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Volume 5, Issue 3, September 2019, Page: 85-96
Forced Nutation for Rigid Earth Model with Different Theories
Mohamed Soliman, Department of Astronomy, National Research Institute of Astronomy and Geophysics, Helwan, Egypt
Hadia Hassan Selim, Department of Astronomy, National Research Institute of Astronomy and Geophysics, Helwan, Egypt
Inal Adham Hassan, Department of Astronomy and Metrology, Al-Azhar University, Cairo, Egpyt
Received: Aug. 13, 2019;       Accepted: Sep. 10, 2019;       Published: Sep. 23, 2019
Abstract
Where Earth is not strictly rigid body but can responds to any effects that tend to its rotation and shape, we will explain, in the present paper, the goal which is to define the forced nutation for a rigid Earth model using two different theories. We will formulate a first order Hamiltonian of a deformable Earth for its rotational motion around the Sun through the contribution of triaxial symmetry of the Earth. The formulation of the theory will be formed twice times. Firstly, deduce the tidal affect’s forces by Luni - Solar attraction coupling with the Earth’s geopotential force. Secondly, through the formulation, we will neglect the coupling between the different effects (the geopotential Earth force effect and the Luni - Solar attraction force), so, we will find the transform of the Hamiltonian for each force separately. The analytical solution for the formulated Hamiltonian will be derived for the two cases by using perturbation technique of Lie - Hori series. Once can get the analytical solution by getting the generation function, we will derive the nutation series analytically and numerically for each case and conclude over the results.
Keywords
Rotation of the Earth, Forced Nutation, Celestial Mechanics
Mohamed Soliman, Hadia Hassan Selim, Inal Adham Hassan, Forced Nutation for Rigid Earth Model with Different Theories, International Journal of Applied Mathematics and Theoretical Physics. Special Issue: Theory and Applications for Rotational Earth and Space Dynamics. Vol. 5, No. 3, 2019, pp. 85-96. doi: 10.11648/j.ijamtp.20190503.16
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