A353770 - OEIS

A353770

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.

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

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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 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.

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

EXAMPLE

0.41975733988710629187374768720081390960585610276177...

MATHEMATICA

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

CROSSREFS

Cf. A353769, A353771, A353772, A353773.

Cf. A070058, A336274, A353407.