02678nam a22002895i 450099100426522720753620240125115716.0190923s2019 gw a fr 001 0|eng d9783030258481Bibl. Dip.le Aggr. Matematica e Fisica - Sez. Fisicaeng530.09223LC QC16.N753.1.5Capuzzo Dolcetta, Roberto A.1434822Classical Newtonian gravity :a comprehensive introduction, with examples and exercises /Roberto A. Capuzzo DolcettaCham :Springer International Publishing,c2019xvi, 176 p. :ill. (some color.) ;24 cmUNITEXT for Physics,2198-7882Chapter 1 -- Elements of Vector Calculus -- Chapter 2 Potential Theory -- Chapter 3 -- Central Force Fields -- Chapter 4 -- Potential Series Developments -- Chapter 5 -- Harmonic and Homogeneous Polynomials -- Chapter 6 -- Series of Spherical HarmonicsThis textbook offers a readily comprehensible introduction to classical Newtonian gravitation, which is fundamental for an understanding of classical mechanics and is particularly relevant to Astrophysics. The opening chapter recalls essential elements of vectorial calculus, especially to provide the formalism used in subsequent chapters. In chapter two Classical Newtonian gravity theory for one point mass and for a generic number N of point masses is then presented and discussed. The theory for point masses is naturally extended to the continuous case. The third chapter addresses the paradigmatic case of spherical symmetry in the mass density distribution (central force), with introduction of the useful tool of qualitative treatment of motion. Subsequent chapters discuss the general case of non-symmetric mass density distribution and develop classical potential theory, with elements of harmonic theory, which is essential to understand the potential development in series of the gravitational potential, the subject of the fourth chapter. Finally, in the last chapter the specific case of motion of a satellite around the earth is considered. Examples and exercises are presented throughout the book to clarify aspects of the theory. The book is aimed at those who wish to progress further beyond an initial bachelor degree, onward to a master degree, and a PhD. It is also a valuable resource for postgraduates and active researchers in the fieldMechanicsSpace sciencesPotential theory (Mathematics)Gravitation991004265227207536Classical Newtonian gravity3590962UNISALENTO