On the deviation of the lunar center of mass to the East. Two possible mechanisms based on evolution of the orbit and rounding off the shape of the Moon
- 86 Downloads
From the observations of the gravitational field and the figure of the Moon, it is known that its center of mass (briefly COM) does not coincide with the center of figure (COF), and the line “COF/COM” is not directed to the center of the Earth, but deviates from it to the South–East. Here we study the deviation of the lunar COM to the East from the mean direction to Earth.
At first, we consider the optical libration of a satellite with synchronous rotation around the planet for an observer at a point on second (empty) orbit focus. It is found that the main axis of inertia of the satellite has asymmetric nonlinear oscillations with amplitude proportional to the square of the orbit eccentricity. Given this effect, a mechanism of tidal secular evolution of the Moon’s orbit is offered that explains up to \(20\%\) of the known displacement of the lunar COM to the East. It is concluded that from the alternative—evolution of the Moon’s orbit with a decrease or increase in eccentricity—only the scenario of evolution with a monotonous increase in orbit eccentricity agrees with the displacement of lunar COM to the East. The precise calculations available confirm that now the eccentricity of the lunar orbit is actually increasing and therefore in the past it was less than its modern value, \(e = 0.0549\).
To fully explain the displacement of the Moon’s COM to the East was deduced a second mechanism, which is based on the reliable effect of tidal changes in the shape of the Moon. For this purpose the differential equation which governs the process of displacement of the Moon’s COM to the East with inevitable rounding off its form in the tidal increase process of the distance between the Earth and the Moon is derived. The second mechanism not only explains the Moon’s COM displacement to the East, but it also predicts that the elongation of the lunar figure in the early epoch was significant and could reach the value \(\varepsilon\approx0.31\). Applying the theory of tidal equilibrium figures, we can estimate how close to the Earth the Moon could have formed.
KeywordsMoon: interiors and formation Gravitation
- Archinal, B.A., Rosiek, M.R., Kirk, R.L., Redding, B.L.: US geological survey, Virginia (2006) Google Scholar
- Bohme, S.: Astron. Nachr. 256, 356 (1953) Google Scholar
- Darwin, G.H.: Tidal Friction in Cosmogony, Scientific Papers 2. Cambridge University Press, Cambridge (1908) Google Scholar
- Deprit, A.: In: Kopal, Z. (ed.) Physics and Astronomy of the Moon. Academic Press, New York (1971) Google Scholar
- Folkner, W.M., Williams, J.G., Boggs, D.H., Park, R.S., Kuchynka, P.: The Interplanetary Network Progress Report, 42–196, 1–81 (2014) Google Scholar
- Iz, H., Ding, X.L., Dai, C.L., Shum, C.K.: J. Geod. 1(4), 348 (2011) Google Scholar
- Khabibullin, Sh.T.: Trudi AOE (31), 1 (1958) Google Scholar
- Khabibullin, Sh.T.: Trudi KMAO (34), 3 (1966) Google Scholar
- Kondratyev, B.P.: Dinamika ellipsoidal’nykh gravitiruiushchikh figure. Nauka, Moscow (1989) Google Scholar
- Kondratyev, B.P.: Kvant (5), 38 (2009) Google Scholar
- Kondratyev, B.P.: Sol. Syst. Res. 45, 38 (2011a) Google Scholar
- Kondratyev, B.P.: Sol. Syst. Res. 45, 458 (2011b) Google Scholar
- Moutsoulas, M.D.: Physics and astronomy of the moon, 29 (1971) Google Scholar
- Sagitov, M.U.: Lunar Gravimetry. Nauka, Moscow (1979) Google Scholar
- Wieczorek, M.A., Neumann, G.A., Nimmo, F., Kiefer, W.S., Taylor, G.J., Melosh, H.J., Phillips, R.J., Solomon, S.C., Andrews-Hanna, J.C., Asmar, S.W., Konopliv, A.S., Lemoine, F.G., Smith, D.E., Watkins, M.M., Williams, J.G., Zuber, M.T.: Science 339(6120), 671 (2013). https://doi.org/10.1126/science.1231530 ADSCrossRefGoogle Scholar
- Williams, J.: J. Geophys. Res. 106, 933 (2001) Google Scholar
- Williams, J.G., Dickey, J.O.: In: 13th International Workshop on Laser Ranging, Washington (2002) Google Scholar
- Williams, J., Boggs, D., Ratcliff, J.: In: Lunar Pl. Sci. Conf., p. 1579 (2014a) Google Scholar