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Space-time and spatial geodesies on a rotating sphere

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Abstract

The motion of free particles and photons constrained to lie on the surface of a rotating sphere is analyzed. Formulas are presented for the surface area and volume of the sphere, the velocity components of free particles and photons, the time of flight between fixed reference points on the sphere, and the spatial distance along null geodesies. Spatial geodesies are also investigated and it is shown that there are many solutions of the geodesic equation joining any two fixed points. A description is given of a curved two-dimensional surface embedded in three-dimensional Euclidean space which has the same intrinsic spatial geometry as the rotating sphere.

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Authors and Affiliations

  1. Department of Theoretical Physics, University of St. Andrews, St. Andrews, Fife, Scotland

    K. McFarlane, N. C. McGill & I. H. McKenna

Authors
  1. K. McFarlane
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  2. N. C. McGill
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  3. I. H. McKenna
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McFarlane, K., McGill, N.C. & McKenna, I.H. Space-time and spatial geodesies on a rotating sphere. Int J Theor Phys 19, 347–368 (1980). https://doi.org/10.1007/BF00671988

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  • DOI: https://doi.org/10.1007/BF00671988

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