Exoplanet Detection Methods Comparator
Calculate transit depth (ppm), radial velocity semi-amplitude (m/s), and equilibrium temperature for any planet-star system.
Different exoplanet detection methods scale differently with planet radius R_p, mass M_p, stellar mass/radius, and orbital semi-major axis a: transit depth scales as (R_p / R_★)², geometric transit probability as R_★ / a, stellar radial velocity wobble as M_p M_★^(−2/3) a^(−1/2), and astrometric signature as (M_p / M_★)(a / d).
Interactive Physics Calculator
Governing Equation & Worked Benchmark
Transit Depth, Radial Velocity Semi-Amplitude, and Equilibrium Temperature
ΔF/F = (R_p / R_★)² ; K_★ = 28.43 m/s · (M_p/M_Jup)(P/yr)^(−1/3)(M_★/M_☉)^(−2/3) ; T_eq = T_★ √(R_★ / 2a) (1 − A_B)^(1/4)In convenient Earth units: ΔF/F (ppm) = 84.0 · (R_p / R_⊕)² / (R_★ / R_☉)² and K_★ (m/s) = 0.0895 · (M_p / M_⊕) / √[ (M_★ / M_☉)(a / AU) ].
| Benchmark Step | Physical Details & Result |
|---|---|
| Scenario | Compare an Earth twin (1 M_⊕, 1 R_⊕) at a = 1.0 AU around a 1.0 M_☉, 1.0 R_☉ Sun-like star versus TRAPPIST-1 e (0.69 M_⊕, 0.92 R_⊕) at a = 0.029 AU around a 0.09 M_☉, 0.12 R_☉ ultracool M dwarf. |
| Calculation | Earth-Sun analog: ΔF/F = 84 ppm, P_transit = 0.47%, K_★ = 0.089 m/s (8.9 cm/s), P = 365.25 d. TRAPPIST-1 e: ΔF/F = 84 × (0.92 / 0.12)² = 4,937 ppm (~0.49%), P_transit = 1.9%, K_★ = 0.0895 × 0.69 / √(0.09 × 0.029) = 1.21 m/s, P = 6.10 d. |
| Physical Takeaway | Around an ultracool M-dwarf host star, a temperate rocky planet produces a 59× deeper transit and a 13.5× larger Doppler wobble repeating 60× more often than an Earth-Sun twin. |
Physical Mechanism & Interpretation
Adjusting planetary mass, radius, orbital distance, and host star type immediately illustrates why early radial velocity surveys first discovered hot Jupiters (51 Pegasi b: K_★ = 56 m/s) and why JWST atmospheric transmission spectroscopy of rocky worlds focuses heavily on compact M-dwarf systems like TRAPPIST-1.
Combining a transit measurement (which gives R_p and inclination i ≈ 90°) with a radial velocity or transit-timing mass measurement (which gives M_p) yields the planet's bulk density ρ_p = 3 M_p / (4π R_p³), distinguishing rocky iron-silicate worlds (ρ ≈ 4–6 g/cm³) from water worlds and gas-rich sub-Neptunes (ρ ≈ 1–2.5 g/cm³).
Model Assumptions & Systematic Uncertainties
Transit depth accuracy depends on knowing the host star's radius R_★ via Gaia parallaxes and stellar interferometry; radial velocity masses for non-transiting planets carry the sin i orbital inclination factor.
Related Concepts & Methods
Scientific Sources & Provenance
- NASA Exoplanet Archive (2026-10-01 snapshot) — Akeson, R. L., et al. 2013, PASP, 125, 989; NASA Exoplanet Archive (IPAC/Caltech). Archive / Reference ↗
- 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). Archive / Reference ↗
- ESA Gaia Archive — Data Release 3 (DR3 (2022-06-13)) — Gaia Collaboration, Vallenari, A., et al. 2023, A&A, 674, A1 (Gaia Data Release 3). Archive / Reference ↗