We characterize the stellar and gas volume density, potential, and gravitational field profiles in the central $sim$ 0.5 pc of the Orion Nebula Cluster (ONC), the nearest embedded star cluster (or rather, proto-cluster) hosting massive star formation available for detailed observational scrutiny. We find that the stellar volume density is well characterized by a Plummer profile $rho_{stars}(r) = 5755,{rm M}_{odot},{rm pc}^{-3},(1+(r/a)^2)^{-5/2}$, where $a = 0.36$ pc. The gas density follows a cylindrical power law $rho_{gas}(R) = 25.9,{rm M}_{odot},{rm pc}^{-3},(R/{rm pc})^{-1.775}$. The stellar density profile dominates over the gas density profile inside $r,sim,1$ pc. The gravitational field is gas-dominated at all radii, but the contribution to the total field by the stars is nearly equal to that of the gas at $r,sim,a$. This fact alone demonstrates that the proto-cluster cannot be considered a gas-free system or a virialized system dominated by its own gravity. The stellar proto-cluster core is dynamically young, with an age of $sim$ 2-3 Myr, a 1D velocity dispersion of $sigma_{rm obs} = 2.6$ km s$^{-1}$, and a crossing time of $sim$ 0.55 Myr. This timescale is almost identical to the gas filament oscillation timescale estimated recently by Stutz & Gould (2016). This provides strong evidence that the proto-cluster structure is regulated by the gas filament. The proto-cluster structure may be set by tidal forces due to the oscillating filamentary gas potential. Such forces could naturally suppress low density stellar structures on scales $gtrsim,a$. The analysis presented here leads to a new suggestion that clusters form by an analog of the slingshot mechanism previously proposed for stars.
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