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This report continues the practice where the IAU Working Group on Cartographic Coordinates and Rotational Elements revises recommendations regarding those topics for the planets, satellites, minor planets, and comets approximately every 3 years. The Working Group has now become a “functional working group” of the IAU, and its membership is open to anyone interested in participating. We describe the procedure for submitting questions about the recommendations given here or the application of these recommendations for creating a new or updated coordinate system for a given body. Regarding body orientation, the following bodies have been updated: Mercury, based on MESSENGER results; Mars, along with a refined longitude definition; Phobos; Deimos; (1) Ceres; (52) Europa; (243) Ida; (2867) Šteins; Neptune; (134340) Pluto and its satellite Charon; comets 9P/Tempel 1, 19P/Borrelly, 67P/Churyumov–Gerasimenko, and 103P/Hartley 2, noting that such information is valid only between specific epochs. The special challenges related to mapping 67P/Churyumov–Gerasimenko are also discussed. Approximate expressions for the Earth have been removed in order to avoid confusion, and the low precision series expression for the Moon’s orientation has been removed. The previously online only recommended orientation model for (4) Vesta is repeated with an explanation of how it was updated. Regarding body shape, text has been included to explain the expected uses of such information, and the relevance of the cited uncertainty information. The size of the Sun has been updated, and notation added that the size and the ellipsoidal axes for the Earth and Jupiter have been recommended by an IAU Resolution. The distinction of a reference radius for a body (here, the Moon and Titan) is made between cartographic uses, and for orthoprojection and geophysical uses. The recommended radius for Mercury has been updated based on MESSENGER results. The recommended radius for Titan is returned to its previous value. Size information has been updated for 13 other Saturnian satellites and added for Aegaeon. The sizes of Pluto and Charon have been updated. Size information has been updated for (1) Ceres and given for (16) Psyche and (52) Europa. The size of (25143) Itokawa has been corrected. In addition, the discussion of terminology for the poles (hemispheres) of small bodies has been modified and a discussion on cardinal directions added. Although they continue to be used for planets and their satellites, it is assumed that the planetographic and planetocentric coordinate system definitions do not apply to small bodies. However, planetocentric and planetodetic latitudes and longitudes may be used on such bodies, following the right-hand rule. We repeat our previous recommendations that planning and efforts be made to make controlled cartographic products; newly recommend that common formulations should be used for orientation and size; continue to recommend that a community consensus be developed for the orientation models of Jupiter and Saturn; newly recommend that historical summaries of the coordinate systems for given bodies should be developed, and point out that for planets and satellites planetographic systems have generally been historically preferred over planetocentric systems, and that in cases when planetographic coordinates have been widely used in the past, there is no obvious advantage to switching to the use of planetocentric coordinates. The Working Group also requests community input on the question submitting process, posting of updates to the Working Group website, and on whether recommendations should be made regarding exoplanet coordinate systems.

The affine coherent state (ACS) quantisation method represents an effective approach to quantisation that can be adapted for the construction of a quantum spherical symmetric gravitational model. The ACS quantisation method is characterised by a relatively straightforward mathematical formalism. The method permits the quantisation of both the spatial and temporal coordinates, thereby enabling the reproduction of the classical quantity as an expectation value of an appropriate quantum observable. This paper presents the ACS quantisation of the Oppenheimer-Snyder (OS) model and discusses the general construction of the ACS quantum space. It also presents a quantum description of the OS model based on the analysis of characteristic quantum observables, with particular emphasis on the gravitational singularity area.

Izračunali smo povprečno odstopanje, postopek transformacije pa nadaljevali tako, da smo za vezne točke vzeli vse trigonometrične točke, ki smo jim odčitali grafično koordinato, za vse preostale trigonometrične točke, za katere smo imeli samo numerične koordinate, pa smo vzeli razliko numeričnih koordinat in povprečnega odstopanja. Na sliki 5 sta prikazana primerjava lokacij stare in transformirane mreže listov načrtov v sistemu Gellért ter primer karte razdelitve na liste, ki smo jih izdelali za vse katastrske občine. 3 UREDITEV OPISNE TABELE LISTOV V SISTEMU GELLÉRT K vsakemu listu mreže so atributno pripisani pripadajoči grafični načrti. 2021. https://www. primorsko-geodetsko-drustvo.si/wp-content/uploads/2021/09/03_ GD49_l_1-Kataster_v_PrekmurJu-Joc_TKglav_compressed.pdf, prídobljeno 31.5.

The discovery of governing equations from scientific data has the potential to transform data-rich fields that lack well-characterized quantitative descriptions. Advances in sparse regression are currently enabling the tractable identification of both the structure and parameters of a nonlinear dynamical system from data. The resulting models have the fewest terms necessary to describe the dynamics, balancing model complexity with descriptive ability, and thus promoting interpretability and generalizability. This provides an algorithmic approach to Occam’s razor for model discovery. However, this approach fundamentally relies on an effective coordinate system in which the dynamics have a simple representation. In this work, we design a custom deep autoencoder network to discover a coordinate transformation into a reduced space where the dynamics may be sparsely represented. Thus, we simultaneously learn the governing equations and the associated coordinate system.We demonstrate this approach on several example high-dimensional systems with low-dimensional behavior. The resulting modeling framework combines the strengths of deep neural networks for flexible representation and sparse identification of nonlinear dynamics (SINDy) for parsimonious models. This method places the discovery of coordinates and models on an equal footing.

Recently, Rozelot & Eren pointed out that the first solar gravitational moment (J 2) might exhibit a temporal variation. The suggested explanation is through the temporal variation of the solar rotation with latitude. This issue is deeper developed due to an accurate knowledge of the long-term variations in solar differential rotation regarding solar activity. Here we analyze solar cycles 12–24, investigating the long-term temporal variations in solar differential rotation. It is shown that J 2 exhibits a net modulation over the 13 studied cycles of ≈(89.6 ± 0.1) yr, with a peak-to-peak amplitude of ≈0.1 × 10−7 for a reference value of 2.07 × 10−7). Moreover, J 2 exhibits a positive linear trend in the period of minima solar activity (sunspot number up to around 40) and a marked declining trend in the period of maxima (sunspot number above 50). In absolute magnitude, the mean value of J 2 is more significant during periods of minimum than in periods of maximum. These findings are based on observational results that are not free of errors and can be refined further by considering torsional oscillations for example. They are comforted by identifying a periodic variation of the J 2 term evidenced through the analysis of the perihelion precession of planetary orbits either deduced from ephemerides or computed in the solar equatorial coordinate system instead of the ecliptic coordinate one usually used.