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. 

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

Charged dust close to outer mean-motion resonances in the heliosphere

We investigate the dynamics of charged dust close to outer mean-motion resonances with planet Jupiter. The importance of the interplanetary magnetic field on the orbital evolution of dust is clearly



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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