can matter.

Summary

If N identical satellites are unresolved and each has magnitude x, the train’s integrated magnitude is simply:

m_train = x − 2.5 · log₁₀(N)

— with the understanding that real Starlink trains often deviate from this because of differing phase angles, attitude variations, and occasional specular glints.

When Compute & show satellite flares is turned on, the simulator runs the specular-reflection geometry for every Starlink each tick and, when a chassis is aligned to reflect sunlight toward your observer location, boosts that satellite’s brightness and draws the flare. Starlink satellites can briefly become very bright this way — these flares are the most likely explanation for many recent UAP reports from pilots and ground observers near twilight.

When this option is turned off, the flare math is skipped entirely. A flaring Starlink will be shown at its dim baseline magnitude instead of its flare-boosted magnitude — so if its baseline is dimmer than the magnitude-slider cutoff, the satellite will not appear at all, even during a bright flare.

The ⚡ indicator flags Starlinks predicted to be flaring at the current simulated instant — the chassis is geometrically aligned to reflect sunlight toward your observer location. You’ll see ⚡ in three places:

• On the sky canvas, the satellite dot grows and brightens during the flare.
• The Satellites Visible list shows a ⚡ prefix on the row, and the magnitude column tracks the instantaneous brightness (not the diffuse value).
• Hovering a flaring satellite shows the live magnitude in the tooltip, with the underlying diffuse mag listed below for context.

You can also click the Predict flares button (below the checkbox) to sweep the loaded simulation timespan and get a sortable list of every predicted flare in your sky — with peak time, peak magnitude, elevation, and azimuth. Click any row to seek the simulation to ~5 seconds before that flare’s peak so you can watch it play out.

Predicted peak magnitudes come from the per-Starlink-generation log curves in Mallama & Cole (2024). The four generations (V1.0, VisorSat, V1.5, V2 Mini) are classified automatically from the SpaceX serial number; unclassifiable rows fall back to the V1.5 curve.

Important caveats:

• Attitude is assumed, not measured. The math assumes a nadir-pointing flat chassis. Real Starlink attitude is not public; satellites slewing during maneuvers will not flare as predicted, and may flare when not predicted.
• The ground footprint is narrow. The specular reflection cone is only tens of kilometers wide on the ground — a flare predicted here may not be visible if you are slightly off-axis from the satellite’s ground track.
• Brief flares may be missed. The live ⚡ indicator is evaluated each propagation tick (around 5 Hz at 1× speed); the Predict sweep uses a 5-second step. Flares shorter than that can fall between ticks.
• Brightness predictions are approximate. The visual icon at peak may read brighter than what you’d actually see — the brightness curves come from a small published dataset and tend to over-saturate at the very center of the flare cone. The geometric “is it flaring now” signal is reliable; the absolute magnitude is approximate.

Currently only Starlink is supported, because it is the only constellation with publicly characterized chassis geometry and a published per-version brightness model. OneWeb and BlueWalker / BlueBird may be added later.

When Show flare traces is turned on, any flaring satellite at or brighter than the chosen magnitude threshold draws its trace as a bright warm yellow-white wake instead of the normal gray. The trace appears even when the global “Show lines” option is turned off — that’s the point of the setting: to make flares easy to spot without having to enable lines for every satellite.

How it works:

• The magnitude slider next to the checkbox sets the cutoff (default +3.0; range −5 to +9). Only flares at or brighter than this magnitude get highlighted. Magnitudes are inverted, so a lower number means brighter.
• The All checkbox bypasses the threshold and highlights every flaring satellite regardless of brightness. It does not relax the “must actually be flaring” requirement — a non-flaring satellite never gets a bright trail.
• Bright trail segments are frozen into the trail’s history. Once a point is laid down bright, it stays bright until it rolls off the end of the trail buffer — so if the same satellite re-flares moments later, the historical bright marks come back into view alongside the new ones.

The flare indicator and prediction model itself (the ⚡ icon, the Predict flares button) are described in the help dialog next to Compute & show satellite flares above. This setting controls only the trace color — it does not change which satellites are flagged as flaring.

When Show satellites in Earth’s shadow is turned on, satellites that are above the horizon but inside Earth’s umbra (the cone of complete shadow behind the planet) are rendered on the canvas instead of being hidden. They show as small dim slate-blue dots, marked with the ⊘ symbol throughout the UI, so the “this object is here but unobservable” signal is unmistakable.

What the rendering means:

• The dot shows where the satellite is, not what it would look like to your eye. A satellite in Earth’s shadow reflects zero sunlight — nothing reaches the observer — so its true apparent magnitude is effectively infinite, and it is invisible to the naked eye and to cameras.
• The same slate-blue colour appears in the tooltip (⊘ In Earth’s shadow annotation), in the Satellites Visible list (⊘ row prefix and ∞ in the magnitude column), and in the trail line if the “Show lines” option is on.
• The magnitude slider still applies: a shadowed satellite whose what-if (as-if-sunlit) magnitude would be too dim to pass the slider is still hidden, so the screen doesn’t fill with sub-cutoff dots.
• In the Satellites Visible list, shadowed rows sort as ∞ — brightest-first puts them at the bottom (physically unobservable), dimmest-first puts them at the top (handy as a “what’s currently hidden in shadow” view).

Typical use: watching a freshly-launched Starlink train light up one satellite at a time as it emerges from shadow; confirming whether a specific satellite is geometrically present at a given instant; identifying which satellites are dark vs. lit when investigating a sighting that occurs near twilight.

This is a diagnostic affordance — it intentionally shows information that is not directly observable. If you want only what an observer could actually see, leave the checkbox off.