Galactic Tide & the Oort Cloud Loss Cone

Galactic Tide

Local density ρ₀ 1.0× (0.10 M☉/pc³)

Galactic plane tilt 63°

Time acceleration 0.6 Myr/s

Loss-cone threshold q< 15 AU

Live Readouts

Simulated elapsed time

0.0 Myr

In loss cone now

0 / 200

Crossings so far

Mean perihelion q

– AU

How it works

Beyond the influence of any single passing star, the whole Oort Cloud sits inside the smooth gravitational field of the Milky Way's disk. A comet displaced a height z above or below the galactic plane feels a restoring pull back toward it — the galactic tide:

F_z ≈ -4πGρ0 · z          (vertical disk tide, Oort's ρ0 ≈ 0.10 M☉/pc³)
a = a_grav(⊙) + a_tide,   a_tide = -(4πGρ0) (r·p̂) p̂

where p̂ = unit vector to the galactic pole

Each of the 200 bodies here is integrated directly in 3D (leapfrog / velocity-Verlet) under the Sun's gravity plus this linear tidal term — no shortcuts or pre-baked orbits. Because the force depends only on height above the galactic plane, orbits steeply inclined to that plane get torqued hardest, while orbits lying in it feel almost nothing — exactly the sin²(i) dependence found in the secular theory of Heisler & Tremaine (1986) and Byl (1983).

The torque slowly exchanges angular momentum for a periodic swap between eccentricity and inclination: over tens to hundreds of millions of years each comet's perihelion distance q = a(1−e) oscillates up and down. When it dips below the loss-cone threshold — typically the giant-planet region — the comet plunges into the inner solar system, exactly the mechanism thought to feed a steady trickle of long-period comets without needing a stellar flyby.

Local density ρ0 — the tidal coupling strength; higher near spiral arms or during a molecular-cloud passage, using the real value 0.10 M☉/pc³ at 1×.
Galactic plane tilt — the ~63° angle between the ecliptic and the galactic plane sets which orbits are steeply inclined (strongly torqued) vs. nearly aligned (weakly torqued).
Time acceleration — real oscillation periods run tens to hundreds of Myr; this only speeds up playback, the integration step itself stays fixed and stable.
Loss-cone threshold — the perihelion distance below which planetary perturbations take over and the comet becomes observable.

Sun Safe Oort body (large q) Inside loss cone (q < threshold) Galactic plane

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