Unveiling the Pear-shape of the Moon

The notion of the ‘Pear-shape of the Earth’ is well-known to many in the field of science. In this study, the possibility of the existence of an analogous ‘Pear-shape of the Moon’ is investigated. We begin with a topographic map of the lunar surface in Lambert’s azimuthal equal-area projection for both the near and far faces of the Moon in selenographic coordinates. A preliminary inspection of this map indicates that a pear-shape of the Moon similar that of the Earth may be possible if the axis of the pear is situated in the prime meridional plane with its north pole tilted 15o towards the direction of the Earth. A Lambert’s azimuthal equi-angular map is constructed on which a simplified highland and lowland areas are drawn. Next, the angular coordinates in pear-axis frame of reference are calculated. A simplified elevation model of the lunar surface is assumed, in which the highland area elevations are assumed to be 1 km above the mean elevation and the lowland areas assumed to be 1 km below the mean elevation. The mean elevations of circles of latitude in the pear-axis coordinates are estimated graphically for intervals of 15o. Finally, these mean elevations are displayed around an axisymmetric Moon. An emphatic pear-shape of the Moon strikingly similar to that of the Earth clearly emerges. The most fascinating feature of this pear-shape is that its amplitude is many times greater than that of the terrestrial counterpart.