Spectroscopic Binary Lab | Physics Library

Orbit & line of sight

Star 1Star 2Earth (+Z)

Barycentric frame · schematic stellar sizes · arrows: orbital velocity

Spectral line

Star 1 contributionStar 2 contributionCombined

Rest line: 500 nm · positive RV = receding / redshift

Radial velocity

Phase

Phase = time / period from periastron · γ: time-average systemic velocity

What the spectra constrain

K₁

K₂

Measured mass ratio

Mass function f(M)

M₁ sin³ i

M₂ sin³ i

Independent inclination hypothesis

These assumptions leave the observed velocities and spectra unchanged.

Inferred M₁
Inferred M₂
M₂ lower bound (i = 90°)

Binary system

Simulation truth

Primary mass M₁

Mass ratio M₂ / M₁

M₂ a

Period

Orbit & observer

Physical inclination i

Face-on 0°Edge-on 90°

Eccentricity e

Periastron angle ω

Systemic velocity γ

Spectrum

Continuum flux ratio F₂ / F₁

Intrinsic line FWHM

Resolving power R

Model & Julia source

Ideal Keplerian two-body orbit. The observer is fixed along +Z; inspection-camera motion does not change the physical inclination. The sky plane is X–Y. ω rotates the relative separation orbit, not the inspection camera.

RV₁ = γ + K₁[cos(ν + ω) + e cos ω]. RV₂ has the opposite orbital term. Wavelengths use the low-velocity optical convention λ = λ₀(1 + RV/c).

One schematic Gaussian absorption line per visible component, convolved with a Gaussian instrument of FWHM c/R. SB1 suppresses secondary absorption, not secondary continuum. Mode selection is a model assumption; blending and real detectability are separate issues.

No eclipses, atmosphere synthesis, spots, tidal distortion, Rossiter–McLaughlin effect, precision barycentric corrections or relativistic effects. Colors identify stars, not their temperatures. This is a noiseless forward model, not a fit to real spectra.

Binary Star Observer & Eclipse Probability
Julia source · Reference states
Reference spectra
Offline project · Provenance
License · Dependencies