The relativistic gravity train

The gravity train that takes 42.2 min from any point A to any other point B that is connected by a straight-line tunnel through Earth has captured the imagination more than most other applications in calculus or introductory physics courses. Brachystochron and, most recently, nonlinear density solut...

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Bibliographic Details
Published in:European journal of physics 2018-05, Vol.39 (3), p.35603
Main Author: Seel, Max
Format: Article
Language:English
Subjects:
gravity train
Newton's cannon ball
relativistic effects
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Summary:The gravity train that takes 42.2 min from any point A to any other point B that is connected by a straight-line tunnel through Earth has captured the imagination more than most other applications in calculus or introductory physics courses. Brachystochron and, most recently, nonlinear density solutions have been discussed. Here relativistic corrections are presented. It is discussed how the corrections affect the time to fall through Earth, the Sun, a white dwarf, a neutron star, and-the ultimate limit-the difference in time measured by a moving, a stationary and the fiducial observer at infinity if the density of the sphere approaches the density of a black hole. The relativistic gravity train can serve as a problem with approximate and exact analytic solutions and as numerical exercise in any introductory course on relativity.
ISSN:0143-0807
1361-6404
DOI:10.1088/1361-6404/aaa8f6