Core concepts
Magnitudes
Apparent, exo-atmospheric and normalised magnitudes, and the equivalent albedo-area.
Apparent V magnitude
Section titled “Apparent V magnitude”The magnitude is the astronomers’ brightness scale: the smaller the number, the brighter the object, and 5 magnitudes are a factor of 100 in flux. LightCurve works in the Johnson V band (around 550 nm).
From the reflected intensity I (m² sr⁻¹, per unit of solar irradiance), the range d and the Sun–object distance r:
m = −26.74 − 2.5 log10( I / d² ) + 5 log10( r / 1 au )−26.74 is the V magnitude of the Sun at 1 au.
The magnitudes shown
Section titled “The magnitudes shown”| Value | Meaning |
|---|---|
| Apparent V magnitude (big number) | Brightness seen from the station, after atmospheric extinction |
| Exo-atmospheric | The same above the atmosphere (what an observer in orbit sees) |
| Extinction | k × X: extinction coefficient times airmass |
| 1σ interval | 68 % interval of the Monte-Carlo uncertainty |
| Magnitude at 1,000 km | Exo-atmospheric magnitude brought to a 1,000 km range: m − 5 log10(d / 1000 km). Comparable between objects at different ranges, at the same phase |
| Equivalent A·σ | Albedo × cross-section of the diffuse sphere that would be as bright at this phase. A quick “optical size” |
Standard magnitudes in the literature
Section titled “Standard magnitudes in the literature”Published “standard” or “intrinsic” magnitudes use different conventions, which Validation reproduces:
- Quicksat (M. McCants): 1,000 km, full phase, “brightest likely” magnitude.
- Molczan: 1,000 km, 90° phase, average magnitude (about 1.4 mag fainter than Quicksat for the same object).
- Characteristic magnitude (Mallama): mean brightness when the satellite is at the zenith at the end of astronomical twilight (phase ≈ 72°), at its operational altitude.
LightCurve’s magnitudes are V-band. An unfiltered CMOS camera calibrated on Gaia G can differ by a few tenths of a magnitude, depending on the colour of the object.