Periodic satellite orbits of the Broucke-Hadjidemetriou-Hénon family of three-body system with unequal masses

Triple systems are common and key objects in astronomy. The three-body problem has received much more attention in recent years [1–3]. All observed periodic triple stars systems [4–6] belong to the Broucke-Hadjidemetriou-Hénon’s (BHH) family [7–9]. The BHH orbits are a family of periodic orbits of the three-body system with the simplest topological free group word [10] a, while Jankovíc and Dmitrasinovíc [1] gained 58 equal-mass BHH satellite orbits which have free group words ak (k > 1), where k is the topological exponent. However, the BHH satellite orbits with equal mass is lack of realistic meaning because they do not exist in practice. Here we present 419743 new BHH orbits and 179253 new BHH satellites (k > 1) for three-body system with unequal mass. Especially, 48761 among the 179253 new BHH satellites are stable and have unequal masses. It suggests that these 48761 stable BHH satellites could be found by the observation. Besides, for the three-body system with equal mass at a fixed energy, it was demonstrated that the relationship between the angular momentum (L) and topological scaled period (T/k) of the BHH satellites is the same as that of the BHH orbits [1]. However, we found that this does not hold for the three-body system with unequal mass. Our findings have broad impact for the astrophysical scenario: they could inspire the theoretical and observational study of the triple system, the formation of triple stars [11], the gravitational waves pattern [12] and the gravitational waves observation [13] of the triple system.

Telescoping Faith

Chapter 6 examines Coleridge’s recourse to the discoveries of William Herschel to conceptualize and communicate his conversion to Trinitarian theology, explaining it as part of a complicated effort to break free from Joseph Priestley’s Socinianism, materialism, and philosophical necessity. Modernizing Priestleian science with a set of spiritual symbols taken from William Herschel was a way in which Coleridge hoped to escape from Priestley’s metaphysics. The handling of Herschelian science—especially infra-red and triple stars—is thus seen as a seismometer for Coleridge’s faith. The implications of this symbolic logic on Coleridge’s epistemological categories of the Reason and the Understanding are explored, together with his persistent use of a telescope as a symbol for faith.