Abstract
The gravitational field of conical mass distributions is formulated using the general theory of relativity. The gravitational metric tensor is constructed and applied to the motion of test particles and photons in this gravitational field. The expression for gravitational time dilation is found to have the same form as that in spherical, oblate spheroidal, and prolate spheroidal gravitational fields and hence confirms an earlier assertion that this gravitational phenomena is invariant in form with various mass distributions. It is shown using the pure radial equation of motion that as a test particle moves closer to the conical mass distribution along the radial direction, its radial speed decreases.
Highlights
In recent articles [1,2,3,4], we introduced an approach of studying gravitational fields of various mass distributions as extensions of Schwarzschild’s method
This study is aimed at studying the behaviour of test particles and photons in the vicinity of conically shaped objects placed in empty space such as Sputnik III
It is well known [5, 6] that the general relativistic metric tensor for flat space-time is invariant and can be obtained in any orthogonal curvilinear coordinate (t, u, V, w) by the transformation (t, x, y, z) → (t, u, V, w)
Summary
In recent articles [1,2,3,4], we introduced an approach of studying gravitational fields of various mass distributions as extensions of Schwarzschild’s method. Of interest in this article is the gravitational field of conical mass distributions placed in empty space. Sputnik III, the third Soviet satellite launched on May 15, 1958 has a conical shape.
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