Two-Body Orbits: Newtonian Gravity

Elliptical orbits around the common center of mass

Parameters

Body 1
Body 2
Speed: 1.0x

Orbital Elements

a1 (body 1)--
a2 (body 2)--
Period T--
Mass ratio m2/m1--

Live State

Time0.00
Mean anomaly M--
True anomaly ν--
Separation r--
|v1|--
|v2|--
KE--
PE--
Total E--

The Physics

Two masses orbit their common center of mass (barycenter, shown as +).

Both orbits share the same eccentricity and period, but their semi-major axes differ:

a1 = a · m2/(m1+m2)

a2 = a · m1/(m1+m2)

The heavier body stays closer to the barycenter. Set m1 ≫ m2 to recover the one-body limit.

Try: Equal masses with high eccentricity. Watch them swing through periapsis together!