Vol 101, No 3 (2024)

In April 2017, the Event Horizon telescope received an image of a supermassive black hole in the Sagittarius A* source. This image consists of a ring-like structure that contains three areas with increased brightness (spots). If we assume that these spots are associated with flares near the event horizon of a black hole, then we can estimate its spin. Our estimate gives a value of the order of a ≈ 0.9.

The kinematics of the e Cha young stellar association close to the Sun has been studied based on a list of candidate stars from the Dickson-Vandervelde work. The working sample consists of 26 stars with parallaxes, proper motions from the Gaia DR3 catalog and radial velocities taken from literary sources. The orbits of the stars back to the past were constructed, and the moment when the association had a minimum spatial size was determined, as well as an analysis of the dependencies of the velocities U, V, W on the coordinates x, y, z was carried out. It is shown that the initial sample is divided into two parts with different kinematic properties. The first sample included 9 stars. Based on the construction of the orbits of these 9 stars, an age estimate of t = 4.9 ± 0.8 million years was obtained. An expansion coefficient in the xz plane with the value K_xz = 135±19 km/s/kpc was also found for them, on the basis of which another age estimate t = 7.2 ± 1.0 million years was obtained. The second sample included 17 stars. The construction of their orbits gave an estimate of age t = 0.2 ± 0.3 million years, and based on the gradient dW/dz = 707 ± 248 km/s/kpc, a second estimate of their age t = 1.4 ± 0.5 million years was obtained. This suggests that the e Cha association either consists of two groupings of different ages, or a younger one arose as a result of a recent outbreak of star formation within a common star system. The question of the gravitational connection of the groupings has not been considered in the framework of this work.

Depending on the distance of the exoplanet from the central star and on the properties of this star, different regimes of stellar wind flow around it arise. If the exoplanet is at a distance up to the Alfven radius at which the wind speed is equal to the Alfven speed, or the Alfven Mach number M_A = 1, then the exoplanet generates Alfven wings. If it is located beyond the Alfven radius, a comet-like magnetosphere appears, like that of the planets of the Solar System. The paper examines how the transition from one flow regime to another can be described on the base of a paraboloid model of the magnetospheric magnetic field using the example of exoplanet HD 209458b.

The restricted circular three-body problem is studied. All global families of periodic orbits adjacent to the libration points are found. A scenario for the evolution of orbits in the family is given. Chains of global families will be highlighted; the chain begins at the triangular libration point, contains global families for the triangular and all collinear libration points, and ends with a family whose orbits are pressed against the main bodies. The evolution of global families in the chain associated with changes in the energy of the system is described. Planar and spatial orbits are studied.

The problem of motion of a zero-mass point under the influence of attraction to the central body and a small perturbing acceleration P′ = P/r ² is considered, where r is the distance to the attracting center, components of the vector P are assumed to be constant in a reference system with axes directed along the radius vector, the transversal and the angular momentum vector. Previously, for this problem, we found equations of motion in the mean elements and formulas for the transition from the osculating elements to the mean elements in the first order of smallness; we neglected second-order quantities. In this work, the Euclidean (root–mean–square over the mean anomaly) displacement norm || dr ||² is obtained, where dr represents the difference between the position vectors on the osculating and mean orbit. It turned out that || dr ||² depends only on the components of the vector P (positive definite quadratic form), the semi–major axis (proportional to the second power) and the eccentricity of the osculating ellipse. The norm || dr ||² is obtained in the form of series in powers of the b = e/(1 + √—1 –— —e—²) and in powers of the eccentricity e. The results are applied to the problem of the motion of asteroids under the influence of a perturbing acceleration inversely proportional to the square of the heliocentric distance, in particular, under the influence of the Yarkovsky effect.