Estimates on a minimal classification o f relative equilibria in the planar n-body problem of celestial mechanics have been announced in [1], [2]. Our main theorem asserts that these estimates are actually met for any n > 3 on an open set in IR~_. For any n > 4, this open set is proper.

One of Donald Bates’s most striking claims was that the bio-medical sciences were central to the Scientific Revolution of the 17th century and that its innovators drew heavily on the “organic mechanism” of the ancients. The paper elaborates on and defends Bates’s proposal against a more conventional reading of the Scientific Revolution as driven by celestial and terrestrial mechanics and physics.

For the circular restricted three-body problem of celestial mechanics with small secondary mass, we prove the existence of uniformly hyperbolic invariant sets of non-planar periodic and chaotic almost collision orbits. Poincaré conjectured existence of periodic ones and gave them the name “second species solutions”. We obtain large subshifts of finite type containing solutions of this type.

Perturbation theory has always been an important part of natural sciences. From celestial mechanics to quantum theory of fields it has always played a central role that this little note would like to analyze briefly. We will show in particular how its epistemological situation has changed, from being a ”tool” to being the basis of definition of objects in quantum field theory.

It is known that for n ≥ 3 centres and positive energies the ncentre problem of celestial mechanics leads to a flow with a strange repellor and positive topological entropy. Here we consider the energies above some threshold and show: Whereas for arbitrary g > 1 independent integrals of Gevrey class g exist, no real-analytic (that is, Gevrey class 1) independent integral exists.

Graph theoretic methods of optimal control in the presence of uncertainty are applied to a celestial mechanics problem. We find a fuel-efficient spacecraft trajectory which starts at infinity and is captured by the smaller member of a binary system, e.g., a moon of Jupiter, using multiple gravity assists.

Belarussian Polytechnical Academy kalashnikov [email protected] www.geocities.com/optomaplev Abstract The basics of the relativistic astrophysics including the celestial mechanics in weak field, black holes and cosmological models are illustrated and analyzed by means of Maple 6 Application Areas/Subjects: Science, Astrophysics, General Relativity, Tensor Analysis, Differential geometry, Differenti...

ABSTRACT We present heyoka, a new, modern and general-purpose implementation of Taylor’s integration method for the numerical solution ordinary differential equations. Detailed tests focused on difficult high-precision gravitational problems in astrodynamics celestial mechanics show how our integrator is competitive with often superior to state-of-the-art specialized symplectic non-symplectic i...