Summary
In this paper a general and exact expression of the gravitational attraction of a right vertical circular cylinder at points external to it is developed. This expression is derived in terms of complete elliptic integrals of the first and second kind and the Neumann's Lambda function. Since the solution involves only tabulated functions, it is well suited for rapid desk calculations with any degree of accuracy at any points, including the points in the plane of the cylinder (outcroping cylinder). For this case, the corresponding master curve is given. Finally, a relation between the abscissa of the inflexion point of the Δg curve and the depth of the cylinder is established.
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Abbreviations
- r, ϕ,z :
-
polar coordinates
- R :
-
the radius of the cylinder
- a 0 :
-
the depth of the cylinder
- a :
-
a 0/R
- x 0 :
-
the horizontal distance between the axis of the cylinder and the point of computation
- K(k) :
-
complete elliptic integral of the first kind
- E(k) :
-
complete elliptic integral of the second kind
- Π(−n 2,k) and Π (m 2,k):
-
complete elliptic integrals of the third kind
- Λ0 (ϕ,k):
-
Neumann's Lambda function
- G :
-
universal gravitational constant
- δ:
-
density of the cylinder
References
Parasnis D. S. (1961): Geophysical Prospecting, IX, number 3, pp. 382–398.
Byrd P. F. &Friedman M. D. (1954):Handbook of elliptic integrals for Engineers and Physicists, Springer Verlag, Berlin.
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Nabighian, M.N. The gravitational attraction of a right vertical circular cylinder at points external to it. Geofisica Pura e Applicata 53, 45–51 (1962). https://doi.org/10.1007/BF02007108
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DOI: https://doi.org/10.1007/BF02007108