This top-down 2D view integrates the exact same orbital-plane physics as a full N-body tidal-disruption model: the host galaxy has a flat rotation curve (a good approximation once a spiral galaxy's dark-matter halo is included), which corresponds to a logarithmic potential Φ(r) = vc² ln r. That gives every star the same circular speed vc regardless of radius, but because angular speed ω = vc/r still falls with radius, stars closer to the center lap the ones farther out. That differential rotation ("shear") is what shreds the cluster.
Host acceleration: a(r) = -v_c² / r (toward center)
Jacobi (tidal) radius: r_J = ( G·m_cluster·r² / (2·v_c²) )^(1/3)
Angular speed: ω(r) = v_c / r
Every tracer star is integrated (leapfrog, kick-drift-kick) under two accelerations at once: the host galaxy's gravity, and a softened point-mass pull toward the cluster's own guiding center standing in for the cluster's self-gravity. Once a star strays beyond r_J the galaxy's tide wins over the cluster's pull — stars pulled just inside r_J pick up angular speed and race ahead, forming the cyan leading arm; stars pulled just outside fall behind, forming the orange trailing arm. Every close pass through perigee strips another layer, exactly as it does for the real globular cluster Palomar 5 and the Sagittarius dwarf galaxy.
- 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 9 kpc takes roughly 250 million years even at v_c = 220 km/s.