Article

Planetary theories in rectangular and spherical variables - VSOP 87 solutions

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Abstract

Up to this time, the VSOP (Variations Séculaires des Orbites Planètaires) analytical solutions of the motion of the planets were only represented in elliptic variables, but the cartesian or spherical variables are much more convenient in many problems: determination of the planetary perturbations of the Moon, analytical expressions for the computation of the apparent places, analytical expressions of nutation, of the difference TDB-TDT. From an analytical solution of the motion expressed with elliptic elements, the authors hence build different representations. The solutions are expressed with rectangular variables X, Y, Z or with spherical variables, longitude, latitude and radius vector. The different reference frames used are the dynamical ecliptic and equinox J2000.0, the ecliptic and equinox of date. The origin is the Sun or the barycenter of the solar system.

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... By default, Stellarium uses the VSOP87 planetary theory, an analytical solution which is able to deliver planetary positions for any input date (P. Bretagnon and Francou, 1988). However, its use is recommended only for the year range −4000 . . . ...
... Stellarium uses by default the widespread VSOP87 theory (P. Bretagnon and Francou, 1988) to calculate the positions of the planets over time. This is an analytical ephemeris modeled to match the numerical integration run DE200 from NASA JPL, which by itself gives positions for 1850. . . ...
... As far as Stellarium is concerned, the user should bear in mind the limits of the VSOP87 and other models (Table F. 1). Accuracy values for VSOP87 are heliocentric as given by P. Bretagnon and Francou (1988). ...
Book
Full-text available
... By default, Stellarium uses the VSOP87 planetary theory, an analytical solution which is able to deliver planetary positions for any input date (P. Bretagnon and Francou, 1988). However, its use is recommended only for the year range −4000 . . . ...
... Stellarium uses by default the widespread VSOP87 theory (P. Bretagnon and Francou, 1988) to calculate the positions of the planets over time. This is an analytical ephemeris modeled to match the numerical integration run DE200 from NASA JPL, which by itself gives positions for 1850. . . ...
... As far as Stellarium is concerned, the user should bear in mind the limits of the VSOP87 and other models (Table F. 1). Accuracy values for VSOP87 are heliocentric as given by P. Bretagnon and Francou (1988). ...
Book
Full-text available
... By default, Stellarium uses the VSOP87 planetary theory, an analytical solution which is able to deliver planetary positions for any input date (P. Bretagnon and Francou, 1988). However, its use is recommended only for the year range −4000 . . . ...
... Stellarium uses by default the widespread VSOP87 theory (P. Bretagnon and Francou, 1988) to calculate the positions of the planets over time. This is an analytical ephemeris modeled to match the numerical integration run DE200 from NASA JPL, which by itself gives positions for 1850. . . ...
... As far as Stellarium is concerned, the user should bear in mind the limits of the VSOP87 and other models (Table F. 1). Accuracy values for VSOP87 are heliocentric as given by P. Bretagnon and Francou (1988). ...
Book
Full-text available
... By default, Stellarium uses the VSOP87 planetary theory, an analytical solution which is able to deliver planetary positions for any input date (P. Bretagnon and Francou, 1988). However, its use is recommended only for the year range −4000 . . . ...
... Stellarium uses by default the widespread VSOP87 theory (P. Bretagnon and Francou, 1988) to calculate the positions of the planets over time. This is an analytical ephemeris modeled to match the numerical integration run DE200 from NASA JPL, which by itself gives positions for 1850. . . ...
... As far as Stellarium is concerned, the user should bear in mind the limits of the VSOP87 and other models (Table F. 1). Accuracy values for VSOP87 are heliocentric as given by P. Bretagnon and Francou (1988). ...
Book
Full-text available
... Regarding the annual periodicity, an obvious candidate for this quasi-period is the Earth orbital period. In fact, the Earth's orbital period is the most important component, at annual scale, in the analytical expansion of the Sun's position around the solar system barycenter (Bretagnon and Francou, 1988). This leads us to consider whether any of these identified periodicities could be associated with solar and planetary motions (Courtillot, Lopes, and Le Mouël, 2021). ...
... Several authors (e.g., Cionco, 2012;Scafetta, 2012;Cionco and Soon, 2015;Stefani, Giesecke, and Weier, 2019) have shown that -based on specific forcing functions (spin-orbit couplings, tidal etc.) -several quasi-periods can be obtained, which can be phenomenologically related to solar activity modulations. For example, many of our detected quasi-periods are intriguingly similar to known periodicities associated with solar barycentric dynamics The 3.5 year is present in the forcing terms on the solar barycentric position related to giant planets (Bretagnon and Francou, 1988;Kudryavtsev and Kudryavtseva, 2009); the 1.7-year periodicity is near the synodic period of Venus and the Earth, which is evident in the velocity and acceleration of the Sun's motion, but unimportant in the solar position (Cionco and Pavlov, 2018). Even the sub-annual quasi-periods detected can be related to planetary terms in the solar barycentric position with a rather small amplitude but persistent quasi-regular oscillation around 0.35 years (Bretagnon and Francou, 1988) and in the harmonic decomposition of the Earth's disturbing function, which is indirectly forced by the solar motion (Cionco, Kudryavtsev, and Soon, 2021). ...
... For example, many of our detected quasi-periods are intriguingly similar to known periodicities associated with solar barycentric dynamics The 3.5 year is present in the forcing terms on the solar barycentric position related to giant planets (Bretagnon and Francou, 1988;Kudryavtsev and Kudryavtseva, 2009); the 1.7-year periodicity is near the synodic period of Venus and the Earth, which is evident in the velocity and acceleration of the Sun's motion, but unimportant in the solar position (Cionco and Pavlov, 2018). Even the sub-annual quasi-periods detected can be related to planetary terms in the solar barycentric position with a rather small amplitude but persistent quasi-regular oscillation around 0.35 years (Bretagnon and Francou, 1988) and in the harmonic decomposition of the Earth's disturbing function, which is indirectly forced by the solar motion (Cionco, Kudryavtsev, and Soon, 2021). ...
Article
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The chromosphere is a highly dynamic outer plasma layer of the Sun. Its physical processes accounting for the variability are poorly understood. We reconstructed the solar chromospheric flare index (SFI) to study the solar chromospheric variability from 1937 to 2020. The new SFI database is a composite record of the Astronomical Institute Ondřejov Observatory of the Czech Academy of Sciences from 1937 – 1976 and the records of the Kandilli Observatory of Istanbul, Turkey from 1977 – 2020. The SFI records are available in daily, monthly, and yearly resolutions. We carried out the time-frequency analyses of the new 84-year long SFI records using the wavelet transform. We report the periodicities of 21.88 (Hale cycle), 10.94 (Schwabe cycle), 5.2 (quasi-quinquennial cycle), 3.5, 1.7, 1, 0.41 (or 149.7 days, Rieger cycle), 0.17 (62.1 days), 0.07 (25.9 days, solar rotational modulation) years. All these periodicities seem always present and persistent throughout the observational interval. Thus, we suggest that there is no reason to assume these solar periodicities are absent from other solar cycles. Time variations of the amplitude of each oscillation or periodicity were also studied using the inverse wavelet transform. We found that for the SFI the most active flare cycles over the record were Cycles 17, 19, and 21, while Cycles 20, 22, 23, and 24 were the weakest ones with Cycle 18 was intermediate in flare activity. This shows several differences to the equivalent relationships for solar activity implied by sunspot number records. Furthermore, this confirms that solar activity trends and variability in the chromosphere as captured by SFI are not necessarily the same as those of the Sun’s photosphere, as implied by the sunspot number activity records, for instance. We have also introduced a new signal/noise wavelet coherence metric to analyze two different chromospheric indices available (i.e. the SFI and the disk-integrated chromospheric Ca ii K activity indices) and to quantify the differences and similarities of the oscillations within the solar chromosphere. Our findings suggest the importance of carrying out additional co-analyses with other solar activity records to find physical inter-relations and connections between the different solar layers from the photosphere, the chromosphere to the corona.
... By default, Stellarium uses the VSOP87 planetary theory, an analytical solution which is able to v0. 15.0 deliver planetary positions for any input date (P. Bretagnon and Francou, 1988). However, its use is recommended only for the year range −4000 . . . ...
... Stellarium uses by default the widespread VSOP87 theory (P. Bretagnon and Francou, 1988) to calculate the positions of the planets over time. This is an analytical ephemeris modeled to match the numerical integration run DE200 from NASA JPL, which by itself gives positions for 1850. . . ...
... As far as Stellarium is concerned, the user should bear in mind the limits of the VSOP87 and other models (Table F.1). Accuracy values for VSOP87 are heliocentric as given by P. Bretagnon and Francou (1988). ...
Book
Full-text available
... By default, Stellarium uses the VSOP87 planetary theory, an analytical solution which is able to v0. 15.0 deliver planetary positions for any input date (P. Bretagnon and Francou, 1988). However, its use is recommended only for the year range −4000 . . . ...
... Stellarium uses by default the widespread VSOP87 theory (P. Bretagnon and Francou, 1988) to calculate the positions of the planets over time. This is an analytical ephemeris modeled to match the numerical integration run DE200 from NASA JPL, which by itself gives positions for 1850. . . ...
... As far as Stellarium is concerned, the user should bear in mind the limits of the VSOP87 and other models (Table F.1). Accuracy values for VSOP87 are heliocentric as given by P. Bretagnon and Francou (1988). ...
Book
Full-text available
... By default, Stellarium uses the VSOP87 planetary theory, an analytical solution which is able to v0. 15.0 deliver planetary positions for any input date (P. Bretagnon and Francou, 1988). However, its use is recommended only for the year range −4000 . . . ...
... Stellarium uses by default the widespread VSOP87 theory (P. Bretagnon and Francou, 1988) to calculate the positions of the planets over time. This is an analytical ephemeris modeled to match the numerical integration run DE200 from NASA JPL, which by itself gives positions for 1850. . . ...
... As far as Stellarium is concerned, the user should bear in mind the limits of the VSOP87 and other models (Table F.1). Accuracy values for VSOP87 are heliocentric as given by P. Bretagnon and Francou (1988). ...
Book
Full-text available
... This is described mainly in chapter 5. The P5 program is based on the French planetary theory VSOP87 [1,2] (see more below). The fundamental idea is that a correlation exists between the three inner planets and the three pyramids of Giza. ...
... For Teotihuacán, the necessary geographical data are provided in inteoti.t. All remaining files from VSOP87A.mer to VSOP87C.nep represent full versions of the planetary theory [1,2] with a very high accuracy. They are also available from the FTP server of the IMCCE website. ...
... After typing the start command, the main menu appears on the monitor: (1) 3D Mer at per (6) Mercury tr (11) GPS m km (16) 2D Mer at aph (2) Keplers equ (7) Venus tr (12) Map mm km (17) constell 3088 (3) constell 3088 (8) syzygy 3 pl (13) GPS log3 (18) 1.5 days 3088 (4) 1.5 days 3088 (9) syzygy 4 pl (14) Map log3 (19) near aphelion (5) F minimized (10) TYMT test (15) The date in the title indicates the most recent update of the program. In the main table there are four different categories. ...
Technical Report
Full-text available
A planetary correlation with the planets of our solar system has been found for the pyramids of Giza and now also for the pyramids at Teotihuacán in Mexico. This is a revised and extended version of the P4 Program Description from June, 2015. Concerning Giza, the extension relates mainly to the comparison between the planetary constellations and the chamber positions in the Great Pyramid. This implies an alternative “Sun position” and a second “Mars position” within the pyramid. The quick start options have been accordingly adapted and the results and text have been changed where necessary. Nevertheless, the astronomical basis of the calculations remains unchanged. As stated above, another planetary correlation has been found with respect to the pyramid area at Teotihuacán. This correlation is of a different kind compared to the situation at Giza, but could be easily included in the program because the astronomical calculations can be performed on the basis of the VSOP87 theory. This description provides the full P5 source code.
... By default, Stellarium uses the VSOP87 planetary theory, an analytical solution which is able to v0. 15.0 deliver planetary positions for any input date (P. Bretagnon and Francou, 1988). However, its use is recommended only for the year range −4000 . . . ...
... Stellarium uses by default the widespread VSOP87 theory (P. Bretagnon and Francou, 1988) to calculate the positions of the planets over time. This is an analytical ephemeris modeled to match the numerical integration run DE200 from NASA JPL, which by itself gives positions for 1850. . . ...
... As far as Stellarium is concerned, the user should bear in mind the limits of the VSOP87 and other models (Table F.1). Accuracy values for VSOP87 are heliocentric as given by P. Bretagnon and Francou (1988). ...
Book
Full-text available
... By default, Stellarium uses the VSOP87 planetary theory, an analytical solution which is able to v0. 15.0 deliver planetary positions for any input date (P. Bretagnon and Francou, 1988). However, its use is recommended only for the year range −4000 . . . ...
... Stellarium uses by default the widespread VSOP87 theory (P. Bretagnon and Francou, 1988) to calculate the positions of the planets over time. This is an analytical ephemeris modeled to match the numerical integration run DE200 from NASA JPL, which by itself gives positions for 1850. . . ...
... As far as Stellarium is concerned, the user should bear in mind the limits of the VSOP87 and other models (Table F.1). Accuracy values for VSOP87 are heliocentric as given by P. Bretagnon and Francou (1988). ...
Book
Full-text available
... E being the solar constant [7] corrected for the Sun-Earth distance [8]. ...
... Due to the lack of dedicated ADMs for that case 7 , we are going to mask these aerosol-loaded regions over ocean pixels. 8 There is an 5 For consistency with an aerosol-optical-depth mask applied in the following, as there is no retrieval at larger zenith angles. 6 The sunglint angle is defined via: cos(sunglint angle) = sin(θ ) sin(θ vz ) cos(φ rel ) + cos(θ ) cos(θ vz ). ...
... However, this correction is not actually applied in the GL-SEV processing. 8 The presence of aerosols results in a quite diffuse reflection; very different from the strong specular reflection in the clear-sky ocean case. The use of clear-sky ocean ADMs that do not take aerosols into account is therefore particularly problematic. ...
Article
Full-text available
Geostationary observations offer the unique opportunity to resolve the diurnal cycle of the Earth's Radiation Budget at the top of the atmosphere (TOA), crucial for climate-change studies. However, a drawback of the continuous temporal coverage of the geostationary orbit is the fixed viewing geometry. As a consequence, imperfections in the angular distribution models (ADMs) used in the radiance-to-flux conversion process or residual angular-dependent narrowband-to-broadband conversion errors can result in systematic errors of the estimated radiative fluxes. In this work, focusing on clear-sky reflected TOA observations, we compare the overlapping views from Meteosat Second Generation satellites at 0° and 41.5°E longitude which enable a quantification of viewing-angle-dependent differences. Using data derived from the Spinning Enhanced Visible and InfraRed Imager (SEVIRI), we identify some of the main sources of discrepancies, and show that they can be significantly reduced at the level of one month. This is achieved, separately for each satellite, via a masking procedure followed by an empirical fit at the pixel-level that takes into account all the clear-sky data from that satellite, calculated separately per timeslot of the day, over the month of November 2016. The method is then applied to each month of 2017, and gives a quadratic mean of the albedo root-mean squared difference over the dual-view region which is comparable from month to month, with a 2017 average value of 0.01. Sources of discrepancies include the difficulty to estimate the flux over the sunglint ocean region close to the limbs, the fact that the data processing does not include dedicated angular distribution models for the aerosol-over-ocean case, and the existence of an observer-dependent diurnal-asymmetry artefact affecting the clear-sky-albedo dependence on the solar zenith angle particularly over land areas.
... E being the solar constant [7] corrected for the Sun-Earth distance [8]. ...
... Due to the lack of dedicated ADMs for that case 7 , we are going to mask these aerosol-loaded regions over ocean pixels. 8 There is an 5 For consistency with an aerosol-optical-depth mask applied in the following, as there is no retrieval at larger zenith angles. 6 The sunglint angle is defined via: cos(sunglint angle) = sin(θ ) sin(θ vz ) cos(φ rel ) + cos(θ ) cos(θ vz ). ...
... However, this correction is not actually applied in the GL-SEV processing. 8 The presence of aerosols results in a quite diffuse reflection; very different from the strong specular reflection in the clear-sky ocean case. The use of clear-sky ocean ADMs that do not take aerosols into account is therefore particularly problematic. ...
Preprint
Full-text available
Geostationary observations offer the unique opportunity to resolve the diurnal cycle of the Earth's Radiation Budget at the top of the atmosphere (TOA), crucial for climate-change studies. However, a drawback of the continuous temporal coverage of the geostationary orbit is the fixed viewing geometry. As a consequence, imperfections in the angular distribution models (ADMs) used in the radiance-to-flux conversion process or residual angular-dependent narrowband-to-broadband conversion errors can result in systematic errors of the estimated radiative fluxes. In this work, focusing on clear-sky reflected TOA observations, we compare the overlapping views from Meteosat Second Generation satellites at 0° and 41.5°E longitude which enable a quantification of viewing-angle-dependent differences. Using data derived from the Spinning Enhanced Visible and InfraRed Imager (SEVIRI), we identify some of the main sources of discrepancies, and show that they can be significantly reduced at the level of one month. This is achieved, separately for each satellite, via a masking procedure followed by an empirical fit at the pixel-level that takes into account all the clear-sky data from that satellite, calculated separately per timeslot of the day, over the month of November 2016. The method is then applied to each month of 2017, and gives a quadratic mean of the albedo root-mean squared difference over the dual-view region which is comparable from month to month, with a 2017 average value of 0.01. Sources of discrepancies include the difficulty to estimate the flux over the sunglint ocean region close to the limbs, the fact that the data processing does not include dedicated angular distribution models for the aerosol-over-ocean case, and the existence of an observer-dependent diurnal-asymmetry artefact affecting the clear-sky-albedo dependence on the solar zenith angle particularly over land areas.
... Their main improvement compared to previous studies lies in the modeling of the planets' motion. RMAN99 abandoned the Keplerian representation of the orbit of Mars and the use of mean orbital elements, and considered instead the rectangular coordinates and distance to the Sun as given by a semi-analytical theory for planetary ephemerides called VSOP87 (Bretagnon and Francou 1988). The acronym VSOP stands for Variations Séculaires des Orbites planétaires (Secular Variations of Planetary Orbits). ...
... with (x M , y M , z M ) as given in VSOP87 (Bretagnon and Francou 1988) for the position of Mars in a reference frame attached to the ecliptic (Earth orbit) and equinox (ascending node of the Earth orbit on the Earth equator) at the J2000 epoch. ...
... 4.1.1). The arguments needed to express the truncated solution will be the mean longitudes of Saturn (Sa), Jupiter (Ju), Mars (Ma), the Earth (Te), and Venus (Ve), see Table 2 of Bretagnon and Francou (1988): ...
Article
Full-text available
The nutations of Mars are about to be estimated to a few milliarcseconds accuracy with the radioscience experiments onboard InSight and ExoMars 2022. The contribution to the nutations due to the liquid core and tidal deformations will be detected, allowing to constrain the interior of Mars. To avoid introducing systematic errors in the determination of the core properties, an accurate precession and nutation model for a rigidly behaving Mars is needed. Here, we develop such a model with adequate accuracy based on the Torque approach and compare it to previous models. We include in the model the forcings by the Sun, Phobos, Deimos, and the other planets of the solar system. We also include the geodetic precession and nutations. We use semi-analytical developments for the solar and planetary torques, and analytical solutions for the effect of Phobos and Deimos and for the geodetic precession and nutations. With a truncation criterion of 0.025 milliarcseconds in prograde and/or retrograde amplitude, we identify 43 nutation terms. The uncertainty on our solution mainly derives from the observational uncertainty on the current determination of the precession rate of Mars. Uncertainties related to our modeling choices are negligible in comparison. Given the current determination of the precession rate (7608.3±2.1 mas/yr, Konopliv et al. in Icarus 274:253–260, 2016. 10.1016/j.icarus.2016.02.052), our model predicts a dynamical flattening HD=0.00538017±0.00000148 and a normalized polar moment of inertia C/MR2=0.36367±0.00010 for Mars.
... Our goal is to find all the candidates with a specific lighting situation. Therefore in the first step the sun position in the sky (Θ i , φ i ) must be calculated given the geographic position p i and the time t i for every data point in the data set [20]. Θ i is the altitude and φ i is the azimuth of the sun for the i-th data point. ...
... The sun position is calculated based on the time and the geographic position [20]. The calculated sun positions are transferred into the coordinate system of the vehicle. ...
... Magnetic dipole model is selected for magnetic field model. VSOP87 theory is used for sun direction vector [14]. Using these two models, sensor measurement models have been established. ...
... In order to construct a sun sensor model, sun direction vector is used. Using VSOP87 theory, a direction cosine matrix is calculated which shows the sun's position relative to Earth in ECI frame [14]. ...
Article
Full-text available
Two most commonly used sensors on nanosatellites are magnetometer and sun sensor. In this paper, magnetometer and sun sensor measurements are combined gyro measurements to produce enhanced attitude estimation. Tri-Axial Attitude Determination (TRIAD) algorithm is used with Kalman filter to form a complete attitude filter. Sun sensor and magnetometer measurements are selected as inputs to TRIAD algorithm and output is fed to Kalman filter as a measurement. Two different Kalman filters, extended and unscented, are used with TRIAD algorithm. A comparison is given between performances of both Kalman filter.
... It may be surprising but important to stress that a general description of these periodic perturbations to the Earth orbital movement (especially of those with shorter time scales) is not widely available, even in astronomy textbooks. Nevertheless, semi-analytic planetary theories such as the VSOP87 (Variations Séculaires des Orbites Planétaires) series (Bretagnon & Francou, 1988) do account for these perturbations in their final products. It is worth noting that in VSOP87 series, the orbital elements of the Earth-Moon barycentre are analyzed rather than the single Earth in its orbit. ...
... where i n is a frequency named the orbital mean motion in the case of the planetary bodies, and in the case of the Moon they correspond to the first-order frequencies associated with the Delaunay arguments of the Moon, , , D F l, and the mean longitude of the Moon in its orbit, L, given with respect to the equinox of date (see e.g., Bretagnon & Francou, 1988). The  0i angle is an initial phase related to the reference time 0 t , the so-called epoch, which in our case was J2000.0, that is, 01/1/2000 about 12 h UTC. ...
Article
Full-text available
Periodicities matching planetary cycles have been argued to be detected in key geophysical time series. In general, these periodicities were indirectly attributed to a planetary influence on solar activity. This supposes that planetary gravity affects the internal functioning of the Sun's dynamo, i.e., the {\it planetary hypothesis} (PH) of the solar cycles. The Earth's heliocentric dynamics already includes the planetary gravitational effects on the Sun. Taking into account this fact, these periodicities, ultimately attributed to possible planetary modulations of the solar activity, could have a more direct origin in cyclical changes in the relative Sun-Earth geometry, but then, wrongly or partially explained invoking internal solar changes. We present an original decomposition analysis of the high-precision ephemeris DE431 from NASA/JPL in order to obtain and classify the most important planetary/lunar purely periodic changes of the Earth's orbital movement at sub-Milanković scales. A comprehensive list of cyclic changes of the Earth's orbital parameters involved in the relative Sun-Earth position and the Earth's speed around the Sun is given. We show that these particular geophysical quasi-periods are identifiable in the cyclic oscillations of these orbital parameters. Since the Earth's movement in space physically affects the manner in which the solar radiant flux reaches the planet, these oscillations provide, unlike the PH, a clear, causal and testable link for their possible attribution.
... Let us now explore the daily Sun-Earth (S-E) distances over the two millennia (600-2600) derived from the ephemeris of VASOP87 -Variations Seculaires des Orbites Planetaires [47] http : ==neoprogrammics:com=vsop87=planetary d istance t ables=: Note that the VSOP87 data up to 6 digits after the decimal coma coincide with the widely used JPL ephemeris [48]. ...
... In this chapter the investigation of Sun-Earth distances from the ephemeris by VSOP87 [47] and JPL ephemeris [48] is presented. The Sun is found shifting in millennia M1 and M2 along the direction of the minor axis towards the spring equinox that leads to a significant reduction of S-E distances in January-June by about 0.005 au in M1 and up to 0.011 au in M2, which are followed by the asymmetric increases in the second half of the year (July-December). ...
Chapter
Full-text available
Daily ephemeris of Sun-Earth distances in two millennia (600–2600) showed significant decreases in February–June by up to 0.005 au in millennium M1 (600–1600) and 0.011au in millennium M2 (1600–2600). The Earth’s aphelion in M2 is shorter because shifted towards mid-July and longer because shifted to mid January naturally explaining two-millennial variations (Hallstatt’s cycle) of the baseline solar magnetic field measured from Earth. The S-E distance variations are shown imposed by shifts of Sun’s position towards the spring equinox imposed by the gravitation of large planets, or solar inertial motion (SIM). Daily variations of total solar irradiance (TSI) calculated with these S-E distances revealed TSI increases in February–June by up to 10–12 W / m 2 in M1 and 14–18 W / m 2 in M2. There is also positive imbalance detected in the annual TSI magnitudes deposited to Earth in millennium M2 compared to millennium M1: up to 1.3 W / m 2 , for monthly, and up to 20–25 W / m 2 for daily TSI magnitudes. This imbalance confirms an ascending phase of the current TSI (Hallstatt’s) cycle in M2. The consequences for terrestrial atmosphere of this additional solar forcing induced by the annual TSI imbalances are evaluated. The implications of extra solar forcing for two modern grand solar minima in M2 are also discussed.
... Il existe en effet de nombreuses références dans la littérature détaillant avec précision le calcul de la position du soleil et les algorithmes utilisés couramment pour réaliser ce calcul (e.g. BLANC & WALD, 2012;BLANCO-MURIEL et al., 2001;BRETAGNON & FRANCOU, 1988;GRENA, 2012;MICHALSKY, 1988;REDA & ANDREAS, 2004;RIGOLLIER et al., 2000). À e à la surface de la Terre à partir de . ...
... cision le calcul de la position du soleil (BRETAGNON & FRANCOU, 1988), ainsi que les algorithmes utilisés couramment pour réaliser ce calcul (BLANC & WALD, 2012;BLANCO-MURIEL et al., 2001;GRENA, 2008GRENA, , 2012MICHALSKY, 1988;REDA & ANDREAS, 2004;RIGOLLIER et al., 2000). Nous ne détaillerons ni ces calculs, ni ces algorithmes ayant chacun un temps de calcul, une précision et une période de validité répondant à un besoin spécifique. ...
Thesis
Cette thèse se propose de contribuer à la caractérisation des variations de long terme de l’éclairement, dans un contexte d’analyse de risque financier de grandes centrales solaires photovoltaïques. L’utilisation d’indicateurs statistiques (e.g. P90) et de l’hypothèse de stationnarité temporelle de l’éclairement a été questionnée. Cela a mené à une caractérisation fine des variations de long terme de l’éclairement grâce à un outil de décomposition temps-fréquence développé au cours de cette thèse. Nous avons distingué trois classes de variabilité : la variabilité intra-annuelle, la variabilité annuelle à décennale, et la variabilité multi-décennale. Pour la première classe, l’utilisation de quatre ans de données historiques est suffisante pour prendre en compte de manière correcte l’ensemble des variations de l’éclairement. Pour la seconde classe, l’utilisation de 30 années de données historiques est recommandée. Pour la variabilité multi-décennale, l’utilisation de plus de 30 années de données est préconisée. Les trois classes de variabilité ont été analysées pour des bases de données de natures diverses : mesures de long terme du réseau GEBA, données satellitales CLARA-A2, données de ré-analyse MERRA-2, et données issues du modèle climatique IPSL-CM6A-LR. Une grande diversité des structures de variabilité en fonction de la base de données considérée a été observée.
... In order to construct a sun sensor model, a sun direction vector is used. Using VSOP87 theory, a direction cosine matrix is calculated which shows the sun's position relative to Earth in ECI frame [6] x 1 y 2 ...
Article
Full-text available
Increasing demand for the space operations, space industry turns its face to cost effective solutions. Small satellites, due to their size and cost, are receiving interest from many organizations. Two of most common sensors that are being used in nanosatellites are magnetometers and sun sensors. In this work, magnetometer and sun sensor measurements are fused together with the TRIAD algorithm to produce body angle estimation. Combining with gyroscopes measurements, an Extended Kalman Filter is used to estimate body angles, angular velocities, gyroscope and magnetometer biases.
... The meteoroid's orbit is constrained by its trajectory and velocity. First, we calculated the absolute heliocentric and rotational position of the Earth at the time when the meteoroid was located at one given point along its trajectory following Urban and Seidelmann (2012) and Bretagnon and Francou (1988). Then, to obtain the meteoroid's true heliocentric velocity vector, we applied corrections for (1) Earth's rotation; (2) zenith attraction (i.e., the gravitational influence of the Earth, which causes a deflection of the original orbit of the meteoroid; Bauschinger, 1928), and (3) Earth's orbital velocity. ...
Article
A common challenge in acoustic meteoroid signal analyses is to discriminate whether the observed wavefield can be better described by line-source or point-source models. This challenge typically arises from a sparse availability of observations. In this work, we present an outstanding record of ground-coupled waves from local large-N seismic and distributed acoustic sensing (DAS) observations of a meteoroid in Iceland. Our complete data set includes additional regional stations located within 300 km of the meteoroid’s trajectory. The dense large-N and DAS data allow identification of acoustic phases that are almost impossible to discriminate on sparser networks, including a weak late arrival resolved mostly only by DAS. Using this data set with a new Bayesian inversion model, we estimate the trajectory parameters of one fragment from the meteoroid. With these results we investigate its orbit in the solar system and propose a classification of the Icelandic event as a slow meteoroid of asteroidal origin with an energy on the order of 4–40 GJ, a probable size on the order of centimeters, and an orbit range consistent with the main asteroid belt.
... It is measured from 0 to 180deg during day time, being 90deg the point where the Sun is at its highest. Both of them can be computed with an overall 99.98% of accuracy based on date, time, latitude, and longitude as described by Bretagnon and Francou [51]. Given their obvious relationship with the available solar resource, these 5 metrics were added to the basic dataset in order to investigate whether they could contribute to accurate forecasts. ...
Article
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Increasingly advanced stochastic energy management systems are employed to facilitate the integration of wind and solar PV in worldwide power grids. In this context, forecasting is a key tool limiting the success of said control actions. This paper explores the suitability of stacked machine learning based models to predict wind and solar power available in the same site using a physics informed approach. The method recombines basic meteorological metrics widely available to compute new physics informed ones facilitating the learning procedure, while other are weak ML-models themselves. Further, to facilitate the integration of the point forecasters in the stochastic optimization field, we propose a simple unsupervised estimation of the error distribution. In this way, scenarios can be easily and homogeneously characterised for different resolutions and horizons. A study case is presented employing the Open Access dataset SOLETE, to facilitate benchmarking and replication of results. The results show accuracy improvements over the previously reported work over the same dataset.
... Accuracy of SolTrack In order to assess the accuracy of our code, we need a comparison. We used the VSOP 87 code to compute very precise positions of the Sun, with an accuracy of 1.4 × 10 −6 between the years 1900 and 2100 (Bretagnon and Francou, 1988). In order to correct for atmospheric refraction, we used an accurate model (Hohenkerk and Sinclair, 1985) that integrates the path of a light beam as it travels through the atmosphere for a given apparent sky position. ...
Preprint
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We present a simple, free, fast and accurate C/C++ and Python routine called SolTrack, which can compute the position of the Sun at any instant and any location on Earth. The code allows tracking of the Sun using a low-specs embedded processor, such as a PLC or a microcontroller, and can be used for applications in the field of (highly) concentrated (photovoltaic) solar power ((H)CPV and CSP), such as tracking control and yield modelling. SolTrack is accurate, fast and open in its use, and compares favourably with similar algorithms that are currently available for solar tracking and modelling. SolTrack computes $1.5 \times 10^6$ positions per second on a single 2.67GHz CPU core. For the period between the years 2017 and 2116 the uncertainty in position is $0.0036 \pm 0.0042^\circ$, that in solar distance 0.0017 $\pm$ 0.0029%. In addition, SolTrack computes rise, transit and set times to an accuracy better than 1 second. The code is freely available online (http://soltrack.sf.net, https://pypi.org/project/soltrack/).
... Algoritma paling akurat untuk menentukan posisi matahari adalah algoritma VSOP87 (Perancis: Variations Séculaires des Orbites Planétaires) (Bretagnon & Francou, 1988). Tingkat akurasinya sangat tinggi, mencapai 0.01 derajat atau lebih kecil dari 1 menit busur (Michalsky, 1988). ...
Article
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The inclusion of prayer time is one of the valid requirements of prayer as explained in the Qur’an and hadiths of the Prophet (s). The Fajr prayer schedule issued by Wahdah Islamiyah is interesting to review because it is different from the official prayer schedule issued by the Ministry of Religious Affairs, Republic of Indonesia. This difference can have implications for the validity or absence of Fajr prayers and fasting performed by Muslims based on the schedule. This study aimed to analyze the method of determining the Fajr prayer schedule issued by Wahdah Islamiyah. This research is qualitative descriptive research through library study methods and content analysis. The results showed that Wahdah Islamiyah compiled its Fajr prayer schedule with a highaccuracy contemporary accounting method using VSOP87 algorithm. The location of markaz da’wah in Makassar City was chosen as the coordinate point of the calculation of the position of the sun. Wahdah Islamiyah’s Fajr prayer schedule uses a sun altitude of 18 degrees below the horizon by adding a two-minute of iḥtiyāṭ. Based on the calculation, the Fajr prayer schedule of Wahdah Islamiyah has been accurately used in the Makassar City area.
... In the process of constructing a planetary theory, two major approaches can be considered: the use of numerical integrators 1,2 or the use of analytical methods to integrate the problem. [3][4][5][6] Analytical methods are based on the solution of the two-body problem (Sun-planet). This solution is given through a set of six orbital elements. ...
Article
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In the present work, we define a new anomaly, Ψ$$\Psi$$, termed semifocal anomaly. It is determined by the mean between the true anomaly, f$$f$$, and the antifocal anomaly, f′$${f}^{\prime }$$; Fukushima defined f′$${f}^{\prime }$$ as the angle between the periapsis and the secondary around the empty focus. In this first part of the paper, we take an approach to the study of the semifocal anomaly in the hyperbolic motion and in the limit case corresponding to the parabolic movement. From here, we find a relation between the semifocal anomaly and the true anomaly that holds independently of the movement type. We focus on the study of the two‐body problem when this new anomaly is used as the temporal variable. In the second part, we show the use of this anomaly—combined with numerical integration methods—to improve integration errors in one revolution. Finally, we analyze the errors committed in the integration process—depending on several values of the eccentricity—for the elliptic, parabolic, and hyperbolic cases in the apsidal region.
... Using the method of Bretagnon and Francou [11], the time-dependent elevation angle θ s (t) and azimuth angle α s (t) of the Sun on the celestial hemisphere were calculated as described by Horváth et al. [12]. ...
Article
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In the Northern Hemisphere, south is the conventional azimuth direction of fixed-tilt monofacial solar panels, because this orientation may maximize the received light energy. How does the morning-afternoon cloudiness asymmetry affect the energy-maximizing azimuth direction of such solar panels? Prompted by this question, we calculated the total light energy received by a fixed-tilt monofacial solar panel in a whole year, using the celestial motion of the Sun and the direct and diffuse radiation measured hourly throughout the year in three North American (Boone County, Tennessee, Georgia) and European (Italy, Hungary, Sweden) regions. Here we show that, depending on the tilt angle and the local cloudiness conditions, the energy-maximizing ideal azimuth of a solar panel more or less turns eastward from south, if afternoons are cloudier than mornings in a yearly average. In certain cases, the turn of the ideal azimuth of such solar panels may be worth taking into consideration, even though the maximum energy gain is not larger than 5% for nearly vertical panels. Specifically, when solar panels are fixed on vertical walls or oblique roofs with non-ideal tilt, the deviation of the energy-maximizing azimuth from the south can be incorporated in the design of buildings.
... This software performs graphical representations implementing the VSOP87 method for the calculation of planetary ephemerides. This mathematical model was developed by P. Bretagnon and G. Francou[1] at the Bureau des Longitudes in Paris in order to describe the long-term variations of planetary orbits. It guarantees for Mercury, Venus, the Earth-Moon barycentre and Mars an accuracy of 1" for 4000 years before and after the J2000 epoch. ...
Preprint
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"El Cielo de Salamanca" ("The Sky of Salamanca") is a quarter-sphere-shaped vault 8.70 metres in diameter. It was painted sometime between 1480 and 1493 and shows five zodiacal constellations, three boreal and six austral. The Sun and Mercury are also represented. It formed part of a three times larger vault depicting the 48 Ptolemaic constellations and the rest of the planets known at the time. This was a splendid work of art that covered the ceiling of the first library of the University of Salamanca, one of the oldest in Europe having obtained its royal charter in 1218. But it was also a pioneering scientific work: a planetarium used to teach astronomy, the first of its kind in the history of Astronomy that has come down to us in the preserved part that we now call "The Sky of Salamanca". We describe the scientific context surrounding the chair of Astrology founded around 1460 at the University of Salamanca, which led to the production of this unique scientific work of art and to the flourishing of Astronomy in Salamanca. We analyse the possible dates compatible with it, showing that they are extremely infrequent. In the period of 1100 years from 1200 to 2300 that we studied there are only 23 years that have feasible days. We conclude that the information contained in "El Cielo de Salamanca" is not sufficient to assign it to a specific date but rather to an interval of several days that circumstantial evidence seems to place in August 1475. The same configuration of the sky will be observable, for the first time in 141 years, from the 22nd to the 25th of August 2022. The next occasion to observe it live will be in 2060.
... Bessel dapat dilihat pada gambar 1.8.Meeus, J., 1998, Astronomical Algorithms Second Edition, Willmann-Bell, Virginia, USA. 9.Bretagnon, P., dan Francou, G., 1988, Planetary Theories in Rectangular Meeus, J., 1989, Elements of Solar Eclipses 1951-2200, Willmann-Bell, Virginia, USA. 11. ...
Article
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The solar eclipse will take place if the moon is between the Earth and sun as well as its shadow touches the Earth. Some hadiths narrated that the phenomena had occurred in the era of Prophet saw. then He commanded Muslims to perform prayer, remembrance, and donation. Hence, the solar eclipse in Islam is crucial as it is respected to worship to God. The objective of this paper is to calculate the solar eclipse using Meeus Algorithm. After preparing the Bessel elements and arranging the Meeus Algorithm, it can be determined accurately both the eclipse type, time, place, path width of the eclipse and the sun position as it lasts. Sun eclipse calculation using Meeus algorithm on June, 21th 2020 results 1.380 N and 18.060 E for the coordinate, 0.28 for altitude, azimuth of 66.56, 84.9 km width, as well as total duration of 1 minutes 22.3 and seconds. Those all are accurate due to the similarity with NASA calculation using ELP and VSOP87 algorithm.
... Posisi matahari dapat ditentukan dengan akurat melalui algoritma VSOP87 (Perancis: Variations Séculaires des Orbites Planétaires) [7]. Dari ribuan suku koreksi dalam algoritma VSOP87 maka yang diperhitungkan dalam algoritma Meeus hanya sekitar ratusan suku-suku yang besar saja [5]. ...
Conference Paper
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Abstrak-Hampir setiap tahun, perbedaan penentuan bulan Islam terjadi di Indonesia, khususnya yang berhubungan dengan puasa, Iedul Fitri dan haji. Salah satu penyebab utama perbedaan tersebut karena belum ada kesepakatan mengenai kriteria hisab yang digunakan dalam menentukan awal bulan Islam di Indonesia. Makalah ini bertujuan untuk mengoptimsi kriteria hisab di Indonesia berdasarkan posisi matahari dan bulan menggunakan Algoritma Meeus. Kriteria hisab berkaitan erat dengan perhitungan astronomis seperti: konjungsi, waktu terbenam matahari dan bulan, maupun posisi matahari dan bulan saat terbenam. Optimasi kriteria hisab di Indonesia dilakukan dengan menggunakan parameter durasi umur bulan Hijriyah, parameter selang-seling, dan sedikitnya jumlah bulan yang mengalami tiga dan empat bulan berturut-turut dengan durasi umur bulan yang sama. Kata kunci: kriteria hisab, posisi matahari dan bulan, algoritma Meeus Abstract-Almost every year, a difference in the determination of Islamic month occurs in Indonesia, especially in the relation with fasting, Iedul Fitri and pilgrimage. One of the main source of the difference is there is no agreement of criterion of Islamic month in Indonesia. The aim of this paper is to optimize the hisab criterion based on sun and moon positions using Meeus's algorithm. The criterion have a relation with astronomical events such as conjuntion, sunset, moonset, and their positions at set. Optimation of hisab criterions in Indonesia is done using the parameter of month age duration, parameter of interval, and the minimum numbers of three and four consecutive month with the same duration.
... Apparent Declination. At present, the calculation methods of the sun's right ascension and declination mainly include the vsop87 theory of France, Michalsky's theory expansion method recommended by WMO, and the precise planetary ephemeris method of NASA [12,13]. On the premise of consideration on both accuracy and onboard computing resources, this paper uses the simplified vsop87 theory proposed by Meeus [14] to calculate, and the accuracy of this method can reach 1′. ...
Article
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In order to grasp the timing of sun calibration in advance, this paper introduces a high-precision method to predict the solar angle by using the current broadcast time and orbital instantaneous root of the satellite platform. By calculating the sun’s apparent right ascension and apparent declination, the conversion matrix from the geocentric inertial coordinate system to the orbital coordinate system, and the satellite attitude correction matrix, the sun vector in the satellite body coordinate system is obtained. This method is used to predict the sun angle of a sun synchronous orbit in the satellite coordinate system, and the prediction results are compared with the STK simulation results. The results show that the sun angle prediction error of this method is less than ±0.003°. It can meet the requirements of on-orbit solar calibration. The main error sources in the prediction method are analysed.
... [60] Berger (1978) [61] Bretagnon and Francou (1988) [62] Berger and Loutre (1991) [63] Laskar et al. (2004) This simulation was only used in Figure 5.8, using NH temperature adjusted by Osborn et al. (2006 This simulation was only used in Figure 5.8, using drift-corrected NH temperature. ...
Book
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International Ocean Discovery Program Expedition 382, Iceberg Alley and Subantarctic Ice and Ocean Dynamics, investigated the long-term climate history of Antarctica, seeking to understand how polar ice sheets responded to changes in insolation and atmospheric CO2 in the past and how ice sheet evolution influenced global sea level and vice versa. Five sites (U1534–U1538) were drilled east of the Drake Passage: two sites at 53.2°S at the northern edge of the Scotia Sea and three sites at 57.4°–59.4°S in the southern Scotia Sea. We recovered continuously deposited late Neogene sediments to reconstruct the past history and variability in Antarctic Ice Sheet (AIS) mass loss and associated changes in oceanic and atmospheric circulation. The sites from the southern Scotia Sea (Sites U1536–U1538) will be used to study the Neogene flux of icebergs through “Iceberg Alley,” the main pathway along which icebergs calved from the margin of the AIS travel as they move equatorward into the warmer waters of the Antarctic Circumpolar Current (ACC). In particular, sediments from this area will allow us to assess the magnitude of iceberg flux during key times of AIS evolution, including the following: The middle Miocene glacial intensification of the East Antarctic Ice Sheet, The mid-Pliocene warm period, The late Pliocene glacial expansion of the West Antarctic Ice Sheet, The mid-Pleistocene transition (MPT), and The “warm interglacials” and glacial terminations of the last 800 ky. We will use the geochemical provenance of iceberg-rafted detritus and other glacially eroded material to determine regional sources of AIS mass loss. We will also address interhemispheric phasing of ice sheet growth and decay, study the distribution and history of land-based versus marine-based ice sheets around the continent over time, and explore the links between AIS variability and global sea level. By comparing north–south variations across the Scotia Sea between the Pirie Basin (Site U1538) and the Dove Basin (Sites U1536 and U1537), Expedition 382 will also deliver critical information on how climate changes in the Southern Ocean affect ocean circulation through the Drake Passage, meridional overturning in the region, water mass production, ocean–atmosphere CO2 transfer by wind-induced upwelling, sea ice variability, bottom water outflow from the Weddell Sea, Antarctic weathering inputs, and changes in oceanic and atmospheric fronts in the vicinity of the ACC. Comparing changes in dust proxy records between the Scotia Sea and Antarctic ice cores will also provide a detailed reconstruction of changes in the Southern Hemisphere westerlies on millennial and orbital timescales for the last 800 ky. Extending the ocean dust record beyond the last 800 ky will help to evaluate dust-climate couplings since the Pliocene, the potential role of dust in iron fertilization and atmospheric CO2 drawdown during glacials, and whether dust input to Antarctica played a role in the MPT. The principal scientific objective of Subantarctic Front Sites U1534 and U1535 at the northern limit of the Scotia Sea is to reconstruct and understand how intermediate water formation in the southwest Atlantic responds to changes in connectivity between the Atlantic and Pacific basins, the “cold water route.” The Subantarctic Front contourite drift, deposited between 400 and 2000 m water depth on the northern flank of an east–west trending trough off the Chilean continental shelf, is ideally situated to monitor millennial- to orbital-scale variability in the export of Antarctic Intermediate Water beneath the Subantarctic Front. During Expedition 382, we recovered continuously deposited sediments from this drift spanning the late Pleistocene (from ~0.78 Ma to recent) and from the late Pliocene (~3.1–2.6 Ma). These sites are expected to yield a wide array of paleoceanographic records that can be used to interpret past changes in the density structure of the Atlantic sector of the Southern Ocean, track migrations of the Subantarctic Front, and give insights into the role and evolution of the cold water route over significant climate episodes, including the following: The most recent warm interglacials of the late Pleistocene and The intensification of Northern Hemisphere glaciation.
... This view makes it possible to zoom in on particular objects, whereas very wide-angle perspective views are extremely distorted and can never show the full sky. Such programs, also based on improved models of planetary motions like VSOP87 (Bretagnon and Francou 1988), finally provided views and a simulation accuracy approaching, or even in some ways surpassing, the quality of the projection planetarium (although lacking the immersive quality of the dome) and thus invited their application in historical research which had hitherto been based on numerical tables (for example , Hunger 1994;. ...
Preprint
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THIS IS NOT A PREPRINT! It was never released as preprint before publication. If somebody knows how to replace/merge this wrongly classified "preprint" by/with the identical final paper please contact Georg Zotti. The final paper has the same DOI 10.1558/jsa.17822 Comments please go to the final paper. https://www.researchgate.net/publication/350441546_The_Simulated_Sky_Stellarium_for_Cultural_Astronomy_Research
... This view makes it possible to zoom in on particular objects, whereas very wide-angle perspective views are extremely distorted and can never show the full sky. Such programs, also based on improved models of planetary motions like VSOP87 (Bretagnon and Francou 1988), finally provided views and a simulation accuracy approaching, or even in some ways surpassing, the quality of the projection planetarium (although lacking the immersive quality of the dome) and thus invited their application in historical research which had hitherto been based on numerical tables (for example , Hunger 1994;. ...
Article
Full-text available
For centuries, the rich nocturnal environment of the starry sky could be modelled only by analogue tools such as paper planispheres, atlases, globes and numerical tables. The immer-sive sky simulator of the twentieth century, the optomechanical planetarium, provided new ways for representing and teaching about the sky, but the high construction and running costs meant that they have not become common. However, in recent decades, "desktop planetarium programs" running on personal computers have gained wide attention. Modern incarnations are immensely versatile tools, mostly targeted towards the community of amateur astronomers and for knowledge transfer in transdisciplinary research. Cultural astronomers also value the possibilities they give of simulating the skies of past times or other cultures. With this paper, we provide Georg Zotti et al. 222 © 2021 EQUINOX PUBLISHING LTD an extended presentation of the open-source project Stellarium, which in the last few years has been enriched with capabilities for cultural astronomy research not found in similar, commercial alternatives.
... Let us note that Stellarium contains implementations of VSOP87 [50] and ELP82B [51], and Vondrak2011 for precession [52]. In the following Figure 6, we can see the data collected from a simulation obtained by means of Stellarium, of the occultation of Venus by the Moon, observed by Abraham Zacut in 1476, the 24 of July. ...
Preprint
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A planetarium software is a software allowing users to simulate the celestial sphere according to a given time and location. Software can simply display a star chart or, with increasing complexity, can give to the observer a photorealistic rendering of the sky. Here we will consider the Stellarium Planetarium and its applications in several studies.
... We transform the LFC and the ThAr wavelength scales to the Solar system barycentre rest-frame using the barycentric velocity shift correction provided by the HARPS pipeline, independently for each quasar exposure. The barycentric correction provided by the pipeline is based on Bretagnon & Francou (1988) and uses the flux-weighted average time of observation. This value agrees down to several mm s −1 with our independent calculation, using the same information and the astropy module 2 . ...
Preprint
New observations of the quasar HE0515$-$4414 have been made using the HARPS spectrograph on the ESO 3.6m telescope, aided by the Laser Frequency Comb (LFC). We present three important advances for $\alpha$ measurements in quasar absorption spectra from these observations. Firstly, the data have been wavelength calibrated using LFC and ThAr methods. The LFC wavelength calibration residuals are six times smaller than when using the standard ThAr calibration. We give a direct comparison between $\alpha$ measurements made using the two methods. Secondly, spectral modelling was performed using Artificial Intelligence (fully automated, all human bias eliminated), including a temperature parameter for each absorption component. Thirdly, in contrast to previous work, additional model parameters were assigned to measure $\alpha$ for each individual absorption component. The increase in statistical uncertainty from the larger number of model parameters is small and the method allows a substantial advantage; outliers that would otherwise contribute a significant systematic, possibly corrupting the entire measurement, are identified and removed, permitting a more robust overall result. The $z_{abs} = 1.15$ absorption system along the HE0515$-$4414 sightline yields 40 new $\alpha$ measurements. We constrain spatial fluctuations in $\alpha$ to be $\Delta\alpha/\alpha \leq 9 \times 10^{-5}$ on scales $\approx 20\;{\rm km\,s}^{-1}$, corresponding to $\approx25\;$kpc if the $z_{abs} = 1.15$ system arises in a $1\;$Mpc cluster. Collectively, the 40 measurements yield $\Delta\alpha/\alpha=-0.27\pm2.41\times10^{-6}$, consistent with no variation.
... The freely available Python package pyephem was used for this purpose. This package uses the XEphem routines, which implement the semianalytic VSOP87 (Bretagnon & Francou, 1988) planetary theory to calculate the ephemerides of the Sun and Moon. While pyephem is now obsolete and one could use the latest version of the astropy library instead, this is not required for our purposes. ...
Article
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A reliable interpretation of solar eclipse effects on the geospace environment, and on the ionosphere in particular, necessitates a careful consideration of the so‐called eclipse geometry. A solar eclipse is a relatively rare astronomical phenomenon, which geometry is rather complex, specific for each event, and fast changing in time. The standard, most popular way to look at the eclipse geometry is via the two‐dimensional representation (map) of the solar obscuration on the Earth's surface, in which the path of eclipse totality is drawn together with isolines of the gradually‐decreasing eclipse magnitude farther away from this path. Such "surface maps” are widely used to readily explain some of the solar eclipse effects including, for example, the well‐known decrease in total ionisation (due to the substantial decrease in solar irradiation), usually presented by the popular and easy to understand ionospheric characteristic of Total Electron Content (TEC). However, many other effects, especially those taking place at higher altitudes, cannot be explained in this fashion. Instead, a more detailed description of the umbra (and penumbra), would be required. This paper addresses the issue of eclipse geometry effects on various ionospheric observations carried out during the total solar eclipse of August 21, 2017. In particular, GPS‐based TEC measurements were analysed and eclipse effects on the ionosphere are interpreted with respect to the actual eclipse geometry at ionospheric heights. Whenever possible, a comparison was made with results from other eclipse events.
Chapter
This chapter presents solar resource‐related notions essential for its measurement, assessment or forecasting. Solar radiation reaching the ground depends on the position of the Sun, extra‐terrestrial radiation and the atmospheric specificities of the site being studied. The chapter presents a general presentation of these concepts. A fraction of the extra‐terrestrial irradiance was absorbed while traveling through the atmosphere. Another fraction of this radiation is scattered, leading to an indirect radiation for the observer. The chapter offers a detailed presentation of the direct and indirect components of the irradiance, as well as the associated measurement instruments. It then presents the forecasting of the solar resource used by concentrated solar power plants, namely the direct normal irradiance. After a review of the essential notions to be known, the various existing approaches for making a direct normal solar irradiance forecasting are presented, differentiating them according to the expected spatial–temporal horizon.
Article
This paper reviews the history of research on the Atlantic Multi-decadal Oscillation (AMO), including its dynamics, global teleconnections, global impacts, and connection to global mean surface temperature. The AMO is a global-scale coupled ocean-atmosphere oscillation of the climate system with significant sea surface temperature (SST) anomalies in all ocean basins. It is associated with significant oscillation of the Atlantic Meridional Overturning Circulation (AMOC), which is likely driven by tidal gravitational forcing through tidal mixing and enhanced by volcano forcing and cloud-radiation feedback. The AMO strongly affects surface air temperature (Tair) and Palmer Drought Severity Index (PDSI) over all the continents. The phase lag varies among different continents. Over the tropical continents, Tair and PDSI tend to be in phase with each other. Over the extratropical continents, Tair and PDSI tend to be out of phase with each other. The AMO contributes significantly to global mean surface temperature and global warming hiatus.
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The incorporation of water isotopologues into the hydrology of general circulation models (GCMs) facilitates the comparison between modeled and measured proxy data in paleoclimate archives. However, the variability and drivers of measured and modeled water isotopologues, as well as the diversity of their representation in different models, are not well constrained. Improving our understanding of this variability in past and present climates will help to better constrain future climate change projections and decrease their range of uncertainty. Speleothems are a precisely datable terrestrial paleoclimate archives and provide well-preserved (semi-)continuous multivariate isotope time series in the lower latitudes and mid-latitudes and are therefore well suited to assess climate and isotope variability on decadal and longer timescales. However, the relationships of speleothem oxygen and carbon isotopes to climate variables are influenced by site-specific parameters, and their comparison to GCMs is not always straightforward. Here we compare speleothem oxygen and carbon isotopic signatures from the Speleothem Isotopes Synthesis and Analysis database version 2 (SISALv2) to the output of five different water-isotope-enabled GCMs (ECHAM5-wiso, GISS-E2-R, iCESM, iHadCM3, and isoGSM) over the last millennium (850–1850 CE). We systematically evaluate differences and commonalities between the standardized model simulation outputs. The goal is to distinguish climatic drivers of variability for modeled isotopes and compare them to those of measured isotopes. We find strong regional differences in the oxygen isotope signatures between models that can partly be attributed to differences in modeled surface temperature. At low latitudes, precipitation amount is the dominant driver for stable water isotope variability; however, at cave locations the agreement between modeled temperature variability is higher than for precipitation variability. While modeled isotopic signatures at cave locations exhibited extreme events coinciding with changes in volcanic and solar forcing, such fingerprints are not apparent in the speleothem isotopes. This may be attributed to the lower temporal resolution of speleothem records compared to the events that are to be detected. Using spectral analysis, we can show that all models underestimate decadal and longer variability compared to speleothems (albeit to varying extents). We found that no model excels in all analyzed comparisons, although some perform better than the others in either mean or variability. Therefore, we advise a multi-model approach whenever comparing proxy data to modeled data. Considering karst and cave internal processes, e.g., through isotope-enabled karst models, may alter the variability in speleothem isotopes and play an important role in determining the most appropriate model. By exploring new ways of analyzing the relationship between the oxygen and carbon isotopes, their variability, and co-variability across timescales, we provide methods that may serve as a baseline for future studies with different models using, e.g., different isotopes, different climate archives, or different time periods.
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The determinant of direction of the Kaaba or Qibla is important to Muslim as it is an obligation for Muslim prayer. A study shows a degree of azimuth displacement will result to a 138.3 km difference, meaning the direction is facing 138.3 km away from Kaaba. Thus, to ensure that the direction is facing the Kaaba, the accuracy of the direction is essential. Therefore, this study aimed to discuss the method of determining the Qibla direction using Sun Shadow, that can determine the times of Sun shadow facing the Qibla direction for various location at various time. The method is published in the form of Microsoft Excel to demonstrate how the formulation is practiced. The method is tested on 5 locations, representing various direction from Mecca, and Equator of the earth, on solar Solstice and Equinox. The method is computed using Jean Meeus Astronomical Algorithm. The result show that the method capable of determining direction of the Qibla at any given location and times with the accuracy error of 30 arc second. The accuracy of the method is better phone compass which has average error of 20 minute. The method will help Muslim in authenticating their Qibla direction by using Sun shadow.
Preprint
In the present work, we define a new anomaly, $\Psi$, termed semifocal anomaly. It is determined by the mean between the true anomaly, $f$, and the antifocal anomaly, $f^{\prime}$; Fukushima defined $f^{\prime}$ as the angle between the periapsis and the secondary around the empty focus. In this first part of the paper, we take an approach to the study of the semifocal anomaly in the hyperbolic motion and in the limit case correspoding to the parabolic movement. From here we find a relation beetween the semifocal anomaly and the true anomaly that holds independently of the movement type. We focus on the study of the two-body problem when this new anomaly is used as the temporal variable.\\ In the second part, we show the use of this anomaly —combined with numerical integration methods— to improve integration errors in one revolution. Finally, we analyze the errors committed in the integration process —depending on several values of the eccentricity— for the elliptic, parabolic and hyperbolic cases in the apsidal region.
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The incorporation of water isotopologues into the hydrology of general circulation models (GCMs) facilitates the comparison between modelled and measured proxy data in paleoclimate archives. However, the variability and drivers of measured and modelled water isotopologues, and indeed the diversity of their representation in different models are not well constrained. Improving our understanding of this variability in past and present climates will help to better constrain future climate change projections and decrease their range of uncertainty. Speleothems are a precisely datable paleoclimate archive and provide well preserved (semi-)continuous multivariate isotope time series in the lower and mid-latitudes, and are, therefore, well suited to assess climate and isotope variability on decadal and longer timescales. However, the relationship between speleothem oxygen and carbon isotopes to climate variables also depends on site-specific parameters, and their comparison to GCMs is not always straightforward. Here we compare speleothem oxygen and carbon isotopic signatures from the Speleothem Isotopes Synthesis and AnaLysis database version 2 (SISALv2) to the output of five different water-isotope-enabled GCMs (ECHAM5-wiso, GISS-E2-R, iCESM, iHadCM3, and isoGSM) over the last millennium (850-1850 common era, CE). We systematically evaluate differences and commonalities between the standardized model simulation outputs. The goal is to distinguish climatic drivers of variability for both modelled and measured isotopes. We find strong regional differences in the oxygen isotope signatures between models that can partly be attributed to differences in modelled temperatures. At low latitudes, precipitation amount is the dominant driver for water isotope variability, however, at cave locations the agreement between modelled temperature variability is higher than for precipitation variability. While modelled isotopic signatures at cave locations exhibited extreme events coinciding with changes in volcanic and solar forcing, such fingerprints are not apparent in the speleothem isotopes, and may be attributed to the lower temporal resolution of speleothem records compared to the events that are to be detected. Using spectral analysis, we can show that all models underestimate decadal and longer variability compared to speleothems, although to varying extent. We found that no model excels in all analyzed comparisons, although some perform better than the others in either mean or variability. Therefore, we advise a multi-model approach, whenever comparing proxy data to modelled data. Considering karst and cave internal processes through e.g. isotope-enabled karst models may alter the variability in speleothem isotopes and play an important role in determining the most appropriate model. By exploring new ways of analyzing the relationship between the oxygen and carbon isotopes, their variability, and co-variability across timescales, we provide methods that may serve as a baseline for future studies with different models using e.g. different isotopes, different climate archives, or time periods.
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In this paper seven different methods are presented to determine the declination of the Sun for a given time in order to calculate the position of the Sun (i.e. azimuth and elevation angle) for a precise place on Earth. The accuracy of these methods were also given and they compared with each other.
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DE200 and DE405 are Development Ephemeris (DE) series released by the National Aeronautics and Space Administration (NASA) in 1981 and 1997. NASA uses DE405 to predict solar eclipses in 2011-2020. While before 2011 and after 2020 NASA uses VSOP87/ELP200 theory-based DE200. Why NASA not only use more updated series DE405 and still use old release DE200? What is the difference of DE200 accuracy compared to DE405 to predict solar eclipse? This needs to be researched because the solar eclipse predicted by NASA is used as a reference by the researchers. To answer this question, this paper proposes a solar eclipse computation algorithm based on DE200 and DE405 data and the results will be compared with the results of observations of the March 9, 2016, solar eclipse that have been carried out langit selatan to find out a more accurate DE series. The results of this study indicate that the DE200 series is more accurate than DE405 with an average difference of 0.5 - 0.6 seconds with the results of observations.
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Plain Language Summary It was postulated for several decades that the lunar horizon glow observed during Apollo epoch was caused by forward scattering of sunlight by the electrostatically levitated dust particles above the sharp sunlight/shadow boundaries in the terminator zone. However, do high concentrations of charged dust particles really exist over the lunar terminator? This question cannot be definitively answered at present. China's Chang'E‐3 (CE‐3) mission provided a unique opportunity to address this long‐standing scientific question because an in situ dust detector was loaded onto the lander. In this letter, the results obtained by the dust detector were demonstrated. It is found that the recently proposed minimalist model is not suitable for the geologically young CE‐3 landing site. Within detector's detection limit, no putative high‐density population of lunar dust particles was found above the sharp sunlight/shadow boundaries. This research, being carried out on the lunar surface rather than in orbit, can provide important new insights into the generation mechanisms about lunar horizon glow.
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We analyzed astronomical data in the Tongmunhwigo, one of the history books containing diplomatic documents of the Joseon government (the last dynasty of Korea). This book contains predictions of solar and lunar eclipses for Seoul and Beijing with specific information such as magnitude and time, sent by the Qing government to the King of Joseon between 1721 to 1881. We analyzed the accuracy of the calculations performed by Qing’s astronomers, by comparing them with the results of modern calculations. Overall, the error value for time of the eclipses was less than ±0.5 hour (±30 minutes) and the error value for magnitude was within ±10%. The results of this study will be helpful for understanding how accurate the predictions calculated by Qing astronomers were during the eighteenth to nineteenth centuries.
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