Online calibration for star trackers

Star trackers are perhaps the most accurate means of measuring a spacecraft's orientation in space and are becoming a popular sensing instrument for attitude determination systems amongst conventional larger satellites as well as micro satellites. In order to produce and maintain high fidelity measurements, the systematic effects of lens distortion and possible sensor alterations due to environmental changes and instrument aging must all be accounted for through calibration, both on the ground and on orbit. In this study, a calibration method is presented to account for errors in star camera parameters, namely the focal length, bore sight offset, higher order radial distortion terms and the tip and tilt of the detector array in relation to the lens arrangement. This method does not depend on a costly high-precision lab setup; instead it simply employs the star camera images and a star catalogue to calibrate the instrument given reasonable initial estimates. This allows for a reduction in pre-mission calibration requirements and is feasible for an online implementation, allowing the star tracker to calibrate itself through out its life-cycle.

Online calibration for star trackers

Star trackers are perhaps the most accurate means of measuring a spacecraft's orientation in space and are becoming a popular sensing instrument for attitude determination systems amongst conventional larger satellites as well as micro satellites. In order to produce and maintain high fidelity measurements, the systematic effects of lens distortion and possible sensor alterations due to environmental changes and instrument aging must all be accounted for through calibration, both on the ground and on orbit. In this study, a calibration method is presented to account for errors in star camera parameters, namely the focal length, bore sight offset, higher order radial distortion terms and the tip and tilt of the detector array in relation to the lens arrangement. This method does not depend on a costly high-precision lab setup; instead it simply employs the star camera images and a star catalogue to calibrate the instrument given reasonable initial estimates. This allows for a reduction in pre-mission calibration requirements and is feasible for an online implementation, allowing the star tracker to calibrate itself through out its life-cycle.

The mystery of Copernicus’ star catalogue (Part III)

The author of “The Catalog of Zodiac signs and stars” published in De Revolutionibus, was Ptolemy. Copernicus used this catalog and all available observations of the Sun, Moon and planets, for improvement of the theory and tables of their motions. E. P. Fedorov wants to support with the authoritative opinion of Copernicus the idea of replacing the main optic reference frame to radio system JCRF. Having mastered the experience of previous generations Copernicus knew that the principles of establishing coordinate systems do not change along with opinions on the structure of the universe. Had the places of stars in catalogs not been dependent on the location of the Sun, Copernicus would have had no opportunity to prepare the time and coordinate systems required for solution of his problem. In his manuscript he preserved the idea the principles of compiling star catalogs, which were not included in the published edition along with excerpts from the originally conceived chapters. The words irrefutably prove that the idea of establishing the main reference system from VLBJ observations without the place of vernal equinox could not be supported by reference to Copernicus`s opinion.

High-Accuracy Guide Star Catalogue Generation with a Machine Learning Classification Algorithm

In order to detect gravitational waves and characterise their sources, three laser links were constructed with three identical satellites, such that interferometric measurements for scientific experiments can be carried out. The attitude of the spacecraft in the initial phase of laser link docking is provided by a star sensor (SSR) onboard the satellite. If the attitude measurement capacity of the SSR is improved, the efficiency of establishing laser linking can be elevated. An important technology for satellite attitude determination using SSRs is star identification. At present, a guide star catalogue (GSC) is the only basis for realising this. Hence, a method for improving the GSC, in terms of storage, completeness, and uniformity, is studied in this paper. First, the relationship between star numbers in the field of view (FOV) of a staring SSR, together with the noise equivalent angle (NEA) of the SSR—which determines the accuracy of the SSR—is discussed. Then, according to the relationship between the number of stars (NOS) in the FOV, the brightness of the stars, and the size of the FOV, two constraints are used to select stars in the SAO GSC. Finally, the performance of the GSCs generated by Decision Trees (DC), K-Nearest Neighbours (KNN), Support Vector Machine (SVM), the Magnitude Filter Method (MFM), Gradient Boosting (GB), a Neural Network (NN), Random Forest (RF), and Stochastic Gradient Descent (SGD) is assessed. The results show that the GSC generated by the KNN method is better than those of other methods, in terms of storage, uniformity, and completeness. The KNN-generated GSC is suitable for high-accuracy spacecraft applications, such as gravitational detection satellites.

The mystery of Copernicus’ star catalogue (The second part) The system of time and determination of the Earth’s triple motion

Objecting to those who consider Copernicus’s work as repeating the achievements of Antiquity, we pay attention to his determination of uniform time necessary for applying any mathematical theory in particular, the one describing the observed uneven movements through a composition of circular and uniform rotations. Using the Egyptian year of 365 solar days, Copernicus analyzed the observations for the period from the first Olympiad up to his own observations. Generalizing the results of observations of two millennia and reducing them to the unique time system enabled his explaining the observed precession of equinoxes, and changes in the angle of inclination of the Earth’s equator to ecliptic by the lag of the Earth’s center rotation from that of its axis, simultaneously to exclude empty spheres from the medieval mechanical models of the Universe. Analyzing the observations of the period 4 times longer than that of Ptolemy, Copernicus managed to obtain the mean value of precession and the period of the Earth axis rotation practically coinciding with modern determinations. The proof of “the triple motion of the Earth” was necessary for affirmation of heliocentric system of the world.

A census of main-sequence interactions in the Multiple Star Catalogue

ABSTRACT Statistics of hierarchical systems containing three or more stars are continuously improving. The Multiple Star Catalogue (MSC) is currently the most comprehensive catalogue of multiple-star systems and contains component masses, orbital periods, and additional information. The systems in the MSC are interesting for several reasons, including the long-term dynamical evolution of few-body systems. Although the secular evolution of triples and quadruples has been explored before, a systematic study of the systems in the MSC including also quintuples and sextuples has not been carried out. Here, we explore the main-sequence (MS) evolution of stars from the MSC based on approximately 2 × 105 secular dynamical integrations. We estimate statistical probabilities for strong interactions during the MS such as tidal evolution and mass transfer, and the onset of dynamical instability. Depending on the assumed model for the unknown orbital elements, we find that the fraction of non-interacting systems is largest for triples (∼0.9), and decreases to ∼0.6–0.8 for sextuples. The fraction of strong interactions increases from ∼0.1 to ∼0.2 from triples to sextuples, and the fraction of dynamically unstable systems increases from ∼0.001 to ∼0.1–0.2. The larger fractions of strong interactions and dynamical instability in systems with increasing multiplicity can be attributed to increasingly complex secular evolution in these systems. Our results indicate that a significant fraction of high-multiplicity systems interact or become dynamically unstable already during the MS, with an increasing importance as the number of stars increases.

Characterization of the precision premium in astrometry

ABSTRACT The precision premium, a concept in astrometry that was first presented by Pascu in 1994, initially means that the relative positional measurement of the Galilean satellites of Jupiter will be more accurate when their separations are small. Correspondingly, many observations have been obtained of these Galilean satellites since it was introduced. However, the exact range of separations at which the precision premium takes effect is not clear yet, nor the variation of the precision with separation. In this article, observations of open cluster M35 are used to study the precision premium and the newest star catalogue Gaia DR2 is used in data reduction. Our results show that the precision premium applies at less than 100 arcsec for two specific objects and the relative positional precision can be well fitted by a sigmoidal function. Observations of Uranian satellites are also reduced as an example of the precision premium.

Uniform Star Catalogue using GWKM Clustering for Application in Star Sensors

In this paper, a novel algorithm of weighted k-means clustering with geodesic criteria is presented to generate a uniform database for a star sensor. For this purpose, selecting the appropriate star catalogue and desirable minimum magnitude and eliminating double stars are among the steps of the uniformity process. Further, Delaunay triangulation and determining the scattered data density by using a Voronoi diagram were used to solve the problems of the proposed clustering method. Thus, by running a Monte Carlo simulation to count the number of stars observed in different fields of view, it was found that the uniformity leads to a significant reduction of the probability of observing a large number of stars in all fields of view. In contrast, the uniformity slightly increased the field of view needed to observe the minimum number of required stars for an identification algorithm.