A353773 - OEIS

A353773

Decimal expansion of the gravitational acceleration generated at a vertex by a unit-mass regular octahedron with edge length 2 in units where the gravitational constant is G = 1.

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

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OFFSET

0,1

COMMENTS

The absolute value of the gravitational attraction force between a homogeneous regular octahedron with mass M and edge length 2*s and a test particle with mass m located at the octahedron'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 octahedron 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.

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

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

FORMULA

Equals sqrt(2)*log(3*(sqrt(2)-1)) + arctan(sqrt(2)/4).

EXAMPLE

0.64705882759784735823790619474617466854774298046786...

MATHEMATICA

RealDigits[Sqrt[2]*Log[3*(Sqrt[2]-1)] + ArcTan[Sqrt[2]/4], 10, 100][[1]]

CROSSREFS

Cf. A070058, A353769, A353770, A353771, A353772.

Sequence in context: A164293 A141796 A105160 * A200228 A309710 A241297

Adjacent sequences: A353770 A353771 A353772 * A353774 A353775 A353776

KEYWORD

nonn,cons

AUTHOR

Amiram Eldar, May 07 2022

STATUS

approved