Orbital Parameters and Binary Properties of 37 FGK Stars in the Cores of Open Clusters NGC 2516 and NGC 2422

We present orbits for 24 binaries in the field of open cluster NGC 2516 (∼150 Myr) and 13 binaries in the field of open cluster NGC 2422 (∼130 Myr) using results from a multiyear radial-velocity (RV) survey of the cluster cores. Six of these systems are double-lined spectroscopic binaries. We fit these RV variable systems with orvara, a MCMC-based fitting program that models Keplerian orbits. We use precise stellar parallaxes and proper motions from Gaia EDR3 to determine cluster membership. We impose a barycentric RV prior on all cluster members; this significantly improves our orbital constraints. Two of our systems have periods between five and 15 days, the critical window in which tides efficiently damp orbital eccentricity. These binaries should be included in future analyses of circularization across similarly-aged clusters. We also find a relatively flat distribution of binary mass ratios, consistent with previous work. With the inclusion of TESS light curves for all available targets, we identity target 378–036252 as a new eclipsing binary. We also identify a field star whose secondary has a mass in the brown dwarf range, as well as two cluster members whose RVs suggest the presence of an additional companion. Our orbital fits will help constrain the binary fraction and binary properties across stellar age and across stellar environment.

Dynamics of Magnetized and Magnetically Charged Particles around Regular Nonminimal Magnetic Black Holes

The present paper is devoted to the study of the event horizon properties of spacetime around a regular nonminimal magnetic black hole (BH), together with dynamics of magnetized and magnetically charged particles in the vicinity of the BH. It is shown that the minimum value of the outer horizon of the extreme charged BH increases with the increase in coupling parameter. It reaches its maximum value of 1.5M when q→∞, while the maximal value of the BH charge decreases and tends toward zero. We also present a detailed analysis of magnetized particles’ motion around a regular nonminimal magnetic black hole. The particle’s innermost circular stable orbits (ISCOs) radius decreases as the magnetic charge and the parameter β increase and the coupling parameter of Yang–Mills field causes a decrease at the values of the magnetic charge near to its maximum. We show that the magnetic charge can mimic the spin of a rotating Kerr black hole up to the value of a=0.7893M, providing the same value for an ISCO of a magnetized particle with the parameter β=10.2 when the coupling parameter is q=0. Moreover, Lyapunov exponents, Keplerian orbits and harmonic oscillations of magnetized particles motion are also discussed.

Distance Between Two Keplerian Orbits

In this paper, constrained minimization for the point of closest approach of two conic sections is developed. For this development, we considered the nine cases of possible conics, namely, (elliptic–elliptic), (elliptic–parabolic), (elliptic–hyperbolic), (parabolic–elliptic), (parabolic–parabolic), (parabolic–hyperbolic), (hyperbolic–elliptic), (hyperbolic–parabolic), and (hyperbolic–hyperbolic). The developments are considered from two points of view, namely, analytical and computational. For the analytical developments, the literal expression of the minimum distance equation (S) and the constraint equation (G), including the first and second derivatives for each case, are established. For the computational developments, we construct an efficient algorithm for calculating the minimum distance by using the Lagrange multiplier method under the constraint on time. Finally, we compute the closest distance S between two conics for some orbits. The accuracy of the solutions was checked under the conditions that L| solution ≤ ɛ1; G| solution ≤ ɛ2, where ɛ1,2 < 10−10. For the cases of (parabolic–parabolic), (parabolic–hyperbolic), and (hyperbolic–hyperbolic), we studied thousands of comets, but the condition of the closest approach was not met.

Non-Keplerian Orbits in Dark Matter

This paper is concerned with the mathematical description of orbits that do not have a constant central gravitating mass. Instead, the attracting mass is a diffuse condensate, a situation which classical orbital dynamics has never encountered before. The famous Coma Cluster of Galaxies is embedded in Dark Matter. Condensed Neutrino Objects (CNO), which are stable assemblages of neutrinos and anti-neutrinos, are candidates for the Dark Matter. A CNO solution has been attained previously for the Coma Cluster, which allows mathematical modeling of galaxy orbital mechanics within Dark Matter, first reported here. For non-zero eccentricity galaxy orbits, each point along the trajectory sees a different gravitating central mass, akin to satellite orbits inside Earth. Mathematically, the galaxy orbits are non-Keplerian, spirographs.

The space of Keplerian orbits and a family of its quotient spaces

Distance functions on the set of Keplerian orbits play an important role in solving problems of searching for parent bodies of meteoroid streams. A special kind of such functions are distances in the quotient spaces of orbits. Three metrics of this type were developed earlier. These metrics allow to disregard the longitude of ascending node or the argument of pericenter or both. Here we introduce one more quotient space, where two orbits are considered identical if they differ only in their longitudes of nodes and arguments of pericenters, but have the same sum of these elements (the longitude of pericenter). The function q is defined to calculate distance between two equivalence classes of orbits. The algorithm for calculation of ̺6 value is provided along with a reference to the corresponding program, written in C++ language. Unfortunately, ̺6 is not a full-fledged metric. We proved that it satisfies first two axioms of metric space, but not the third one: the triangle inequality does not hold, at least in the case of large eccentricities. However there are two important particular cases when the triangle axiom is satisfied: one of three orbits is circular, longitudes of pericenters of all three orbits coincide. Perhaps the inequality holds for all elliptic orbits, but this is a matter of future research.

Pairs of Trans-Neptunian Objects with close orbits

A search for pairs of dynamically correlated trans-Neptunian objects with semi-major axes of more than 30 au was performed. The Kholshevnikov metrics in the space of Keplerian orbits are used. Found 27 pairs with metrics less than 0.07 au1/2, 22 pairs in which one of the components is binary, for metrics less than 0.12 au1/2, and 11 pairs of binary trans-Neptunian objects with metrics less than 0.3 au1/2. It is concluded that the pair 2004 VA131 — 2004 VU131 may be the youngest pair of trans-Neptunian objects known today.

EnckeHH: an integrator for gravitational dynamics with a dominant mass that achieves optimal error behaviour

We present EnckeHH, a new, highly accurate code for orbital dynamics of perturbed Keplerian systems such as planetary systems or galactic centre systems. It solves Encke’s equations of motion, which assume perturbed Keplerian orbits. By incorporating numerical techniques, we have made the code follow optimal roundoff error growth. In a 1012 day integration of the outer Solar System, EnckeHH was 3.5 orders of magnitude more accurate than IAS15 in a fixed time step test. Adaptive steps are recommended for IAS15. Through study of efficiency plots, we show that EnckeHH reaches significantly higher accuracy than the Rebound integrators IAS15 and WHCKL for fixed step size.