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Focusing on the legend of Phaedra and Hippolytus as developed in Euripides and Seneca and especially in Racine’s Phèdre and taking into account as well its further development in works by Camillo Boito, Luchino Visconti, and Yukio Mishima, I make the following arguments: (1) Contrary to many theologians and philosophers of love, a pathological form of love that issues in murder and suicide should not be regarded as unworthy of serious attention. Racine’s tragedy provides a catharsis for universal experiences of unrequited love and jealousy, a major human phenomenon. (2) Contrary to Paul Valéry, Phèdre’s love cannot be called merely animal, since the analytical insight she develops into her morbid passion carries tremendous moral force and lies at the origin of the European psychological novel, as launched by Madame de La Fayette a year later. (3) Contrary to François Mauriac, even if she is a heroine of desire or concupiscence rather than of “true love” (in contrast to the relatively innocent affections of Hippolyte and Aricie), the incredible beauty of her language resists such an easy categorization. (4) Study of concrete presentations of “love” in literature confirms that the meaning and use of this word is marked by an irreducible pluralism. Philosophical and theological analysis of love has to come to terms with this. (5) The role of a work of art, in crystallizing archetypical emotions and situations in a way that carries authority, is to provide the middle ground between the abstractions of philosophy on the one hand and the uncontrollable diversity of the empirical on the other. Even psychologies or sociologies of love, which claim to be close to the concrete data, need to be anchored in and corrected by the special concrete vision that only great literature can bring.

On its seventeenth centenary, I seek to reassess the theological significance of the Nicene Creed, drawing inspiration from Athanasius, who came to see the Creed as a privileged transmission of the apostolic teaching based on the Revelation granted by Christ. I attempt to bring into focus the nature of Revelation, referring to Karl Barth and Jean-Luc Marion. Criticizing the deflationary approach to Nicaea and Athanasius, which has been common of late, I read the layers of meaning in the Creed with special attention to the way the Creed builds on Johannine themes, and I reassess its ousia language.

This article presents the algorithms for integrating the motion and the attitude reference frame of a deep space probe in a native relativistic framework. There are two possible applications: modeling the cruise orbits of space probes in the Solar System and ephemeris modeling. The main features are a symplectic integrator that guarantees the long-term stability of modeled orbits with a design specific to general relativity, and the calculation of a co-moving, non-rotating reference frame with respect to distant stars. These features enable stable instrument orientation of the probe bus and the modeling of non-gravitational forces, thanks to a drag-free design of the spacecraft. The algorithms in this article have been rigorously tested using GRAPE, a development software package written in the Julia computer language.

Spacecraft propagation tools describe the motion of near-Earth objects and interplanetary probes using Newton’s theory of gravity supplemented with the approximate general relativistic n-body Einstein–Infeld–Hoffmann equations of motion. With respect to the general theory of relativity and the long-standing recommendations of the International Astronomical Union for astrometry, celestial mechanics and metrology, we believe modern orbitography software is now reaching its limits in terms of complexity. In this paper, we present the first results of a prototype software titled General Relativistic Accelerometer-based Propagation Environment (GRAPE). We describe the motion of interplanetary probes and spacecraft using extended general relativistic equations of motion which account for non-gravitational forces using end-user supplied accelerometer data or approximate dynamical models. We exploit the unique general relativistic quadratic invariant associated with the orthogonality between four-velocity and acceleration and simulate the perturbed orbits for Molniya, Parker Solar Probe and Mercury Planetary Orbiter-like test particles subject to a radiation-like four-force. The accuracy of the numerical procedure is maintained using a 5-stage, 10th-order structure-preserving Gauss collocation symplectic integration scheme. GRAPE preserves the norm of the tangent vector to the test particle worldline at the order of 10-32.

We describe the phase space structures related to the semi-major axis of Molniya-like satellites subject to tesseral and lunisolar resonances. In particular, the questions answered in this contribution are: (1) we study the indirect interplay of the critical inclination resonance on the semi-geosynchronous resonance using a hierarchy of more realistic dynamical systems, thus discussing the dynamics beyond the integrable approximation. By introducing ad hoc tractable models averaged over fast angles, (2) we numerically demarcate the hyperbolic structures organising the long-term dynamics via fast Lyapunov indicators cartography. Based on the publicly available two-line elements space orbital data, (3) we identify two satellites, namely Molniya 1-69 and Molniya 1-87, displaying fingerprints consistent with the dynamics associated to the hyperbolic set. Finally, (4) the computations of their associated dynamical maps highlight that the spacecraft are trapped within the hyperbolic tangle. This research therefore reports evidence of actual artificial satellites in the near-Earth environment whose dynamics are ruled by hyperbolic manifolds and resonant mechanisms. The tools, formalism and methodologies we present are exportable to other region of space subject to similar commensurabilities as the geosynchronous region.

Einstein’s theory of general relativity is playing an increasingly important role in fields such as interplanetary navigation, astrometry, and metrology. Modern spacecraft and interplanetary probe prediction and estimation platforms employ a perturbed Newtonian framework, supplemented with the Einstein-Infeld-Hoffmann n -body equations of motion. While time in Newtonian mechanics is formally universal, the accuracy of modern radiometric tracking systems necessitate linear corrections via increasingly complex and error-prone post-Newtonian techniques—to account for light deflection due to the solar system bodies. With flagship projects such as the ESA/JAXA BepiColombo mission now operating at unprecedented levels of accuracy, we believe the standard corrected Newtonian paradigm is approaching its limits in terms of complexity. In this paper, we employ a novel prototype software, General Relativistic Accelerometer-based Propagation Environment, to reconstruct the Cassini cruise-phase trajectory during its first gravitational wave experiment in a fully relativistic framework. The results presented herein agree with post-processed trajectory information obtained from NASA’s SPICE kernels at the order of centimetres.

Examining the ways in which two representatives of the “theological turn in French phenomenology” speak of the interrelationship between philosophy and theology, one may detect a number of tendencies which are deleterious both to philosophy and theology. The idea of an autonomous philosophy, pursued as an end in itself, needs to be defended against claims that philosophy can only flourish under theological tutelage. Again, the integrity of theology as a science of faith excludes any identification of theology as a kind of philosophy. Interaction between the two disciplines, especially in the border areas of apologetics, fundamental theology, religious philosophy, and philosophy of religion, can be fruitful only if a keen sense of their radical difference of orientation is sustained. Behind the swamping of phenomenology by theological concerns lies a series of misunderstandings of metaphysics and its overcoming as well as a misguided notion that phenomenology allows revealed theology to re-enter the French university under the rubric of philosophy.