PAPER 2 OF THE LEF SERIES
LEF Mechanism in Principle
Corotation and angular momentum
Abstract
Material that is part of a spinning planet turns with it, and its speed grows with distance, while the speed of a free circular orbit falls with distance. At the corotation radius the two are equal: material carried there while still turning with the parent, and released there, already moves at orbital speed. We examine whether transferring lunar material outward from a terrestrial parent, with corotation maintained, can reach a state whose orbital velocity and angular-momentum budget match the present Earth–Moon system. For an initial day of 5.5 hours the corotation radius is 15,818 km and the orbital speed there is 5,020 m/s. Described as a uniform Maclaurin spheroid with a volume-equivalent radius of 6,517 km, the parent holds about 3.466×10^34 kg m² s⁻¹. That is 0.7% above the present budget, the small surplus that later loss to solar tides requires; vector addition at the angles tested gives 1.5–2.5%. During the transfer the lengthening pear slows the Earth and the sinking core speeds it up. Together they give a day of 5.77 hours at release, with the corotation line at about 16,400 km, where the Moon's centre of mass is released. The orbital angular momentum at release is about 17% of the initial budget, transferred within the system. The speed a corotating mass needs is thus supplied by the rotation itself, and the angular momentum the transfer requires is available in the parent. The conditions this places on the mechanism are stated explicitly and examined in the companion paper: release beyond corotation, survival inside the fluid Roche limit, and a connection that carries the load.
Keywords: Moon; lunar origin; corotation radius; angular momentum; Earth–Moon system; Maclaurin spheroid; early Earth rotation; Roche limit
How to cite
Duran, Z. (2026). LEF Mechanism in Principle: Corotation and angular momentum. Paper 2 of the LEF series. https://lef-model.com/paper02.html