The gravity fields containing the self-gravitation have been considered for studying shapes of celestial bodies. However, assuming the hydrostatic equilibrium, the self-gravitation does not deform the shape to deviate from the sphere . Therefore, it is not necessary to con sider the self-gravitation when we discuss deviations from spherical shapes for celestial bodies.This study introduced the concept of the residual gravity field to exclude the self -gravitation from the gravity field, and discussed the lunar shape and history . Employing the lunar grav ity model (GLGM-2) and the topography model (GLTM-2B), following results were obtained. (a) There is a strong positive correlation between the residual gravity and the lunar geoid. The present lunar geoid is explained by two interpretations: The Moon was asynchronously rotating. The angular velocity was 2.1 times as fast as the present one . By the other interpretation, the present geoid is fitting the equilibrium state when the distance from the Earth was 1.81 x 105 km. (b) Correlations between the residual gravity and the topography have regionaldifferences. The correlation on the far side is strong . On the contrary, the correlation on the near side is weak. This difference can be explained as follows: When the magma ocean solidified, the lunar topography must have been an equilibrium shape fitting the residual gravity of the synchronous rotation at the time. After that, the mare formation has erased the topogra phy affected by the residual gravity on the near side. From the correlation on the far side, it is inferred that the Moon had been synchronously rotating when the lunar surface were covered by the magma ocean. (c) Assuming that both the geoid and the topography have somecorrelations with the residual gravity, the lunar center of gravity is located in the position of1.96 km toward the Earth from its center of figure.
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