Binary Orbits Sandbox

Explore two-body orbital mechanics: both bodies orbit the barycenter

Station Card (PDF)
Barycenter M₁ M₂ a = 1.00 AU
Log scale: 0.1 - 100 M☉
Log scale: 0.1 - 100 M☉
Log scale: 0.01 - 100 AU
Log scale: 1× - 200× (caps to fit view)
Period (P)
1.00
yr
v₁ (Primary)
0.00
AU/yr
v₂ (Secondary)
0.00
AU/yr
Separation (r)
1.00
AU
a₁ (Orbit size)
0.50
AU
a₂ (Orbit size)
0.50
AU
Advanced readouts
Barycenter
0
km from M₁
T₁ (Temp)
5778
K
Type₁
G
spectral
Type₂
G
spectral
Radial velocity method (RV curve + spectral line)

This view connects the orbit to what a spectrograph measures. The star’s line-of-sight velocity produces a Doppler shift in a spectral line. Tracking that shift over time produces an RV curve.

Convention: Δλ = λobs − λ0. Positive RV means receding (redshift).

RV amplitude ∝ sin i (0° face-on → no RV signal)
RV curve (primary)
Spectral line inset
Conservation laws (energy & angular momentum)

These are relative-orbit specific quantities (per unit reduced mass). Kinetic and potential terms change around the orbit, but their sum stays constant. Angular momentum sets the areal sweep rate.

Kinetic (v²/2)
0
AU²/yr²
Potential (−μ/r)
0
AU²/yr²
Total ε
0
AU²/yr²
Angular momentum (h)
0
AU²/yr
Areal velocity (dA/dt)
0
AU²/yr
Star + Planet
Binary Stars

Two-Body Physics

Both bodies orbit their common center of mass (barycenter). Neither body is truly "fixed" - even the Sun wobbles due to Jupiter!

Orbit sizes are inversely proportional to masses. The heavier body has the smaller orbit.

(years, AU, M☉)

Drag the bodies or use sliders to explore. Watch how changing masses shifts the barycenter!