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

Offset: 0

Author

Amiram Eldar, May 07 2022

Keywords

• nonn
• cons

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.

Examples

			0.64705882759784735823790619474617466854774298046786...
		

Links

• 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.

Crossrefs

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

Programs

Mathematica

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

Formula

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