PAPER 4 OF THE LEF SERIES
The Orbit
After release: the inclination, the survival and the recession from the detachment conditions
Abstract
A body released from a rotating parent, with tangential velocity in the direction of rotation only, starts on an orbit inclined to the parent's equator by the latitude of its centre. In the LEF model the Moon's centre at release lay at latitude 22.5°, the centre of the 3,000-km contact on which it sat. Off the equator the rotation carries the body at ωr cos λ, so orbital speed is reached at about 17,287 km, the corotation line for that latitude. With the Earth day at 5.77 hours, the Moon begins to separate as its centre of mass reaches this line. It is released about 210 km beyond, at about 17,496 km, onto a nearly circular orbit (e ≈ 0.04) inclined 22.5° to the equator of that time, with the release point as perigee. The tide pushes outward from the first moment, so the Moon recedes from the start; it lies about 7,200 km outside the rigid Roche limit. Under the tan-law of the reduced decay equation, 22.5° returns today's 5.145°; a 25° sensitivity case returns 5.79°. The release distance is set where two reduced tests meet: the present inclination and the present eccentricity. Tests of the Laplace-plane transition, tidal dissipation and thermal history follow. The established result is a geometric source of the initial inclination and a mapping from release conditions to initial orbits. A joint reconstruction of the present distance, inclination, eccentricity and recession rate remains to be computed.
Keywords: Moon; lunar orbit; orbital inclination; tidal evolution; corotation radius; Roche limit; Laplace plane; Earth–Moon system
How to cite
Duran, Z. (2026). The Orbit: After release: the inclination, the survival and the recession from the detachment conditions. Paper 4 of the LEF series. https://lef-model.com/paper04.html