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München, Germany

Horedt G.P.,Kronwinkler 50
Planetary and Space Science | Year: 2012

We derive in the plane problem a new closed solution of the Lagrangian equations for resonant motion, concomitantly including zeroth order, and approximate first order and secular perturbations. A major aim is the determination of simple lower limits for the maximum eccentricities and variations of semimajor axes (intrinsic values). Applications of the general solution are made for each perturbation separately. (i) Zeroth and first order perturbations: a new closed solution for the principal zeroth order variation of semimajor axes is obtained. The maximum eccentricity and relative change of semimajor axis of any lunar orbit cannot be lower than 0.019 and 0.018, respectively. (ii) Secular perturbations: with the angular momentum integral our secular perturbations can be easily extended to the spatial problem. The planetary Lidov-Kozai problem is extended to retrograde orbits, showing that large variations of eccentricity and inclination occur for initially circular orbits, if initial mutual inclinations are between about 40°and 150°. (iii) Resonant perturbations: for first and second order resonances, and initially circular orbits our formulas generally approximate just the calculated orbital elements during the whole motion. As a new unexpected result, the numerical exploration of the asteroid belt reproduces most of its overall characteristics up to third order resonances within the restricted three-body problem and modest initial eccentricities ≤0.05. © 2012 Elsevier Ltd. All rights reserved. Source

Horedt G.P.,Kronwinkler 50
Astrophysics and Space Science | Year: 2016

The initial orbit of a prestellar core in the resisting intercore medium is found to be an elliptic spiral round the mass centre of the parent molecular cloud (clump), with exponentially decreasing semiaxes, high constant eccentricity, and constant period. Prestellar cores are stable against perturbations caused by the parent cloud, if the corresponding mean density contrast is larger than about 10. This value defines the safe boundary of a prestellar core within its parent cloud and is in accordance with observations. © 2016, Springer Science+Business Media Dordrecht. Source

Horedt G.P.,Kronwinkler 50
Planetary and Space Science | Year: 2015

Within the plane planetary problem we present two new approaches for the determination of purely resonant eccentricity and semimajor axis variations in terms of simple, closed algebraic relationships. We consider the motion of two Jovian exoplanets in 2:1, 3:1, and 7:4 resonance. Even with initial eccentricities of 0.05, we have found two numerical examples of purely resonant motion of two Jovian exoplanets in 2:1 and 3:1 resonance, fitting throughout the theoretical relationships for over 105 revolutions of the outer exoplanet. The maximum eccentricities of the two Jovian exoplanets are <0.15, if the initial ratio of semimajor axes is <0.6992 and the initial eccentricities are ≤0.05. During intervals of negligible secular perturbations, the agreement between theoretical and numerical maximum resonant eccentricity variations is generally much better than within a factor of 2. The theoretical and calculated maximum eccentricity of a Plutino in 2:3 resonance with Neptune is >0.053. © 2015 Elsevier Ltd. All rights reserved. Source

Horedt G.P.,Kronwinkler 50
Astrophysical Journal | Year: 2013

Prestellar cores are approximated by singular polytropic spheres. Their early evolution is studied analytically with a Bondi-like scheme. The considered approximation is meaningful for polytropic exponents γ between 0 and 6/5, implying radial power-law density profiles between r -1 and r -2.5. Gravitationally unstable Jeans and Bonnor-Ebert masses differ at most by a factor of 3.25. Tidally stable prestellar cores must have a mean density contrast ≳ 8 with respect to the external parent cloud medium. The mass-accretion rate relates to the cube of equivalent sound speed, as in Shu's seminal paper. The prestellar masses accreted over 105 years cover the whole stellar mass spectrum; they are derived in simple closed form, depending only on the polytropic equation of state. The stellar masses that can be formed via strict conservation of angular momentum are at most of the order of a brown dwarf. © 2013. The American Astronomical Society. All rights reserved. Source

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