An efficient integrator for stellar dynamics in effective gravity fields based on the isochrone potential

Open Access

Table 1

Classification of isochrone bound orbits.

Orbit shape	Isochrone parameter	Orbital parameters
Orbit shape	Isochrone parameter	Semi-major axis	Eccentricity
Point		α = b	ε = 0
Circle	b ≥ 0		ε = 0
Line segment		α > b	ε = 1 − b/α
Ellipse	b = 0	α > b	0 < ε < 1
Rosette	b > 0		ε ≠ 1 − b/α

Notes. Rosette orbits consist of a succession of loops of the same size. Special cases of rosette orbits include the ellipse, circle, and line segment (the loop has zero area). The orbit shape called ‘Point’ corresponds to a situation where the particle does not move.

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