## Elaboration of an Effective Method of Determing the Fundamental Constants of the Earth Gravitational Field on the Basis of GPS Measurements and Satellite Data on the Gradients of the Potential

Transactions of IAA RAS, issue 20, 460–462 (2009)

**Keywords**:
радиоинтерферометрия со сверхдлинными базами, фундаментальные константы гравитационного поля Земли, градиенты потенциала тяготения, прямоугольные геоцентрические координаты, модели геопотенциала, небесная механика, спутниковая градиентометрия, спутниковая геодезия

### Abstract

A general non-singular expression is derived for the gradient of the Earth potential of an arbitrary order with respect to the rectangular geocentric coordinates. It has the same simple form as the potential itself. Simple linear relations are constructed, connecting the coefficients of the potential and its gradients. These relations can be solved in both directions. The obtained results can be applied for constructing geopotential models from satellite gradiometry measurements and for solving many other problems of celestial mechanics and satellite geodesy

### Citation

`M. S. Petrovskaya, A. N. Vershkov . Elaboration of an Effective Method of Determing the Fundamental Constants of the Earth Gravitational Field on the Basis of GPS Measurements and Satellite Data on the Gradients of the Potential // Transactions of IAA RAS. — 2009. — Issue 20. — P. 460–462.`

```
@article{petrovskaya2009,
abstract = {A general non-singular expression is derived for the gradient of the Earth potential of an arbitrary order with respect to the rectangular geocentric coordinates. It has the same simple form as the potential itself. Simple linear relations are constructed, connecting the coefficients of the potential and its gradients. These relations can be solved in both directions. The obtained results can be applied for constructing geopotential models from satellite gradiometry measurements and for solving many other problems of celestial mechanics and satellite geodesy},
author = {M.~S. Petrovskaya and A.~N. Vershkov},
issue = {20},
journal = {Transactions of IAA RAS},
keyword = {радиоинтерферометрия со сверхдлинными базами, фундаментальные константы гравитационного поля Земли, градиенты потенциала тяготения, прямоугольные геоцентрические координаты, модели геопотенциала, небесная механика, спутниковая градиентометрия, спутниковая геодезия},
pages = {460--462},
title = {Elaboration of an Effective Method of Determing the Fundamental Constants of the Earth Gravitational Field on the Basis of GPS Measurements and Satellite Data on the Gradients of the Potential},
url = {http://iaaras.ru/en/library/paper/675/},
year = {2009}
}
```

```
TY - JOUR
TI - Elaboration of an Effective Method of Determing the Fundamental Constants of the Earth Gravitational Field on the Basis of GPS Measurements and Satellite Data on the Gradients of the Potential
AU - Petrovskaya, M. S.
AU - Vershkov, A. N.
PY - 2009
T2 - Transactions of IAA RAS
IS - 20
SP - 460
AB - A general non-singular expression is derived for the gradient of the
Earth potential of an arbitrary order with respect to the rectangular
geocentric coordinates. It has the same simple form as the potential
itself. Simple linear relations are constructed, connecting the
coefficients of the potential and its gradients. These relations can
be solved in both directions. The obtained results can be applied for
constructing geopotential models from satellite gradiometry
measurements and for solving many other problems of celestial
mechanics and satellite geodesy
UR - http://iaaras.ru/en/library/paper/675/
ER -
```