A theoretic model to investigate the dynamics of the longitudinal nucleus-acoustic waves (NAWs) in gyrogravitating electrostatically confined degenerate quantum plasma (DQP) system in spherically symmetric geometry is constructed. The model setup consists of non-degenerate heavy nuclear species (HNS), lighter nuclear species (LNS), and quantum degenerate electronic species (DES). It specifically considers the influences of the Bohm potential, Coriolis rotation, viscoelasticity, and electrostatic confinement pressure (ECP, scaling quadratically in density). A standard normal spherical mode analysis gives a generalized dispersion relation (septic). It highlights the dependency of various atypical instability response on the equilibrium plasma parameters. A numerical illustrative platform portrays that the relative nuclear charge-to-mass coupling parameter ($$\beta$$ β ) acts as a destabilizing agency and the heavy-to-light nuclear charge density ratio ($$\mu$$ μ ) acts as a stabilizing agency in both the non-relativistic (NR) and ultra-relativistic (UR) limits. Another interesting conjuncture is that the Coriolis rotation introduces a destabilizing influence on the system in both the limits. The progressive analysis presented herein has correlations and consistencies in the dynamic growth backdrop of various compact astro objects and their circumvent atmospheres, such as white dwarfs, neutron stars, etc.

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