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Collisionless encounters and the origin of the lunar inclination

Nature 527, 492–494 (26 November 2015) | Download Citation

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Abstract

The Moon is generally thought to have formed from the debris ejected by the impact of a planet-sized object with the proto-Earth towards the end of planetary accretion1,2. Models of the impact process predict that the lunar material was disaggregated into a circumplanetary disk and that lunar accretion subsequently placed the Moon in a near-equatorial orbit3,4,5,6. Forward integration of the lunar orbit from this initial state predicts a modern inclination at least an order of magnitude smaller than the lunar value—a long-standing discrepancy known as the lunar inclination problem7,8,9. Here we show that the modern lunar orbit provides a sensitive record of gravitational interactions with Earth-crossing planetesimals that were not yet accreted at the time of the Moon-forming event. The currently observed lunar orbit can naturally be reproduced via interaction with a small quantity of mass (corresponding to 0.0075–0.015 Earth masses eventually accreted to the Earth) carried by a few bodies, consistent with the constraints and models of late accretion10,11. Although the encounter process has a stochastic element, the observed value of the lunar inclination is among the most likely outcomes for a wide range of parameters. The excitation of the lunar orbit is most readily reproduced via collisionless encounters of planetesimals with the Earth–Moon system with strong dissipation of tidal energy on the early Earth. This mechanism obviates the need for previously proposed (but idealized) excitation mechanisms12,13, places the Moon-forming event in the context of the formation of Earth, and constrains the pristineness of the dynamical state of the Earth–Moon system.

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Acknowledgements

This research was carried out as part of a Henri Poincaré Fellowship at the Observatoire de la Côte d’Azur (OCA) to K.P. The Henri Poincaré Fellowship is funded by the OCA and the City of Nice, France. A.M. thanks the European Research Council Advanced Grant ACCRETE (no. 290568).

Author information

Affiliations

  1. Laboratoire Lagrange, Université Côte d’Azur, Observatoire de la Côte d’Azur, CNRS Boulevard de l’Observatoire CS 34229, 06304 Nice Cedex 4, France

    • Kaveh Pahlevan
    •  & Alessandro Morbidelli

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Contributions

K.P. and A.M. discussed every step of the project, designed the simulation set-up and co-wrote the numerical code. K.P. performed the simulations and the statistical analysis.

Competing interests

The authors declare no competing financial interests.

Corresponding author

Correspondence to Kaveh Pahlevan.

Extended data

Extended data figures

  1. 1.

    Properties of planetesimal populations.

  2. 2.

    Tests and outcomes for reproducibility.

  3. 3.

    Effect of partial damping due to LMO obliquity tides.

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DOI

https://doi.org/10.1038/nature16137

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