Numerical calculations of the cross-section for the accretional capture of the moon by the earth
If a primary body is increasing in mass the hyperbolic orbit of a secondary body can become an elliptic orbit. In order to determine the cross-section for the accretional capture of the moon by the earth, a series of numerical calculations has been carried out. Calculations have been carried out for various orbital ellipticities and separations and for various accretion rates. Accretional capture is favored if significant accretion occurs in a period of less than 100 yr. A window for accretional capture occurs if the minimum initial separation of the earth and moon (in astronomical units) is nearly equal to the initial heliocentric lunar eccentricity.