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 1924, 2016 
Issue:

2016 
Year:


Pages:

714 
. 
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:

20170620T12:59:42Z 
Last updated:

20181023 
Stable URL:

http://hdl.handle.net/10338.dmlcz/702992 
. 