%I #6 May 07 2022 09:41:12

%S 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,

%T 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,

%U 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

%N Decimal 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.

%C 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.

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

%H 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.

%H 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.

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

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

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

%e 0.41975733988710629187374768720081390960585610276177...

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

%Y Cf. A353769, A353771, A353772, A353773.

%Y Cf. A070058, A336274, A353407.

%K nonn,cons

%O 0,1

%A _Amiram Eldar_, May 07 2022