Orbital mechanics, or astrodynamics, is the science of how spacecraft and celestial bodies move under gravity, and how to steer a vehicle from one orbit to another. It sits on classical mechanics but adds its own vocabulary of orbital elements, transfers, and perturbations, and its books build steadily from the clean two-body idealization to the messy realities of mission design.
Reading in order matters because every advanced technique is a correction to a simpler model. Master the two-body problem and Keplerian orbits first, and the perturbation methods, optimization, and multi-body dynamics that follow have something to modify.
Build the classical foundation
Astronomy, principles and practice by A. E. Roy gives the celestial-mechanics backdrop that frames the whole subject. Then the standard teaching texts: Fundamentals of astrodynamics by Roger Bate, Donald Mueller, and Jerry White is the beloved concise classic, and Orbital mechanics for engineering students by Howard Curtis is the modern, thorough textbook with worked examples and code. Read one of these completely before going further. For the rigorous mathematical treatment, An introduction to the mathematics and methods of astrodynamics by Richard Battin is the deep reference to grow into.
Move to designing real missions
Once orbits are second nature, you design trajectories. Spacecraft mission design by Charles Brown introduces the practical craft, and Interplanetary Mission Analysis and Design by Stephen Kemble covers the harder problem of getting between planets. Analytical Mechanics of Space Systems by Hanspeter Schaub and John Junkins adds attitude dynamics and control, the other half of flying a spacecraft.
Reach the advanced methods
Methods of Orbit Determination for the Microcomputer by Pedro Escobal covers how you actually figure out where something is from observations. Optimal control and estimation by Robert Stengel supplies the control-theory machinery for optimal maneuvers. And Dynamical Systems, the Three-Body Problem and Space Mission Design by Wang Sang Koon and colleagues opens the modern world of low-energy transfers and chaotic dynamics.
Read in this order and each layer refines the last. Follow the full path to keep the trajectory smooth.
