Anomalies of the Earth’s gravitational field in applied problems of ballistics

Authors: Kolesnikova D.S.
Published in issue: #6(59)/2021
DOI: 10.18698/2541-8009-2021-6-709

Category: Aviation and Rocket-Space Engineering | Chapter: Aircraft Dynamics, Ballistics, Motion Control

Keywords: full vector of the gravitational field strength, anomalous gravitational field, Earth ellipsoid, Krasovsky ellipsoid, central gravitational field, model of the Earth’s figure, mathematical modeling, trajectory of an aircraft
Published: 08.07.2021

The paper considers the most common gravitational models in ballistics problems used in calculating the trajectories of aircraft movement: the central gravitational field, the PZ-90 gravitational model, the Krasovsky normal model. A comparative analysis of various Earth’s gravitational models with varying degrees of accuracy describing the gravity field is carried out. The anomalous gravitational field is analyzed and the most characteristic areas are identified, in which it is not recommended to neglect the gravitational field influence. The influence is shown of anomalous gravitational field on the results of modeling gravity models. The estimation of the methodological errors of the gravitational field models is carried out. Recommendations on the appropriateness of using a particular model have been formulated.


[1] Lysenko L.N. Navedenie i navedenie ballisticheskikh raket [Targeting and navigation of ballistic rockets]. Moscow, Bauman MSTU Publ., 2007 (in Russ.).

[2] Grushinskiy N.P. Teoriya figury Zemli [Theory of Earth figure]. Moscow, Fizmatgiz Publ., 1963 (in Russ.).

[3] Zakharin M.I., Zakharin F.M. Kinematika inertsial’nykh sistem navigatsii [Kinematics of inertial navigation systems]. Moscow, Mashinostroenie Publ., 1968 (in Russ.).

[4] Parametry Zemli 1990 goda (PZ-90.11) [Earth parameters of 1990 (PZ-90.11)]. Moscow, Voenno-topograficheskoe upravlenie general’nogo shtaba vooruzhennykh sil RF Publ., 2020 (in Russ.).

[5] GRACE gravity map image gallery. csr.utexas.edu: website. URL: http://www2.csr.utexas.edu/grace/gallery/gravity (accessed: 15.05.2021).

[6] GOST 20058-80. Dinamika letatel’nykh apparatov v atmosfere. Terminy, opredeleniya i oboznacheniya [State standard 20058-80. Aircraft dynamics in atmosphere. Terms, definitions and symbols]. Moscow, Izd-vo standartov Publ., 1981 (in Russ.).

[7] Andreev V.D. Teoriya inertsial’noy navigatsii. Avtonomnye sistemy [Theory of inertial navigation. Autonomous systems]. Moscow, Nauka Publ., 1966 (in Russ.).

[8] Dmitrievskiy A.A., Lysenko L.N. Vneshnyaya ballistika [External ballistics]. Moscow, Mashinostroenie Publ., 2005 (in Russ.).

[9] Komarovskiy Yu.A. Ispol’zovanie razlichnykh referents – ellipsoidov v sudovozhdenii [Using of different references – ellipsoids in ship navigation]. Vladivostok, DVGMA Publ., 1990 (in Russ.).

[10] Chernobotarev G.A. Analiticheskie i chislennye metody nebesnoy mekhaniki [Analitical and numerical methods of celestial mechanics]. Moscow, Nauka Publ., 1965 (in Russ.).