### Abstract

A frequency-dependent model of tidal friction is used in the determination of the time rate of change of the lunar orbital elements and the angular velocity of the Earth. The variational equations consider eccentricity, the solar tide on the Earth, Earth oblateness, and higher-order terms in the Earth's tidal potential. A linearized solution of the equations governing the precission of the Earth's rotational angular momentum and the lunar ascending node is found. This allows the analytical averaging of the variational equations over the period of relative precession which, though large, is necessarily small in comparison to the time step of the numerical integrator that yields the system history over geological time. Results for this history are presented and are identified as consistent with origin of the Moon by capture. This model may be applied to any planet-satellite system where evolution under tidal friction is of interest.

Original language | English (US) |
---|---|

Pages (from-to) | 610-622 |

Number of pages | 13 |

Journal | Icarus |

Volume | 51 |

Issue number | 3 |

DOIs | |

State | Published - Sep 1982 |

### Fingerprint

### ASJC Scopus subject areas

- Astronomy and Astrophysics
- Space and Planetary Science

### Cite this

*Icarus*,

*51*(3), 610-622. https://doi.org/10.1016/0019-1035(82)90150-6

**On the history of the lunar orbit.** / Conway, Bruce A.

Research output: Contribution to journal › Article

*Icarus*, vol. 51, no. 3, pp. 610-622. https://doi.org/10.1016/0019-1035(82)90150-6

}

TY - JOUR

T1 - On the history of the lunar orbit

AU - Conway, Bruce A

PY - 1982/9

Y1 - 1982/9

N2 - A frequency-dependent model of tidal friction is used in the determination of the time rate of change of the lunar orbital elements and the angular velocity of the Earth. The variational equations consider eccentricity, the solar tide on the Earth, Earth oblateness, and higher-order terms in the Earth's tidal potential. A linearized solution of the equations governing the precission of the Earth's rotational angular momentum and the lunar ascending node is found. This allows the analytical averaging of the variational equations over the period of relative precession which, though large, is necessarily small in comparison to the time step of the numerical integrator that yields the system history over geological time. Results for this history are presented and are identified as consistent with origin of the Moon by capture. This model may be applied to any planet-satellite system where evolution under tidal friction is of interest.

AB - A frequency-dependent model of tidal friction is used in the determination of the time rate of change of the lunar orbital elements and the angular velocity of the Earth. The variational equations consider eccentricity, the solar tide on the Earth, Earth oblateness, and higher-order terms in the Earth's tidal potential. A linearized solution of the equations governing the precission of the Earth's rotational angular momentum and the lunar ascending node is found. This allows the analytical averaging of the variational equations over the period of relative precession which, though large, is necessarily small in comparison to the time step of the numerical integrator that yields the system history over geological time. Results for this history are presented and are identified as consistent with origin of the Moon by capture. This model may be applied to any planet-satellite system where evolution under tidal friction is of interest.

UR - http://www.scopus.com/inward/record.url?scp=0041144054&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0041144054&partnerID=8YFLogxK

U2 - 10.1016/0019-1035(82)90150-6

DO - 10.1016/0019-1035(82)90150-6

M3 - Article

AN - SCOPUS:0041144054

VL - 51

SP - 610

EP - 622

JO - Icarus

JF - Icarus

SN - 0019-1035

IS - 3

ER -