In what type of trajectory do the Magellanic clouds move through our galaxy? In what type of trajectory do the Magellanic clouds move through our galaxy? Can be estimated is it a elliptical, parabolic or hyperbolic trajectory? Although it may be a problem due to dark matter gravitational effect.
 A: Quoting from The Magellanic Stream at 20 kpc: A New Orbital History for the Magellanic Clouds (I have added some additional abbreviation definition and deleted references for clarity):

However, as these models have improved, one piece of the puzzle has
remained unconstrained: the exact past orbits of the Large Magellanic
Cloud (LMC) and Small Magellanic Cloud (SMC). Proper motion (PM)
measurements for the Magellanic Clouds have become very precise, but
the total mass of the Milky Way (MW) and the LMC are still imprecisely
known. The PM measurements favor a first-infall scenario, which is
supported by the LMC’s wake in the dark matter (DM) distribution of
the MW halo.

Based on this sounds like the LMC and SMC are not in orbit around the Milky Way at all and are encountering it for the first time.  Whether it end up in orbit or be absorbed is not know at this time but is the subject of numerous simulations.
My cursory literature survey on this topic does make it clear that this is not a settle matter and additional investigation and modeling will probably be required to reach a confident consensus.
