Origin of the lunar inclination from tidal interaction of multiple-moon system

Abstract

According to the giant impact theory, the Moon formed through accreting the debris disk produced by a collision between Theia and the proto-Earth, and the predicted lunar orbital inclination relative to the Earth's equatorial plane is about within one degree when Moon formed. However, the current lunar orbital inclination with five degrees relative to the Earth's orbital plane requires the Moon's orbital inclination relative to the Earth's equator to be about ten degrees when traced back to the time of lunar formation. Since two moons are also a natural outcome of simulations of lunar formation from a protolunar disk produced by a giant impact, here we show that, under solar perturbation, gravitational tidal interaction between Earth and its two moons with negligible orbital inclination relative to Earth's equatorial plane could lead to a merger of one moon with Earth, or a merger of the two moons or an ejection of one moon, resulting that the surviving moon's orbital inclination relative to Earth's equator could exceed ten degrees. The theory proposed here may provide a way of explaining the initial large lunar inclination relative to the Earth's equator.

Figures (4)

• Figure 1: Left and right show the surviving moon's orbital inclination relative to the Earth's equatorial plane and eccentricity along with semimajor axis from the 156 runs. Black dots, blue dots and red dots represent the outcomes of the survival of the low mass moon, the merger of the two moons and the survival of the large mass moon, respectively. Semimajor axis is in unit of Earth radius and inclination is in unit of degree.
• Figure 2: The first column is the ratio the semimajor axis of the large mass moon to that of the low mass moon at each timestep, and the black line and the black dotted line represent $3:1$ MMR and $4:1$ MMR, respectively. The second column presents the semimajor axis, periapse and apoapse of the two moons at each timestep, blue dots and yellow dots represent the results of the large mass moon and that of the low mass moon, respectively. The third and fourth column are the eccentricity and the inclination at each timestep, respectively. The blue dots and yellow dots in the third and fourth column represent the results of the large mass moon and that of the low mass moon, respectively. The lower panel is a close-in view of the upper panel. T is in unit of year. The semimajor axis, periapse and apoapse of the two moons are in unit of Earth radius, and inclination is in unit of degree.
• Figure 3: Same as Figure 2 but the two moons' initial inclinations relative to Earth's equator are $0^\circ$ and the large mass moon's initial longitude of ascending node is $\Omega_2=121^\circ$. The black line and the black dotted line in the first column represent 3 : 1 MMR and 2 : 1 MMR, respectively.
• Figure 4: Same as Figure 2 but without solar perturbation and the large mass moon's initial longitude of ascending node is $\Omega_2=149^\circ$. The black line and the black dotted line in the first column represent 3 : 1 MMR and 4 : 1 MMR, respectively.