A353769 - OEIS

%I #8 May 07 2022 09:41:22

%S 6,4,9,2,2,4,1,4,4,5,6,4,5,9,1,2,6,4,7,1,2,4,7,4,7,4,2,4,4,6,6,8,2,0,

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

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

%N Decimal expansion of the gravitational acceleration generated at the center of a face 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 center of face is c*G*M*m/s^2, where G is the gravitational constant (A070058) and c is this constant.

%C The centers of the faces are the positions where the gravitational field that is generated by the cube attains its maximum 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 Pi/2 + log((sqrt(2) + 1)*(sqrt(6) - 1)/sqrt(5)) - 2*arcsin(sqrt(2/5)).

%e 0.64922414456459126471247474244668203153595016469104...

%t RealDigits[Pi/2 + Log[(Sqrt[2] + 1)*(Sqrt[6] - 1)/Sqrt[5]] - 2*ArcSin[Sqrt[2/5]], 10, 100][[1]]

%Y Cf. A353770, A353771, A353772, A353773.

%Y Cf. A070058, A336274, A353407.

%K nonn,cons

%O 0,1

%A _Amiram Eldar_, May 07 2022