Existence of a class of irregular bodies with a higher convergence rate of Laplace series for the gravitational potential

The main form of the representation of a gravitational potential V for a celestial body T in the outer space is the Laplace series in solid spherical harmonics ( R / r ) n + 1 Y n ( R , θ , λ ) with R being the radius of enveloping T sphere. It is well known that Y n satisfy the inequality ⟨ Y n ⟩ < C n - σ . The angular brackets mark the maximum of a function’s modulus over a unit sphere. For bodies of irregular structure σ = 5 / 2 , and this value cannot be increased in general case. At the same time modern models of the geopotential show more rapid rate of decreasing of Y n . We have found a class T of irregular bodies for which σ = 3 . The Earth and (at least a part of) other terrestrial planets, satellites, and asteroids most likely belong to this class. In this paper we describe T proving the above inequality for σ = 3 .