A thermodynamic and mechanical model for formation of the Solar System via 3-dimensional collapse of the dusty pre-solar nebula

The fundamental and shared rotational characteristics of the Solar System (nearly circular, co-planar orbits and mostly upright axial spins of the planets) record conditions of origin, yet are not explained by prevailing 2-dimensional disk models. Current planetary spin and orbital rotational energies (R.E.) each nearly equal and linearly depend on gravitational self-potential of formation (Ug), revealing mechanical energy conservation. We derive −ΔUg≅Δ.R.E. and stability criteria from thermodynamic principles, and parlay these relationships into a detailed model of simultaneous accretion of the protoSun and planets from the dust-bearing 3-d pre-solar nebula (PSN). Gravitational heating is insignificant because Ug is negative, the 2nd law of thermodynamics must be fulfilled, and ideal gas conditions pertain to the rarified PSN until the objects were nearly fully formed. Combined conservation of angular momentum and mechanical energy during 3-dimensional collapse of spheroidal dust shells in a contracting nebula provides ΔR.E.≅R.E. for the central body, whereas for formation of orbiting bodies, ΔR.E.≅R.E.f(1−If/Ii), where I is the moment of inertia. Orbital data for the inner planets follow 0.04×R.E.f≅−Ug which confirms conservation of angular momentum. Significant loss of spin, attributed to viscous dissipation during differential rotation, masks the initial spin of the un-ignited protoSun predicted by R.E.=−Ug. Heat production occurs after nearly final sizes are reached via mechanisms such as shear during differential rotation and radioactivity. We focus on the dilute stage, showing that the PSN was compositionally graded due to light molecules diffusing preferentially, providing the observed planetary chemistry, and set limits on PSN mass, density, and temperature. From measured planetary masses and orbital characteristics, accounting for dissipation of spin, we deduce mechanisms and the sequence of converting a 3-d dusty cloud to the present 2-d Solar System, and infer the evolution of dust and gas densities. Duration of events is obtained from the time-dependent virial theorem. As the PSN slowly contracted, collapse of pre-solar dust in spheroidal shells simultaneously formed rocky protoplanets embedded in a dusty debris disk, creating their nearly circular co-planar orbits and upright axial spins with the same sense as orbital rotation, which were then enhanced via subsequent local contraction of nearby nebulae. Because rocky kernels at great distance out-competed the pull of the co-accreting star, gas giants formed in the outer reaches within ∼3 Ma as PSN contraction hastened. This pattern repeated to form satellite systems. The PSN imploded, once constricted to within Jupiter's orbit. Afterwards, disk debris slowly spiraled toward the protoSun, cratering and heating intercepted surfaces. Our conservative 3-d model, which allows for different behaviors of gas and dust, explains key Solar System characteristics (spin, orbits, gas giants and their compositions) and second-order features (dwarf planets, comet mineralogy, satellite system sizes).

► Our thermodynamic model of 3-d accretion explains planetary orbits and spins.
► The Sun and planets formed simultaneously during gravitational collapse.
► Our stability criteria explain compositional gradients across the Solar system.
► Planet mass is connected to satellite system size via gravitational competition.
► The nebula was graded in accord with light molecules diffusing out faster.