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Cf. A070058, A336274, A353407.

allocated for Amiram EldarDecimal expansion of the gravitational acceleration generated at a vertex by a unit-mass cube with edge length 2 in units where the gravitational constant is G = 1.

4, 1, 9, 7, 5, 7, 3, 3, 9, 8, 8, 7, 1, 0, 6, 2, 9, 1, 8, 7, 3, 7, 4, 7, 6, 8, 7, 2, 0, 0, 8, 1, 3, 9, 0, 9, 6, 0, 5, 8, 5, 6, 1, 0, 2, 7, 6, 1, 7, 7, 2, 6, 6, 1, 3, 8, 7, 8, 2, 7, 5, 6, 1, 7, 1, 2, 7, 6, 5, 7, 4, 5, 1, 0, 4, 7, 7, 6, 7, 5, 7, 6, 6, 1, 4, 8, 8, 7, 0, 3, 0, 2, 5, 9, 9, 8, 8, 7, 0, 6, 4, 5, 9, 7, 1

0,1

The absolute value of the gravitational attraction force between a homogeneous cube with mass M and edge length 2*s and a test particle with mass m located at the cube's vertex is c*G*M*m/s^2, where G is the gravitational constant (A070058) and c is this constant.

The vertices are the positions where the gravitational field that is generated by the cube on its surface attains its minimum absolute value.

Murray S. Klamkin, <a href="https://www.jstor.org/stable/2132789">Extreme Gravitational Attraction</a>, Problem 92-5, SIAM Review, Vol. 34, No. 1 (1992), pp. 120-121; <a href="https://www.jstor.org/stable/2132502">Solution</a>, by Carl C. Grosjean, ibid., Vol. 38, No. 3 (1996), pp. 515-520.

J. A. Lira, <a href="https://doi.org/10.1088/1361-6552/aadb25">If the Earth were a cube, what would be the value of the acceleration of gravity at the center of each face?</a>, Physics Education, Vol. 53, No. 6 (2018), 065013.

Eric Weisstein's World of Physics, <a href="https://scienceworld.wolfram.com/physics/CubeGravitationalForce.html">Cube Gravitational Force</a>.

Eric Weisstein's World of Physics, <a href="https://scienceworld.wolfram.com/physics/PolyhedronGravitationalForce.html">Polyhedron Gravitational Force</a>.

Equals (sqrt(3)/2)*(Pi/12 + log(sqrt(2) + 1) - log(sqrt(3) + 2)/2).

0.41975733988710629187374768720081390960585610276177...

RealDigits[(Sqrt[3]/2)*(Pi/12 + Log[Sqrt[2] + 1] - Log[Sqrt[3] + 2]/2), 10, 100][[1]]

Cf. A353769, A353771, A353772, A353773.

Cf. A070058, A336274.

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Amiram Eldar, May 07 2022

approved

editing

allocated for Amiram Eldar

allocated

approved