An Introduction to Celestial Mechanics

  title={An Introduction to Celestial Mechanics},
  author={Richard Fitzpatrick},
Preface 1. Newtonian mechanics 2. Newtonian gravity 3. Keplerian orbits 4. Orbits in central force-fields 5. Rotating reference frames 6. Lagrangian mechanics 7. Rigid body rotation 8. Three-body problem 9. Secular perturbation theory 10. Lunar motion Appendix A: useful mathematics Appendix B: derivation of Lagrange planetary equations Appendix C: expansion of orbital evolution equations Bibliography Index. 
On the Intrinsic Precession of the Perihelion of Planets of the Solar System
By analytically solving a corrected balance between the force given by the Newton’s 2nd law and the Newton gravitational force in polar coordinates, an equation for the intrinsic (i.e. two-body
Verified solutions for the gravitational attraction to an oblate spheroid: Implications for planet mass and satellite orbits
Abstract Forces external to the oblate spheroid shape, observed from planetary to galactic scales, are demonstrably non-central, which has important ramifications for planetary science. We simplify
Orbital dynamics in the post-Newtonian planar circular restricted Sun–Jupiter system
The theory of the post-Newtonian (PN) planar circular restricted three-body problem is used for numerically investigating the orbital dynamics of a test particle (e.g. a comet, asteroid, meteor or ...
Orbital dynamics satisfying the 4th-order stationary extended Fisher-Kolmogorov equation
In this study, we discuss the central force problem by using the nonlocal-in-time kinetic energy approach. At low length scales, the system is dominated by the generalized 4th-order extended
Orbital Dynamics in the Restricted Three Body Problem: Overview of Recent Analytical Advances Obtained by Separating Rapid and Slow Subsystems in Non-Planar Configurations
Analytical solutions to a variety of simplified versions of the restricted three-body problem in celestial mechanics possess long running history that encompasses several centuries. Most of the
Regularization of circular restricted three-body problem accounting radiation pressure and oblateness
In this paper, a time- and space-coordinate transformation, commonly known as the Kustaanheimo–Stiefel (KS)-transformation, is applied to reduce the order of singularities arising due to the motion
Satellite Orbits and Attitude
This chapter discusses fundamentals of orbital dynamics and provides a description of key perturbations affecting global navigation satellite system (GNSS ) satellites along with their impact on the
A minimizing property of hyperbolic Keplerian orbits
In this short note, we characterize hyperbolic Keplerian orbits as minimizing paths of the Keplerian action functional in the space of curves from a ray emanating from the attractive focus to a point
Mechanical analysis of Qi four-wing chaotic system
This paper decomposes vector field of the Qi four-wing chaotic system into four types of torques: inertial torque, internal torque, dissipation and external torque by comparing the system with
Natural formations at the Earth–Moon triangular point in perturbed restricted problems
Previous studies for small formation flying dynamics about triangular libration points have determined the existence of regions of zero and Minimum Relative Radial Acceleration with respect to the


The third (mostly) excluded topic is astrodynamics: the application of Newtonian dynamics to the design and analysis of orbits for artificial satellites and space probes
  • Interested readers are directed to Bate, Mueller, and White (1977). The final excluded topic is the determination of the orbits of celestial objects from observational data. Interested readers are again directed to Danby (1992).
  • 1992
The fact that so many celebrated mathematicians
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