Interactive Observational Astronomy Calculator

Exoplanet Transit & Equilibrium Calculator

Compute photometric transit depth ΔF/F (in % and parts per million) and planetary equilibrium temperature T_eq (K) from stellar radius, stellar temperature, planet radius, orbital distance, and Bond albedo.

Governing Formula: ΔF / F = (R_p / R_★)² ; T_eq = T_★ × √(R_★ / (2 a)) × (1 − A_B)^(1/4)

Interactive Calculation Workbench

Computed Output: Transit Depth ΔF/F = 0.504% (5042 ppm) · Equilibrium Temp T_eq (A_B=0.30) = 225 K

Derivation & Physical Background

Space photometry missions (Kepler, TESS, JWST) measure the fractional drop in starlight ΔF/F = (R_p / R_★)² when an exoplanet transits across its host star's disk. Because Earth's radius is 1/109.2 of a solar radius, an Earth-Sun analog produces a tiny 84 ppm (0.0084%) dip, whereas the same Earth-sized planet transiting an ultracool M8V dwarf like TRAPPIST-1 (R_★ ≈ 0.119 R☉) produces a 0.59% (5,900 ppm) transit.

Simultaneously, balancing intercepted stellar flux against thermal infrared re-radiation yields the planet's zero-greenhouse equilibrium temperature T_eq as a function of orbital semi-major axis a (AU) and Bond albedo A_B.

Worked Benchmark Example: For TRAPPIST-1 e (R_p = 0.92 R⊕) orbiting TRAPPIST-1 (R_★ = 0.119 R☉, T_★ = 2,566 K) at a = 0.02925 AU with Bond albedo A_B = 0.30: transit depth is ΔF/F = 0.504% (5,040 ppm) and equilibrium temperature is T_eq = 225 K.

Assumptions, Approximations & Validity Limits

  • Transit depth formula assumes a uniform, non-limb-darkened stellar disk and a non-grazing transit (impact parameter b < 1 − R_p/R_★).
  • Equilibrium temperature T_eq assumes isotropic heat redistribution across the planet and omits atmospheric greenhouse warming (which adds +33 K on Earth and +500 K on Venus).
Reference Guide

Exoplanet Transit & Radial Velocity Methods

How astronomers detect and characterize exoplanets using photometric transit depth ((Rp/R*)²), Doppler radial velocity (M sin i), and JWST transmission spectra.

Reference Guide

Stellar Spectral Classification (OBAFGKM)

Reference guide to Morgan-Keenan (MK) stellar classification (O B A F G K M), luminosity classes (I–V, WD), color index (B-V), and the H-R diagram.

Temperate terrestrial exoplanet in a 7-planet resonant chain

TRAPPIST-1 e (Temperate Terrestrial World)

Coordinates, Gaia distance (12.47 pc), 6.10-day orbital period, mass 0.692 M⊕, radius 0.920 R⊕, and JWST transit spectroscopy for TRAPPIST-1 e.

First transiting exoplanet & first exoplanet with a detected atmosphere

HD 209458 b (Osiris First Transiting Planet)

Coordinates, Gaia DR3 distance (48.3 pc), 3.5247-day transit period, 1.359 R♃ inflated radius, and atmospheric escape data for HD 209458 b.

Low-density inflated Saturn-mass exoplanet (JWST ERS benchmark)

WASP-39 b (JWST Benchmark Saturn Exoplanet)

Coordinates, Gaia DR3 distance (213 pc), 4.055-day period, 0.28 M♃ mass, 1.27 R♃ radius, and JWST CO2/SO2 photochemical spectrum of WASP-39 b.

Temperate sub-Neptune exoplanet with methane- and CO2-rich H2 atmosphere

K2-18 b (Temperate Sub-Neptune in Leo)

Coordinates, Gaia DR3 distance (38.07 pc), 32.94-day habitable-zone orbit, 8.63 M⊕ mass, 2.61 R⊕ radius, and JWST CH4/CO2 spectrum of K2-18 b.

Nearest known exoplanet (radial-velocity habitable-zone terrestrial candidate)

Proxima Centauri b (Nearest Exoplanet)

Coordinates, ESPRESSO minimum mass (1.07 M⊕), 11.186-day habitable-zone orbit at 0.04856 AU, and stellar flare environment of Proxima Centauri b.

Scientific Standards & References

  • NASA Exoplanet Archive (2026-10-01 snapshot): Akeson, R. L., et al. 2013, PASP, 125, 989; NASA Exoplanet Archive (IPAC/Caltech) — NASA Exoplanet Science Institute (NExScI / Caltech / IPAC)
  • JWST / MAST Science Archive & Mission Documentation (Cycle 1–4 Public Releases (2022–2026)): Rigby, J., et al. 2023, PASP, 135, 048001 (The Science Performance of JWST as Characterized in Commissioning) — NASA / ESA / CSA / STScI