For systems where one mass is significantly greater than the others, the motion of objects around the central mass can be simplified to motion around a fixed point.  The type of motion can be subdivided into two main categories - orbits that are bounded and orbits that are unbounded.  For bounded orbits, two categories exist - circular and elliptical orbits. In both cases the orbiting body returns to something very close to the initial conditions.  The circular orbit exists for initial velocity vector pointing tangential to the line connecting the orbited and orbiting body with magnitude that balances 'centrifugal' acceleration (or acceleration of circular motion) with the acceleration caused by the mass of the orbited body.  For these conditions to be met the initial velocity magnitude of the orbiting body will be v=(GM/R)^1/2, where M is the orbited body, R is the distance between them, and G is the fundamental constant of gravity.
For the orbit to be elliptical, the same initial conditions apply accept for the initial velocity magnitude - this value must be less than or greater than that of a circular orbit, up to the limiting value of the velocity of a parabolic orbit, where the kinetic energy of motion is equal to the gravitational energy of gravity, to wit:
KE=PE ==> mv²/2 = GMm/R ==> v(parabolic)=(2GM/R)^1/2.
Velocities greater than that of parabolic orbits are hyperbolic, and never return to their initial conditions.  Ostensibly, a parabolic orbit will return to its initial conditions when time = infinity.
An example of initial conditions for the characteristic orbits:

In this example, M1=3e13 kg, v1=0; m2-m5=100 kg (nominal).  v2=2^1/2, v3=2, v4=2.828, v5=5.29 m/s.  After one-half period of the elliptical orbit, it evolves to look like:

Eventually, four characteristic orbits evolve:
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