A353769 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.

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, 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, 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

Offset

0,1

Comments

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.

The centers of the faces are the positions where the gravitational field that is generated by the cube attains its maximum absolute value.

Links

Table of n, a(n) for n=0..104.

Murray S. Klamkin, Extreme Gravitational Attraction, Problem 92-5, SIAM Review, Vol. 34, No. 1 (1992), pp. 120-121; Solution, by Carl C. Grosjean, ibid., Vol. 38, No. 3 (1996), pp. 515-520.

J. A. Lira, If the Earth were a cube, what would be the value of the acceleration of gravity at the center of each face?, Physics Education, Vol. 53, No. 6 (2018), 065013.

Eric Weisstein's World of Physics, Cube Gravitational Force.

Eric Weisstein's World of Physics, Polyhedron Gravitational Force.

Formula

Equals Pi/2 + log((sqrt(2) + 1)*(sqrt(6) - 1)/sqrt(5)) - 2*arcsin(sqrt(2/5)).

Example

0.64922414456459126471247474244668203153595016469104...

Mathematica

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

Crossrefs

Cf. A353770, A353771, A353772, A353773.

Cf. A070058, A336274, A353407.

Sequence in context: A096499 A179258 A365937 * A248930 A021158 A231535

Adjacent sequences: A353766 A353767 A353768 * A353770 A353771 A353772

Keyword

nonn,cons

Author

Amiram Eldar, May 07 2022

Status

approved