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The Exact Solution of the Falling Body Problem in Three-Dimensions: Comparative Study

Author

Listed:
  • Abdelhalim Ebaid

    (Department of Mathematics, Faculty of Science, University of Tabuk, Tabuk 71491, Saudi Arabia)

  • Weam Alharbi

    (Department of Mathematics, Faculty of Science, University of Tabuk, Tabuk 71491, Saudi Arabia)

  • Mona D. Aljoufi

    (Department of Mathematics, Faculty of Science, University of Tabuk, Tabuk 71491, Saudi Arabia)

  • Essam R. El-Zahar

    (Department of Mathematics, Faculty of Sciences and Humanities in Al-Kharj, Prince Sattam bin, Abdulaziz University, Al-Kharj 11942, Saudi Arabia
    Department of Basic Engineering Science, Faculty of Engineering, Menofia University, Shebin El-Kom 32511, Egypt)

Abstract

Very recently, the system of differential equations governing the three-dimensional falling body problem (TDFBP) has been approximately solved. The previously obtained approximate solution was based on the fact that the Earth’s rotation (ER) is quite slow and hence all high order terms of ω in addition to the magnitude ω 2 R were neglected, where ω is the angular velocity and R is the radius of Earth. However, it is shown in this paper that the ignorance of such magnitudes leads, in many cases, to significant errors in the estimated falling time and other physical quantities. The current results are based on obtaining the exact solutions of the full TDFBP-system and performing several comparisons with the approximate ones in the relevant literature. The obtained results are of great interest and importance, especially for other planets in the Solar System or exterior planets, in which ω and/or ω 2 R are of considerable amounts and hence cannot be ignored. Therefore, the present analysis is valid in analyzing the TDFBP near to the surface of any spherical celestial body.

Suggested Citation

  • Abdelhalim Ebaid & Weam Alharbi & Mona D. Aljoufi & Essam R. El-Zahar, 2020. "The Exact Solution of the Falling Body Problem in Three-Dimensions: Comparative Study," Mathematics, MDPI, vol. 8(10), pages 1-15, October.
    • Handle: RePEc:gam:jmathe:v:8:y:2020:i:10:p:1726-:d:424662
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    Citations

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    Cited by:

    1. Ebrahem A. Algehyne & Abdelhalim Ebaid & Essam R. El-Zahar & Musaad S. Aldhabani & Mounirah Areshi & Hind K. Al-Jeaid, 2023. "Projectile Motion in Special Theory of Relativity: Re-Investigation and New Dynamical Properties in Vacuum," Mathematics, MDPI, vol. 11(18), pages 1-21, September.

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