Galactic Tidal Stream Simulator

Cluster & Orbit

Cluster mass 2.0×10⁵ M☉

Orbit eccentricity 0.45

Time speed 25 Myr/s

Live Readouts

Jacobi (tidal) radius

— pc

Galactocentric distance

— kpc

Bound fraction / elapsed time

—

Legend

Bound stars (inside r_J) Leading arm (r < r_cluster, races ahead) Trailing arm (r > r_cluster, falls behind)

How it works

The host galaxy is modeled with a flat rotation curve (a good approximation for a real spiral like the Milky Way once its dark-matter halo is included), which corresponds to a logarithmic potential Φ(r) = v_c² ln r. This gives every star the same circular orbital speed v_c regardless of radius — but because angular speed ω = v_c/r still falls with radius, stars closer to the center complete each orbit faster than stars farther out. That differential rotation ("shear") is what shreds a cluster apart.

Acceleration toward center:  a(r) = -v_c² / r
Jacobi (tidal) radius:       r_J = ( G·m_cluster·r² / (2·v_c²) )^(1/3)
Angular speed:                ω(r) = v_c / r

Every star in the cluster feels two pulls at once: the host galaxy's gravity, and the cluster's own gravity. Beyond r_J the galaxy wins — stars there drift onto a slightly different orbit than the cluster's center. Because ω falls with r, stars pulled just inside r_J (smaller r) pick up angular speed and race ahead of the cluster, forming the cyan leading arm; stars pulled just outside (larger r) fall behind, forming the orange trailing arm. Each close pass through perigee (lowest point of the orbit, where the tide is strongest) strips another layer, exactly as it does for the real globular cluster Palomar 5 and for the Sagittarius dwarf galaxy currently being torn apart by the Milky Way.

Cluster mass — a heavier cluster holds on to more of its stars and has a larger r_J.
Orbit eccentricity — higher eccentricity means a sharper perigee passage and stronger, more sudden stripping bursts.
Time speed — a full orbit at 8 kpc takes roughly 220 million years even at v_c = 220 km/s.

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