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

Abdelhalim Ebaid, Weam Alharbi, Mona D. Aljoufi and Essam R. El-Zahar
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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

Mathematics, 2020, vol. 8, issue 10, 1-15

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.

Keywords: falling body problem; angular velocity; projectile motion; three dimensions; Earth’s rotation; Laplace transform (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2020
References: View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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