We characterize the stellar and gas volume density, potential, and gravitational field profiles in the central ∼0.5 pc of the Orion Nebula Cluster (ONC), the nearest embedded star cluster (or rather, protocluster) hosting massive star formation available for detailed observational scrutiny. We find that the stellar volume density is well characterized by a Plummer profile ρstars(r) = 5755 M☉ pc^- 3^ (1 + (r/a)2)^- 5/2^, where a = 0.36 pc. The gas density follows a cylindrical power law ρgas(R) = 25.9 M☉ pc^- 3^ (R/pc)^- 1.775^. The stellar density profile dominates over the gas density profile inside r ∼ 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 ∼ a. This fact alone demonstrates that the protocluster cannot be considered a gas-free system or a virialized system dominated by its own gravity. The stellar protocluster core is dynamically young, with an age of ∼2-3 Myr, a 1D velocity dispersion of σobs = 2.6 km s–1, and a crossing time of ∼0.55 Myr. This time-scale is almost identical to the gas filament oscillation time-scale estimated recently by Stutz & Gould. This provides strong evidence that the protocluster structure is regulated by the gas filament. The protocluster 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 >= a. The analysis presented here leads to a new suggestion that clusters form by an analogue of the 'slingshot mechanism' previously proposed for stars.