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This work considers the study of libration dynamics of the planets? moons. To analysis such processes, it is necessary to use methods for investigating complex systems, as an influence from neighboring celestial bodies on spin-orbital motion of a moon should be taken into account. This fully applies to the Moon?s rotation about its axis. The construction of modern theories of the physical libration of the Moon (PLM) is based on gravimetric, seismic, satellite observations, and lunar laser ranging, which in its tur...

The Auto-Regressive Integrated Moving Average (ARIMA) model is widely used to forecast non-stationary time series data. In a model of ARIMA (p, d, q), AR is autoregressive, p is the number of regression terms, MA is the moving average, q is the number of moving average terms, and d is the difference time to make the data a stationary series. It can be used to forecast the trend of geomagnetic disturbances. Firstly, the non-stationary historical data xt is processed by the d difference to develop the stable histori...

In this work, the physical parameters of near Earth objects (NEO) are studied. The search for parent bodies of low-activity small meteor showers ? k-Cygnids, ?-Cancrids, and Virginids are performed among asteroids that could be faded comets. For k-Cygnids by all the catalogues of meteor orbits 2 asteroids are selected ? 153311 2001MG1, 385343 2002LV, whose orbits provide from 90% to 100% compliance with meteoroids? orbits of a shower. The 2012LL9 is only selected by 3 catalogues of meteor orbits. By catalogue of A...

This work focuses on the creation of a selenocentric satellite simulation navigation system (SSSNS) using a set of reference objects on the lunar surface. The latter is based on the data from the modern space missions ?LRO?, ?Clementine?, ?GRAIL? (all ? NASA, USA), ?SELENE? (JAXA, Japan), and ?SMART-1? (European Space Agency). The SSSNS was created to transform measurements taken from in-orbit satellite into the selenocentric inertial reference system. The measurements should be taken by on-board altimeter and las...

This work focuses on the use of projective geometry methods to determine star positions produced on the basis of positional observations. As is known, projective geometry studies invariant projective transformations. The main feature of projective geometry is the principle of duality, which adds elegant symmetry to many designs. While the properties of the figures that Euclidean geometry deals with are metric, but there are figures that can be converted into one another by movement while maintaining the metric pro...