A353772 Decimal expansion of the gravitational acceleration generated at a vertex by a unit-mass regular tetrahedron with edge length 2 in units where the gravitational constant is G = 1.

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

Offset: 0

Author

Amiram Eldar, May 07 2022

Keywords

• nonn
• cons

Comments

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

Examples

			0.95485466596615678014550952803369058960247147098757...
		

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

Crossrefs

Cf. A070058, A353769, A353770, A353771, A353773.

Programs

Mathematica

RealDigits[6*Sqrt[3]*(Pi/3 - ArcTan[Sqrt[2]]), 10, 100][[1]]

Formula

Equals 6*sqrt(3)*(Pi/3 - arctan(sqrt(2))).

Equals 3*sqrt(3)*(Pi/6 - arctan(sqrt(2)/4)).