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Title: A. C. Clarke's Space Odyssey and Newton's law of gravity (English)
Author: Bartoň, Stanislav
Author: Renčín, Lukáš
Language: English
Journal: Programs and Algorithms of Numerical Mathematics
Volume: Proceedings of Seminar. Janov nad Nisou, June 19-24, 2016
Issue: 2016
Pages: 7-14
Category: math
Summary: In his famous tetralogy, Space Odyssey, A. C. Clarke called the calculation of a motion of a mass point in the gravitational field of the massive cuboid a classical problem of gravitational mechanics. This article presents a proposal for a solution to this problem in terms of Newton's theory of gravity. First we discuss and generalize Newton's law of gravitation. We then compare the gravitational field created by the cuboid -- monolith, with the gravitational field of the homogeneous sphere. This is followed by the calculation of the shape of free fall trajectories and the solving of Newton's equations of motion, defining the motion of the mass point in the monolith's gravitational field for general initial conditions. The final section describes the procedures for calculating the shape of the monolith's equipotential surfaces. Due to the complexity of the problems, all calculations are performed in the Maple program. The results of the calculations are illustrated using both 2D and 3D graphs. (English)
Keyword: law of gravity
Keyword: gravitational force
Keyword: potential
Keyword: power
Keyword: acceleration
Keyword: equations of motion
Keyword: trajectory
Keyword: Maple
MSC: 34A34
MSC: 65D30
MSC: 65Z05
MSC: 68W30
MSC: 70F15
DOI: 10.21136/panm.2016.01
Date available: 2017-06-20T12:59:42Z
Last updated: 2023-06-05
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