Keplerian and Transit Guestimator
Precision-RV helper for quick-order detectability and climate context. Enter stellar and planetary masses, then explore stellar reflex semi-amplitude K and equilibrium temperature as functions of orbital period. Designed for exoplanet follow-up triage.
Stellar properties
Planet properties
RV assumptions
Period sampling
Stellar luminosity-
Stellar radius-
Stellar Teff-
Conservative HZ period-
Optimistic HZ period-
Detailed printout at target period
Orbit & Radial Velocity
Target period-
Semi-major axis-
Input planet mass-
Teq-
HZ membership-
RV semi-amplitude K-
pRV precision σinst-
Stellar jitter σjitter-
K / pRV-
Detectability-
Min. detectable mass-
NRV for mass precision-
Transit & Atmosphere
Transit depth-
Planetary log(g) [cgs]-
Scale height-
Atm. transit signal-
Astrometry & Imaging
Astrometric α*-
Orbital separation-
Reflected (panchromatic)-
Thermal 1 µm-
Thermal 5 µm-
Thermal 10 µm-
Thermal 25 µm-
1) Reflex semi-amplitude assumes circular orbit and sin(i) = 1: K = [(2piG)/P]1/3 * Mp / (Mstar + Mp)2/3.
2) Main-sequence scaling uses piecewise Lstar(Mstar) and Rstar proportional to Mstar0.8 (quick-look approximation).
3) Equilibrium temperature uses configurable redistribution efficiency ε: Teq = [Lstar(1 - A) / (4pi sigma a2(2 + 2ε))]1/4, with ε = 1 for full redistribution and ε = 0 for dayside-only re-radiation.
Assumption note: A is the Bond albedo (fraction of incident stellar flux reflected at all wavelengths and phase angles). Real planets with inefficient redistribution or strong greenhouse effects can have dayside temperatures higher than this quick-look Teq estimate.
4) Habitable-zone limits are from Kopparapu et al. 2013 (ApJ 765, 131) and updated coefficients from Kopparapu et al. 2014 (ApJL 787, L29), converted to period using Kepler's third law.
5) Spectral-type to stellar-mass quick-look mapping uses representative dwarf values from Pecaut and Mamajek 2013 (ApJS 208, 9) (main-sequence dwarf parameter table, updated online).
6) Transit depth = (Rp/Rstar)2. Planet radius Rp inferred from mass using piecewise empirical mass-radius relations:
| Mass range | Relation | Reference |
| < 10 M⊕ (rocky) | R = 1.02 × M0.28 | Parc et al. 2024 (A&A 688, A59) |
| 10–138 M⊕ (volatile-rich) | R = 0.61 × M0.67 | Parc et al. 2024 (A&A 688, A59) |
| 138–4100 M⊕ (giant planets) | R = 11.9 × M0.01 | Parc et al. 2024 (A&A 688, A59) |
| 4100–50000 M⊕ (brown dwarfs) | R ∝ M0.08 (Baraffe) | Baraffe et al. model grid |
| > 50000 M⊕ (M dwarfs) | R = 1.06 × M0.57 | Pecaut & Mamajek 2013 |
Range reflects ~15% natural scatter in M-R relations across different compositions and stellar activity.
7) Surface gravity: log(g) = log(GM/R2).
8) Atmospheric scale height: H = Rspecific × Teq / g, where Rspecific = Rgas / Mmol for H₂ (2 g/mol), N₂ (28 g/mol), and CO₂ (44 g/mol).
9) Number of RV observations to measure planet mass at fractional precision p (white noise, Cloutier et al. 2018, AJ 156, 82, eq. 18): NRV = 2 × (σeff / (p × K))2, where σeff = √(σinst2 + σjitter2).
10) Astrometric semi-amplitude (sky plane): α* = (Mp / (M* + Mp)) × (a / d) in arcsec, with a in au and d in pc.
11) Atmospheric transmission signal: Total transit depth ≈ geometric depth + (~3 scale heights) × 2H/Rp × (geometric depth), representing additional depth from atmospheric absorption and scattering extending ~3 scale heights above the nominal photosphere.
Planets below the stellar activity line
They are not automatically lost: they can still be recovered, but doing so requires increasingly accurate modeling and correction of the activity signal as the planetary RV amplitude drops further below the activity level.
Understanding atmospheric signals:
The atmospheric signal shows the total observed transit depth when the planet's atmosphere is present, versus the bare geometric (solid-body) transit depth listed in the row above.
Why atmospheres deepen transits: During transit, starlight passes through the planet's limb and is absorbed and scattered by atmospheric gases high above the solid surface. Since the atmosphere has a finite scale height H, it extends roughly 3–5 H above the apparent photosphere (the "surface" radius measured in transit). This extended absorbing layer increases the projected cross-section, which deepens the observed transit depth beyond geometry alone. This is called atmospheric transmission or the atmospheric signal.
Composition sets the amplitude:
- H₂-dominated (light gas): Smallest molecular mass → largest scale height → tallest atmosphere → largest atmospheric signal. Typical for hot Jupiters.
- N₂ (terrestrial air): Intermediate molecular mass → intermediate scale height and signal. Reference for Earth-like atmospheres.
- CO₂ (heavy): Largest molecular mass → smallest scale height → most compressed atmosphere → smallest signal. Limits detectability for CO₂-rich worlds.
Key insight: Strong atmospheric signals = extended atmospheres = light gases (H/He). Weak or absent signals = compressed atmospheres or no atmosphere = heavy gases or rocky bodies. The three values (H₂, N₂, CO₂) bracket the plausible range for most solar-system-like and exoplanet atmospheres.
12) Contrast ratios
Reflected light (panchromatic): Crefl = Ag × (Rp / a)2 at full phase (opposition), where the geometric albedo Ag ≈ ⅔ × ABond (Lambertian sphere approximation).
Thermal emission: Ctherm(λ) = (Rp / R*)2 × B(λ, Teq) / B(λ, Teff), where B(λ, T) is the Planck function. Contrast values are expressed in scientific notation and in magnitudes: Δmag = −2.5 × log10(C).
13) Orbital separation on sky: θ = a (au) / d (pc) in arcsec, converted to mas.