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A345449
Decimal expansion of Gascheau's value, which is defined as the smaller solution of 27*x*(1 - x) = 1.
0
3, 8, 5, 2, 0, 8, 9, 6, 5, 0, 4, 5, 5, 1, 3, 9, 7, 0, 7, 8, 6, 5, 2, 0, 6, 9, 7, 2, 7, 3, 6, 1, 5, 5, 4, 9, 8, 7, 0, 9, 9, 2, 0, 8, 3, 9, 1, 3, 5, 2, 4, 5, 6, 6, 9, 8, 2, 1, 1, 7, 5, 7, 2, 7, 5, 6, 8, 9, 7, 2, 0, 3, 6, 5, 3, 8, 0, 4, 6, 8, 1, 1, 8, 4, 7, 7, 8, 6, 0, 6, 5, 3, 7, 5, 7, 9, 4, 1, 6, 5, 1, 9, 4, 3, 6, 6
OFFSET
-1,1
COMMENTS
Gascheau's value is the maximum mass fraction of the second largest mass in a restricted three-body problem with stable rotating equilateral configuration. Named after French scientist Gabriel Gascheau. Also called Routh's value. If the mass fraction of the second massive object is lower than Gascheau's value, the trojan points L4 and L5 are stable for the zero-mass object.
The Gascheau value G arises in a simplified model of the three body problem. The simplifications are: the mass of the lightest body is negligible ("the restricted three body problem") and the orbits occur on a two-dimensional plane ("the Euler model"). This is "the circular restricted three body problem". In such a system the stability of the Lagrangian points L4 and L5 depends on the mass ratio of the primary masses M1, M2, letting M3 = 0. Assuming M1 > M2 the Lagrangian points are stable only when M2/(M1 + M2 ) < G. - Peter Luschny, Jul 14 2021
LINKS
FORMULA
Equals (1-sqrt(23/27))/2.
Equals 1/(25+1/(1+1/(23+1/(1+1/(23+1/(1+1/(23+1/(1+1/(23+..))))))))) - Peter Luschny, Jul 14 2021
EXAMPLE
0.038520896504551397078652...
MAPLE
with(NumberTheory): Digits:=200:
evalf(Value(ContinuedFraction([[0, 25], [1, 23]]))); # Peter Luschny, Jul 10 2021
MATHEMATICA
First[RealDigits[N[(1-Sqrt[23/27])/2, 106]]] (* Stefano Spezia, Jun 20 2021 *)
CROSSREFS
Sequence in context: A131653 A011239 A261644 * A348026 A200699 A113813
KEYWORD
nonn,cons
AUTHOR
Donghwi Park, Jun 19 2021
STATUS
approved