Introduction to orbital perturbations - Longuski, James M.; Hoots, Felix R. 1947-; Pollock, George E. (Springer, 2022)
This textbook provides details of the derivation of Lagrange's planetary equations and of the closely related Gauss's variational equations, thereby covering a sorely needed topic in existing literature. Analytical solutions can help verify the results of numerical work, giving one confidence that his or her analysis is correct. The authors—all experienced experts in astrodynamics and space missions—take on the massive derivation problem step by step in order to help readers identify and understand possible analytical solutions in their own endeavors. The stages are elementary yet rigorous; suggested student research project topics are provided.After deriving the variational equations, the authors apply them to many interesting problems, including the Earth-Moon system, the effect of an oblate planet, the perturbation of Mercury's orbit due to General Relativity, and the perturbation due to atmospheric drag. Along the way, they introduce several useful techniques such as averaging, Poincaré's method of small parameters, and variation of parameters. In the end, this textbook will help students, practicing engineers, and professionals across the fields of astrodynamics, astronomy, dynamics, physics, planetary science, spacecraft missions, and others
1 The n-Body Problem2 General Perturbations 3 Evaluation of Lagrange’s Brackets 4 Lagrange’s Planetary Equations 5 Expansion of the Perturbation Function 6 The Earth-Moon System 7 Potential of an Oblate Spheroid8 Effects of General Relativity9 Perturbations due to Atmospheric Drag 10 Periodic Solutions in Nonlinear OscillationsBibliography Projects