Compression of ephemerides

Approximations in the normL ₁ by Chebyshev polynomials are generated to represent astronomical ephemerides over large intervals of time.     

Association of spherical and ellipsoidal gravity coefficients of the Earth's potential

A comparison is drawn between the expansion of the potential in spherical harmonics on the one hand and in ellipsoidal harmonics on the other, with the objective of associating the spherical and ellipsoidal gravity coefficients of the Earth's potential.For this purpose the properties of orthogonality of the Lamé functions of the first kind have been tailored to this subject of investigation and become instrumental in establishing the mathematical expressions which relate the two classes of gravity coefficients to each other. In deriving the elements of the transition matrices elliptic integrals have been encountered whose reduction to the three kinds of canonical elliptic integrals is discussed.Presented at the Conference on Celestial Mechanics, Oberwolfach, Germany, August 17–23, 1969.     

Non-divergent oscillations in the solar atmosphere

Non-divergent oscillations having the form of deep water waves are shown to form normal modes or free oscillations of the solar atmosphere under two approximations: the chromosphere-coronal interface behaves like a free surface, and the density scale height is sufficiently large in the convective zone. These modes show the temporal and spatial characteristics of the 300 second chromospheric oscillations.     

Lamé functions of the first kind generated by computer

The definitions of the Lamé functions and the ellipsoidal coordinates inherent to them are introduced. Proceeding from Lamé's differential equation the four classes of Lamé functions of the first kind are generated by computer with the aid of formula manipulation techniques. For this purpose algebraic expressions for the coefficients in the Lamé polynomials are constructed by virtue of recurrence formulae and presented in tabular as well as machine readable form for further processing. The determination of a parameter appearing in the polynomial coefficients leads to an algebraic eigenvalue problem. It is shown how this eigenvalue problem is amenable to numerical treatment. The polynomial coefficients together with the eigenvalues are characteristic for the Lamé functions and define them completely.     

Theory of linear cosmological perturbations in flat space-time theory of gravitation

Covariant linear cosmological perturbations are considered in flat space-time theory of gravitation. The background metric is not altered. The perturbed energy-momentum is given. The basic equations for the propagation of the perturbations are presented. The perturbed equations for a homogeneous, isotropic universe are stated.