Showing papers on "Trojan published in 1984"

Reflections on trusting trust

Abstract: To what extent should one trust a statement that a program is free of Trojan horses? Perhaps it is more important to trust the people who wrote the software.

Trojan Orbits in Secular Resonances

Abstract: A near equality between the nodal rates of suitably defined Trojan orbits and Jupiter represents an important type of a secular resonance. This case is realized by the model Sun-Jupiter-Saturn-Trojan, referred to the invariable plane. A second theoretical example is based on the elliptic three-body problem Sun-Jupiter-Trojan, where the vanishing nodal rate of a special Trojan orbit and the vanishing rate of Jupiter’s longitude of perihelion define a secular resonance.

Critical Inclination of Trojan Asteroids

Abstract: The author’s earlier solution for Trojan asteroids is developed further. It is shown that depending on the amplitude of libration around the Lagrangian point L4, there is a critical inclination which determines the sign of the variation of the ascending node. If the orbital inclination if a Trojan is smaller than the critical one, then the ascending node decreases and otherwise it increases. The variation of the eccentricity and of the longitude of the perihelion has also a dependence on the critical inclination.

Trojan orbits with mass exchange of the primaries

Abstract: The librational motion round the Lagrangian triangular points L4, L5 with mass exchange of the primaries is investigated according to Brown's theory. The results are the same as in the case of isotropic mass variation studied earlier (Horedt, 1974a): (i) The extrema of the elongations with respect to the small mass are unaffected by mass exchange. (ii) The equations for the extrema of the Trojan's distance from the Sun and for the libration period are formally the same as in the constant mass problem, but with the understanding that the masses are now time dependent quantities. A Trojan cannot leave the libration domain due to a mass variation of the primaries obeying the constraints from Equation (2.4), with a mass ratio of the primaries m/M≤0.0401.

On the Brown conjecture.

Abstract: In 1911 E. W. Brown conjectured that the family of long-periodic orbits in the Trojan case of the restricted problem of three bodies terminates in an asymptotic orbit that passes through the Langrangian point L3, for t = ± ∞. The paper refutes this conjecture analytically, thereby confirming the previously published numerical refutation by Henrard (1983).