Same governing equations as the 3D detector, rendered as two genuinely 2D-native diagrams instead of a planet floating past a camera:
log10(L / L_sun) ≈ -3.6 + 1.6·log10(M / M_Jup) - 0.9·log10(t / 10 Myr)
T_eff = ( L / (4π R² σ) )^(1/4), R ≈ 1 R_Jup
M_bol = 4.83 - 2.5·log10(L / L_sun)
m = M_bol + 5·log10(d / 10 pc)
Top panel — cooling track. A real astrophysical isochrone diagram: luminosity vs. age on log–log axes, exactly how astronomers plot substellar cooling tracks. Faint reference curves show fixed masses (1, 6, 12, 20 MJup); the bright curve is the track for the current mass slider, and the dot marks the planet's live position on it. The dashed horizontal line is the minimum luminosity the chosen telescope could detect at the current distance — cross above it and the dot turns green.
Bottom panel — brightness vs. distance. A parameter-space plot, not a spatial one: apparent magnitude (brighter = higher on the axis, matching astronomical convention) traced across the full 1–300 pc range at the current mass and age, with the telescope's limiting magnitude as a horizontal line. Where the curve is above that line, the planet is detectable; the live marker shows exactly where the current distance sits relative to that crossing.
- Mass — sets how much gravitational energy is available to radiate; heavier tracks sit higher on the cooling-track panel at every age.
- Age — moves the dot rightward along its track as luminosity falls with a power law in time.
- Distance — moves the marker rightward on the bottom panel; brightness dims with the inverse-square law (linear in the log-distance, semi-log view here).
- Survey telescope — sets both horizontal threshold lines; a deeper survey (larger limiting magnitude) pushes its line down on the bottom panel and its line down (fainter luminosity) on the top panel, making detection easier.
This is one of two real ways astronomers find rogue planets — the other is gravitational microlensing, covered in this site's separate microlensing light-curve simulator. Direct infrared imaging only works for young, still-warm free-floating planets; older ones are far too cold and faint for any current telescope to image directly.