Letter | Published:

Tidal evolution of the Moon from a high-obliquity, high-angular-momentum Earth

Nature volume 539, pages 402406 (17 November 2016) | Download Citation

Abstract

In the giant-impact hypothesis for lunar origin, the Moon accreted from an equatorial circum-terrestrial disk; however, the current lunar orbital inclination of five degrees requires a subsequent dynamical process that is still unclear1,2,3. In addition, the giant-impact theory has been challenged by the Moon’s unexpectedly Earth-like isotopic composition4,5. Here we show that tidal dissipation due to lunar obliquity was an important effect during the Moon’s tidal evolution, and the lunar inclination in the past must have been very large, defying theoretical explanations. We present a tidal evolution model starting with the Moon in an equatorial orbit around an initially fast-spinning, high-obliquity Earth, which is a probable outcome of giant impacts. Using numerical modelling, we show that the solar perturbations on the Moon’s orbit naturally induce a large lunar inclination and remove angular momentum from the Earth–Moon system. Our tidal evolution model supports recent high-angular-momentum, giant-impact scenarios to explain the Moon’s isotopic composition6,7,8 and provides a new pathway to reach Earth’s climatically favourable low obliquity.

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Acknowledgements

This work was supported by NASA’s Emerging Worlds programme, award NNX15AH65G.

Author information

Affiliations

  1. Carl Sagan Center, SETI Institute, 189 North Bernardo Avenue, Mountain View, California 94043, USA

    • Matija Ćuk
  2. Department of Astronomy, University of Maryland, Physical Sciences Complex, College Park, Maryland 20742, USA

    • Douglas P. Hamilton
  3. Department of Earth and Planetary Sciences, Harvard University, 20 Oxford Street, Cambridge, Massachusetts 02138, USA

    • Simon J. Lock
  4. Department of Earth and Planetary Sciences, University of California Davis, One Shields Avenue, Davis, California 95616, USA

    • Sarah T. Stewart

Authors

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Contributions

M.Ć. designed the study, wrote the software, analysed the data and wrote the paper. Co-authors contributed ancillary calculations, discussed the results and wider implications of the work, and helped edit and improve the paper.

Competing interests

The authors declare no competing financial interests.

Corresponding author

Correspondence to Matija Ćuk.

Reviewer Information Nature thanks D. Stevenson and the other anonymous reviewer(s) for their contribution to the peer review of this work.

Extended data

Supplementary information

Videos

  1. 1.

    Animation of relative orientations of Earth's spin and the Moon's orbit during the Laplace plane transition, following the simulation plotted in black in Fig. 1.

    The system is seen from the direction of Earth's vernal equinox, the blue arrow is plotted along Earth's spin axis and points to the north, while the lunar orbit is plotted in red. Initially the Earth has a high obliquity, the Moon has low inclination and the Laplace plane is close to Earth's equator. As the animation progresses and the lunar orbit grows due to tidal dissipation, the Laplace plane shifts to the ecliptic plane (horizontal in this view). The moon acquires a large inclination during the Laplace plane transition, while Earth's obliquity decreases. The labels show time, Earth's spin period, total angular momentum (scaled to the present value) and angular momentum of the Earth-Moon system where only the ecliptic component (i.e. that along the vertical axis) of the lunar orbital momentum is taken into account. Unlike total angular momentum, this ecliptic component will be conserved during the Cassini state transition.

  2. 2.

    Animation of relative orientations of lunar figure and orbit during the Cassini state transition, following the simulation plotted in Fig. 4.

    The Moon is seen from the direction of the ascending node of lunar orbit, with the ecliptic plane (i.e. the Moon's Laplace plane at this time) parallel to the horizontal axis. The red arrow shows the orientation of the Moon's orbit normal. At first the Moon's orbit normal and spin axis are on the same side of the normal to the ecliptic, indicating that the Moon is in Cassini state 1. Once the Cassini state 1 is destabilized, after some wobbling, the Moon settles in a non-synchronous state somewhat similar to the Cassini state 2 (with the orbit normal and the spin axis being on opposite sides of the normal to the ecliptic). During this time both the inclination and obliquity (which is forced by inclination) are being damped by strong obliquity tides. At the semimajor axis of 35.1 Earth radii, the Moon becomes synchronous again and enters the Cassini state 2, where it stays for the rest of the simulation (this event is visible as a 5-degree jump in obliquity).

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https://doi.org/10.1038/nature19846

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