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The most general motion of a rigid body can be described by the combination of the translational motion of its center of mass and the rotational motion of all points of the body about an axis through the center of mass. In this chapter, we apply kinematics, dynamics, and conservation laws to investigate rolling motion, which is a special case of this most general motion. This chapter represents the culmination of all the topics we cover in the first six chapters of this book.
In this chapter, we begin by examining the work due to a torque. We then define the concept of the rotational kinetic energy for a point mass, systems of discrete masses, and continuous rigid bodies. We develop the angular work-kinetic energy theorem and use it to study the conservation of energy and the conservation of mechanical energy in systems involving rotational motion. To develop these theorems, we draw from our understanding of the analogous theorems in linear motion.
We begin our study of rotational motion with the definitions and detailed examination of the fundamental quantities which we will use throughout this book. We then proceed with a description of kinematics in rotational motion by drawing analogies from our knowledge of one-dimensional kinematics in linear motion.
The journey through rotational motion is not quite done. In fact, we are just beginning. This chapter introduces a few topics which would be covered in an intermediate-level mechanics course. The topics include more advanced physical phenomena, such as gyroscopic precession, and the mathematical formalism of parameterizing rotations using matrices.
The concept of mass in linear motion was quite simple. However, the rotational analog, the moment of inertia, is comparatively complicated. In this chapter, we present a thorough introduction to the moment of inertia, and we develop the tools needed to compute this quantity for point masses, systems of discrete masses, and continuous rigid bodies about different axes of rotation. The chapter ends with some useful theorems that allow us to extend the application of these fundamental tools.
The Australian SKA Pathfinder (ASKAP) is being used to undertake a campaign to rapidly survey the sky in three frequency bands across its operational spectral range. The first pass of the Rapid ASKAP Continuum Survey (RACS) at 887.5 MHz in the low band has already been completed, with images, visibility datasets, and catalogues made available to the wider astronomical community through the CSIRO ASKAP Science Data Archive (CASDA). This work presents details of the second observing pass in the mid band at 1367.5 MHz, RACS-mid, and associated data release comprising images and visibility datasets covering the whole sky south of $\delta_{\text{J2000}}=+49^\circ$. This data release incorporates selective peeling to reduce artefacts around bright sources, as well as accurately modelled primary beam responses. The Stokes I images reach a median noise of 198 $\mu$Jy PSF$^{-1}$ with a declination-dependent angular resolution of 8.1–47.5 arcsec that fills a niche in the existing ecosystem of large-area astronomical surveys. We also supply Stokes V images after application of a widefield leakage correction, with a median noise of 165 $\mu$Jy PSF$^{-1}$. We find the residual leakage of Stokes I into V to be $\lesssim 0.9$–$2.4$% over the survey. This initial RACS-mid data release will be complemented by a future release comprising catalogues of the survey region. As with other RACS data releases, data products from this release will be made available through CASDA.
A model of dynamical evolution of meteoroid swarm is applied to study the problem of difference in mass spectra of meteoric bodies during meteor showers and for sporadic meteors. It is demonstrated that mass spectra forms within meteoroid stream. Qualitative behavior of mass index in model is consistent with observational data.
Deep-learning algorithms have gained much popularity in the past decade. However, their supervised nature makes them fully dependent on the quality and completeness of the data samples used in the training processes. And when it comes to galaxy spectra for instance, there is simply no suited training sample available yet. This is where unsupervised classification (clustering) can come to the rescue.
Using the discriminant latent mixture-model based algorithm Fisher-EM, we 1) demonstrate the discriminative capacity of the method and its robustness with respect to noise on a sample of galaxy spectra simulated with the code CIGALE, 2) manage to classify ∼700 000 spectra of galaxies from the SDSS, and 3) extend this classification to higher redshifts thanks to the VIPERS data (∼80 000 spectra up to a redshift of 1.2). Finally, it appears that FisherEM is efficient for images of galaxies as well.
We present a machine learning method to estimate the physical parameters of classical pulsating stars such as RR Lyrae and Cepheid variables based on an automated comparison of their theoretical and observed light curve parameters at multiple wavelengths. We train artificial neural networks (ANNs) on theoretical pulsation models to predict the fundamental parameters (mass, radius, luminosity, and effective temperature) of Cepheid and RR Lyrae stars based on their period and light-curve parameters. The fundamental parameters of these stars can be estimated up to 60 percent more accurately when the light-curve parameters are taken into consideration. This method was applied to the observations of hundreds of Cepheids and thousands of RR Lyrae in the Magellanic Clouds to produce catalogs of estimated masses, radii, luminosities, and other parameters of these stars.
In this work we reviewed the Gauss method to infer the orbits of minor bodies of the solar system, as the identification of optimization parameters to infer the orbital elements of two asteroids near to the Earth (NEAs): 5587 (1990 SB) and 4953 (1990 MU)), already cataloged and named by the Minor Planet Center - MPC. We used the database of JPL - Horizons and also included an analysis using data of Gaia Data Release 3 (DR3). We did an statistic analysis between distribution of points correspondent to orbital elements that we obtained and the inferred by the Jet Propulsion Laboratory-JPL. When data is crossed with the orbital parameters of Small-Body Database (JPL), we analyzed the deficiency grades of the method by statistic comparation with state vector method between orbital elements inferred with the implemented method and the accepted by the community, obtaining a relative error for the orbits calculated of 0.424149% and 0.416237% for the body 5587 (1990SB), and 0.257968% and 0.223521% for the body 4953 (1990MU). The first error value mentioned corresponds to an orbit calculated with the database JPL- Horizons, and the second value to an orbit calculated with the database Gaia (DR3), for each body in study. In the first phases of implementation of the code, it was found that the restrictions of the traditional method are overcome under the additional parameters that are proposed, resulting in orbits that are better approximated than those determined by NASA Team at the time of observation corresponding to the collection of data for the different bodies analyzed in the framework of this work.The best approximations are established with respect to the calculation of the orbital elements through the numerical solutions incorporated in the NASA SPICE kernel in python for a period of 100 years, with a step of 1 month. We found that our data are quite close to the curves that represent the variations of each of the 5 orbital elements involved in our analysis, namely: a, e, i, ω, Ω. Finally, it should be noted that our method could contribute to the estimation of orbits for minor bodies of the Solar System from observational data, which could easily be taken by using small telescopes. Thus, it would enrich processes that seek to expand the coverage of observatories focused on estimating the orbits of minor bodies in the solar system.
Massive spectroscopic surveys targeting tens of millions of galaxies are starting to dominate the observational landscape in the 2020 decade. For instance, a night of observation with the Dark Energy Spectroscopic Instrument (DESI) can measure around of 100,000 spectra, with each spectrum sampled over 2,000 wavelength points. Assessing the quality of such a massive data flow requires new approaches to complement visual inspection by humans. In this work, we explore the Uniform Manifold Approximation and Projection (UMAP) as a technique to assess the data quality of DESI. We use UMAP to project DESI data into a 2-dimensional space. In this space, we are able to find outliers that correspond to instrument fluctuations that can be fully diagnosed by inspecting the raw data. These results pave the way for to use machine learning to monitor the health of massive spectroscopic surveys automatically.
Binary Neutron star mergers (BNS) are of particular interest for the possibility of multi-messenger astronomy. We investigate if BNS gravitational waves trigger detection should be preferably conducted in a representation instead of another, we inspect time strains, Fourier transform, and spectrograms. We recreate the data stream of the LIGO detector, which could contain noise only or signals hidden in the noise. We train a binary classifier able to distinguish if a merger is present. We create two distinguished datasets, one with the LIGO detector instrumental noise and one whitened with respect to the detector PSD. We obtain the highest accuracy for whitened spectrograms - 93% correct classifications of an external validation dataset. Fourier transforms show similar behavior in both colored and whitened datasets with an accuracy of ∼77%. Whitened time strains have a substantial increase in accuracy from the colored to the whitened dataset, respectively 50% and 73%.
Using deep learning (DL) with the Adam optimizer, I detected 15 previously undiscovered exoplanets in the Kepler data collected by the National Aeronautics and Space Administration (NASA). Some of the exoplanet transit signals were evident, but others were not as strong. Further evaluation is needed. By using my own code and DL libraries including TensorFlow, I built a Python program to search for exoplanets. Among the new candidate exoplanets detected by my program, 13 of them are ultra-short-period (USP) exoplanets with orbital periods shorter than a day. Moreover, I experimented on this Python DL program with current candidate and confirmed exoplanets in the NASA database and was able to detect more than 200 candidate exoplanets and 94 of the 116 confirmed exoplanets in the NASA database. These findings show that DL can be an effective tool to detect objects of interest, such as exoplanets, in astronomy big data.
The history of crater formation on the Moon idicates that the number of NEAs larger than 50 m practically did not change over the past 2–3 Gyr. On the other hand a dynamic scale of the NEA population, which could be characterized by the depletion time by half tNEA, is many orders of magnitude shorter. There are significant variations of tNEA estimates by other authors. It is important to know this value more precisely, since this knowledge imposes restrictions on the mechanisms of replenishment of the NEAs, the lifetime of the Main Asteroid Belt, etc. In the Zolotarev & Shustov (2021) we have estimated tNEA as 3.5 million years. We noted either that tNEA for subgroups of NEAs depends on the initial orbital parameters of the subgroups. In the current study we considered this dependence quantitively. We have integrated orbits of 10 000 asteroids larger than 1 km and q<1.72 AU over 20 Myr. These sample essentially includes all large NEAs (>1km). The NEA subsample is considered to be complete. We made integrations with the REBOUND software package using the MERCURIUS hybrid scheme (Rein et al. (2019)). To reveal dependence of tNEA on orbital parameters tNEA(a, e, i) we divided the NEA subsample into 18 subgroups according to their orbital parameters. We found that tNEA is substantially higher for subgroups with higher i and e. There is strong dependence of tNEA on a. All these dependencies are explained by a different number of close approaches of asteroids from NEA subgroups to planets. We found that depletion of total NEO population can be approximated remarkably well with the following expression: N(t)/N0 = exp(−0.5×t0.33)where N0 is an initial number and N(t) – a current number of NEAs.
Determination of membership of star clusters is a very important criterion in their study as they effect determination of cluster parameters like radius, age, distance, mass functions, etc. In an earlier study, we used published membership data of nine open star clusters as a training set to find new members from Gaia DR2 data using a supervised Random Forest (RF) model with a precision of around 90%. The number of new members found was almost double the published number. In this work, we would like to compare the earlier results with results obtained by applying the unsupervised method of Gaussian Mixture Modelling (GMM) and Density-Based Spatial Clustering of Applications with Noise (DBSCAN) to study the membership of open star clusters of varying ages and locations in the Galaxy using Gaia DR2 and EDR3 data. We shall discuss these techniques and focus on the caveats involved.
Galaxy mergers are central to our current understanding of the universe. These events are known to change the morphologies of the merging galaxies, accompanied by changes to physical processes Galaxy mergers are rare events and to better study them we need larger, statistical samples.
Greater use of machine learning and artificial intelligence has seen galaxy mergers become a target for these techniques. Recently, application of these techniques has gone from proof of concept to using machine learning galaxy merger catalogues for science.
In this proceedings, we will examine how extraction of morphological parameters by traditional methods can be used to aid neural networks in classification of galaxy mergers. We will see how current networks may not be extracting all the information from imaging data. We will also discuss how samples of rare objects can be contaminated and the impact this has on our science. This contribution is based on Pearson et al. (2022).
The orbital evolution of NEA Apophis was investigated for the time interval of 12 kyrs, geocentric coordinates of radiants and velocities of theoretically related meteor showers were calculated, as well the dates of their activity were determined. As a result of a search among the fireball observations, on two fireballs for northern and southern branches of the nighttime shower were found. These fireballs, having the parameters close to predicted ones, probably, were produced by the fragments of the asteroid Apophis. It is recommended to carry out meteor and fireball observations on the predicted dates of shower activity of ±7 days in order to record meteor phenomena, possibly generated by fragments of asteroid Apophis.