Inverse Problem of Astrodynamics

Author(s)
Yuri Menshikov

Affiliation(s)

Department of Mechanics and Mathematics, Dnepropetrovsk University, Dnepropetrovsk, Ukraine.

Department of Mechanics and Mathematics, Dnepropetrovsk University, Dnepropetrovsk, Ukraine.

ABSTRACT

We consider the problem of determining the center of mass of an unknown gravitational body, using the disturbances in the motion of observed celestial bodies. In this paper an universal approach to obtain the approximate and stable estimate of problem solution is suggested. This approach can be used in other fields of Science. For example, it can be applied for investigation of interactions between fields of forces and elementary particles using known trajectories of elementary particles motions.

We consider the problem of determining the center of mass of an unknown gravitational body, using the disturbances in the motion of observed celestial bodies. In this paper an universal approach to obtain the approximate and stable estimate of problem solution is suggested. This approach can be used in other fields of Science. For example, it can be applied for investigation of interactions between fields of forces and elementary particles using known trajectories of elementary particles motions.

Cite this paper

Menshikov, Y. (2015) Inverse Problem of Astrodynamics.*World Journal of Mechanics*, **5**, 249-256. doi: 10.4236/wjm.2015.512023.

Menshikov, Y. (2015) Inverse Problem of Astrodynamics.

References

[1] Lykawka, P.S. and Mukai, T. (2008) An Outer Planet beyond Pluto and the Origin of the Trans-Neptunian Belt Architecture. Astronomical Journal, 135, 1161-1200.

http://dx.doi.org/10.1088/0004-6256/135/4/1161

[2] Luhman, K.L. (2014) The Search for a Distant Companion to the Sun with the Wide-Field Infrared Survey Explorer. Astrophysical Journal, 781, 4 (7pp).

[3] Seidelmann, P.K. and Harrington, R.S. (1987) Planet X—The Current Status. Celestial Mechanics, 43, 55-68.

http://dx.doi.org/10.1007/BF01234554

[4] Krasovskii, N.N. (1968) Theory of Motion Control. Science, Moscow.

[5] Tikhonov, A.N. and Arsenin, V.Ya. (1979) Methods of Ill-Posed Problems Solving. Science, Moscow.

[6] Trenogin, V.A. (1980) Functional Analysis. Science, Moscow.

[7] Goncharsky, A.V., Leonov, A.S. and Yagola, A.G. (1972) Regularizing Algorithm for Ill-Posed Problems with an Approximately Given Operator. Journal of Computational Mathematics and Mathematical Physics, 12, 1592-1594.

[8] Menshikov, Y.L. (1986) Regularising Algorithm for a Class of Approximate Functional Equations of the First Kind. Journal of Differential Equations and Their Applications, Dnepropetrovsk, 80-87.

[9] Menshikov, Y.L. (2013) Synthesis of Adequate Mathematical Description as Solution of Special Inverse Problems. European Journal of Mathematical Sciences, 2, 256-271.

[10] Vasil’ev, F.P. (1980) Numerical Methods for Solving Extreme Problems. Science, Moscow.

[1] Lykawka, P.S. and Mukai, T. (2008) An Outer Planet beyond Pluto and the Origin of the Trans-Neptunian Belt Architecture. Astronomical Journal, 135, 1161-1200.

http://dx.doi.org/10.1088/0004-6256/135/4/1161

[2] Luhman, K.L. (2014) The Search for a Distant Companion to the Sun with the Wide-Field Infrared Survey Explorer. Astrophysical Journal, 781, 4 (7pp).

[3] Seidelmann, P.K. and Harrington, R.S. (1987) Planet X—The Current Status. Celestial Mechanics, 43, 55-68.

http://dx.doi.org/10.1007/BF01234554

[4] Krasovskii, N.N. (1968) Theory of Motion Control. Science, Moscow.

[5] Tikhonov, A.N. and Arsenin, V.Ya. (1979) Methods of Ill-Posed Problems Solving. Science, Moscow.

[6] Trenogin, V.A. (1980) Functional Analysis. Science, Moscow.

[7] Goncharsky, A.V., Leonov, A.S. and Yagola, A.G. (1972) Regularizing Algorithm for Ill-Posed Problems with an Approximately Given Operator. Journal of Computational Mathematics and Mathematical Physics, 12, 1592-1594.

[8] Menshikov, Y.L. (1986) Regularising Algorithm for a Class of Approximate Functional Equations of the First Kind. Journal of Differential Equations and Their Applications, Dnepropetrovsk, 80-87.

[9] Menshikov, Y.L. (2013) Synthesis of Adequate Mathematical Description as Solution of Special Inverse Problems. European Journal of Mathematical Sciences, 2, 256-271.

[10] Vasil’ev, F.P. (1980) Numerical Methods for Solving Extreme Problems. Science, Moscow.