A Prograde Gravitational Capture Model for the Origin and Evolution of the Earth-Moon System

Abstract

The origin of the Moon is one of the outstanding unsolved problems in the natural sciences. Cursory examination of college-level textbooks in the Earth and Planetary Sciences leaves one with the impression that the Moon is simply a “night lantern” and that the moon effects the Earth in only minor ways, such as controlling the tidal waters on the planet.

Of the other alternatives, it is perhaps just possible that the moon was originally an independent planet, though it is much less massive than any existing planet.

Jeffreys (1929), p. 37

….capture of the entire moon is an inherently improbable event because of the narrow range of orbital elements for which the relatively slow-working tidal friction could dissipate sufficient energy to prevent escape.

Kaula (1971), p. 224

The basic geochemical model of the structure of the Moon proposed by Anderson, in which the Moon is formed by differentiation of the calcium, aluminum, titanium-rich inclusions in the Allende meteorite, is accepted, and the conditions for formation of this Moon within the solar nebula models of Cameron and Pine are discussed. The basic material condenses while iron remains in the gaseous phase, which places the formation of the Moon slightly inside the orbit of Mercury.

From Cameron 1973, p. 377

Appendix

This appendix consists mainly of plots of orbits and tidal amplitudes for Luna during an orbit circularization sequence and for the generation of the second phase of a lunar magnetic field. Another favorable feature of this capture model is that it is compatible with traceback calculations of Hansen (1982) and Webb (1982). They both suggested that the lunar orbit could be as large as 30 to 40 earth radii early in the history of the Solar System. Hansen (1982), in particular, suggested capture of the Moon into a geocentric orbit with the angular momentum equivalent of about 30 earth radii.

Fig. 4.35

Normal 2-B timescale vs. condensed 3-B timescale. a Normal 2-B calculated timescale, 200 Ma intervals. b Condensed 3-B timescale, 200 Ma intervals

Fig. 4.36

Plots of orbits for condensed timescale. a Time of capture to 31.6 Ma. b 31.6–1030 Ma (~ 10 % eccentricity)

Fig. 4.37

a 8 years of orbits soon after capture. b 8 years of lunar tidal amplitudes soon after capture

Fig. 4.38

a 8 years of orbits ~ 126 years after capture. b 8 years of lunar tidal amplitudes ~ 126 years after capture

Fig. 4.39

a 8 years of orbits ~ 281 years after capture. b 8 years of lunar tidal amplitudes ~ 281 years after capture

Fig. 4.40

a 8 years of orbits ~ 481 years after capture. b 8 years of lunar tidal amplitudes ~ 481 years after capture

Fig. 4.41

a 8 years of orbits ~ 748 years after capture. b 8 years of lunar tidal amplitudes ~ 748 years after capture

Fig. 4.42

a 8 years of orbits ~ 1085 years after capture. b 8 years of lunar tidal amplitudes ~ 1085 years after capture

Fig. 4.43

a 8 years of orbits ~ 1515 years after capture. b 8 years of lunar tidal amplitudes ~ 1515 years after capture

Fig. 4.44

a 8 years of orbits ~ 2033 years after capture. b 8 years of lunar tidal amplitudes ~ 2033 years after capture

Fig. 4.45

a 8 years of orbits ~ 2733 years after capture. b 8 years of lunar tidal amplitudes ~ 2733 years after capture

Fig. 4.46

a 8 years of orbits ~ 3467 years after capture. b 8 years of lunar tidal amplitude ~ 3467 years after capture

Fig. 4.47

a 8 years of orbits ~ 4347 years after capture. b 8 years of lunar tidal amplitudes ~ 4347 years after capture

Fig. 4.48

a 8 years of orbits ~ 18.59 Ka after capture. b 8 years of lunar tidal amplitudes ~ 18.59 Ka after capture

Fig. 4.49

a 8 years of orbits ~ 61.04 Ka after capture. b 8 years of lunar tidal amplitudes ~ 61.04 Ka after capture

Fig. 4.50

a 8 years of orbits ~ 160 Ka after capture. b 8 years of lunar tidal amplitudes ~ 160 Ka after capture

Fig. 4.51

a 8 years of orbits ~ 347 Ka after capture. b 8 years of lunar tidal amplitudes ~ 347 Ka after capture

Fig. 4.52

a 8 years of orbits ~ 3.857 Ma after capture. b 8 years of lunar tidal amplitudes ~ 3.857 Ma after capture

Fig. 4.53

a 4 years of orbits ~ 31.6 Ma after capture. b 4 years of lunar tidal amplitudes ~ 31.6Ma ago

Fig. 4.54

a 2 years of orbits ~ 149 Ma after capture. b 2 years of lunar tidal amplitudes ~ 149 Ma after capture

Fig. 4.55

a 2 years of orbits ~ 304 Ma after capture. b 2 years of lunar tidal amplitudes ~ 304 Ma after capture

Fig. 4.56

a 2 years of orbits ~ 485 Ma after capture. b 2 years of lunar tidal amplitudes ~ 485 Ma after capture

Fig. 4.57

a 2 years of orbits ~ 671 Ma after capture. b 2 years of lunar tidal amplitudes ~ 671 years after capture

Fig. 4.58

a 2 years of orbits ~ 863 Ma after capture. b 2 years of lunar tidal amplitudes ~ 863 Ma after capture

Fig. 4.59

a 2 years of orbits ~ 1030 Ma after capture. b 2 years of lunar tidal amplitudes ~ 1030 Ma after capture

Fig. 4.60

a Plot of lunar tidal amplitudes (C to 25 Ka). b Plot of energy dissipation in Luna (C to 25 Ka)