A. C. Clarke's space odyssey and Newton's law of gravity

Bartoň, Stanislav; Renčín, Lukáš

  • Programs and Algorithms of Numerical Mathematics, Publisher: Institute of Mathematics CAS(Prague), page 7-14

Abstract

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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.

How to cite

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Bartoň, Stanislav, and Renčín, Lukáš. "A. C. Clarke's space odyssey and Newton's law of gravity." Programs and Algorithms of Numerical Mathematics. Prague: Institute of Mathematics CAS, 2017. 7-14. <http://eudml.org/doc/288158>.

@inProceedings{Bartoň2017,
abstract = {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.},
author = {Bartoň, Stanislav, Renčín, Lukáš},
booktitle = {Programs and Algorithms of Numerical Mathematics},
keywords = {law of gravity; gravitational force; potential; power; acceleration; equations of motion; trajectory; Maple},
location = {Prague},
pages = {7-14},
publisher = {Institute of Mathematics CAS},
title = {A. C. Clarke's space odyssey and Newton's law of gravity},
url = {http://eudml.org/doc/288158},
year = {2017},
}

TY - CLSWK
AU - Bartoň, Stanislav
AU - Renčín, Lukáš
TI - A. C. Clarke's space odyssey and Newton's law of gravity
T2 - Programs and Algorithms of Numerical Mathematics
PY - 2017
CY - Prague
PB - Institute of Mathematics CAS
SP - 7
EP - 14
AB - 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.
KW - law of gravity; gravitational force; potential; power; acceleration; equations of motion; trajectory; Maple
UR - http://eudml.org/doc/288158
ER -

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