CALCULATION OF CORRECTIONS TO THE SPHERICAL APPROXIMATION OF THE COMPONENTS OF THE EARTH’S ANOMALOUS GRAVITY FIELD

The spherical approximation is mapping the points of the ellipsoid with geodetic coordinates to the points on the sphere, the spherical coordinates of which are assumed to be the coordinates of the points on the ellipsoid. Moreover, the values of the first order and terms of higher orders are neglected.

It is necessary to find the same mapping by numerical comparison of geodesic coordinates on the ellipsoid and the sphere, but with the preservation of the first-order values. Therefore, it is logical that to obtain higher accuracy in calculations of the components of the anomalous gravitational field of the Earth, ellipsoidal corrections should be taken into account.

The methodology of such scientific research consists in the expansion of some arbitrary element F of the anomalous gravitational field (disturbing potential, geoid height, gravity anomaly, etc.) in a series according to a small parameter characterizing the deviation of the reference ellipsoid from the sphere. The height of the geoid, the gravity deviation, the gravity anomaly, and other similar elements of some function F0 on the sphere are uniquely determined through the basic function of the perturbing potential T0 using spherical relations. The corresponding functions F will be the values ​​of the elements on the ellipsoid and are also uniquely related to T=T0 using some ellipsoidal formulas. Thus, the functions F1 can be defined.

Based on our research of the components of the anomalous gravitational field of the Earth, we can summarize the following. Since the gravity anomaly practically does not depend on the displacement of the reference coordinate system, the ellipsoidal correction cannot be taken into account when calculating the Earth’s force field. However, the gravity anomaly depends quite strongly on the harmonics of the second degree, in particular, on the second zonal harmonic coefficient С20, and therefore on the compression f of the reference ellipsoid. The obtained value of the ellipsoidal correction   is of the same order as modern high-precision gravimetric satellite data, so it must be taken into account when determining the Earth’s force field.

The results of the calculations performed in the spherical approximation showed that there is a strong dependence between the height of the geoid and the displacement of the reference coordinate system. Ellipsoidal corrections  ,   and   must also be taken into account, since their values are of the same order as modern high-precision altimetric-gravimetric calculations of the anomalous gravitational field of the Earth.

Thus, the novelty and relevance of such scientific solutions lie in the expediency of considering ellipsoidal corrections when determining the anomalous Earth’s gravity field. Neglecting these corrections on average for the territory of Ukraine gives an error in the order of accuracy of modern gravimetric satellite data and altimetric-gravimetric calculations of the Earth’s anomalous gravity field.