On the gradient line of the moon's zonal gravitational potential field

The analytical expression of the gradient line, i.e. the perpendicular to the Moon's zonal equipotential surfaces is derived. Being a sensitive indicator of the geometric structure of the gravitational field, the shape of the trajectory, its direction field and curvature, the points of inflection, etc., are computed at elevations 0 km, 250 km, 1000 km and 10000 km above the Moon's surface. The numerical results were derived from the coefficients of Liu and Laing (1971) and are compared- whenever suitable - with the results obtained from the coefficients of Michaelet al. (1969).