Most books on orbital motion fall into one of two traps: some are elegant enough to admire but never actually compute an answer, while others hand you formulas to apply but never show where they came from. Spaceflight demands both, the derivation and the number.
If you are studying or working in astronautics, you have felt the gap. A lecture builds a beautiful equation; the problem set then asks for a result in kilometers per second, and the path between the two is left to you. Notation drifts from chapter to chapter, and worked examples skip the exact steps where you are stuck. You can recite the theory but hesitate when it is time to produce a number you can trust.
This handbook is written to close that gap. It derives each result honestly from first principles and carries it all the way to a worked number, in SI units, that an engineer could actually use. Every assumption is stated, the notation is fixed once and reused everywhere, and each calculation is shown step by step, units included, so you can move confidently from concept to answer.
Inside, you will:
Understand where each equation comes from, through complete derivations rather than quoted results.
Work fully worked SI examples that show every step, then test yourself on practice problems with boxed answers and a full appendix of solutions.
Describe any orbit with its elements, locate a body on it at any time, and determine an orbit from observations.
Plan maneuvers, transfers, plane changes, phasing, and rendezvous, and estimate their velocity cost.
Design interplanetary trajectories, size launch windows, use gravity-assist flybys, and account for the perturbations that reshape real orbits.
Propagate an orbit numerically when no formula suffices, and estimate rocket performance and launch requirements.
Key Topics: reference frames and time; the two-body problem and orbital elements; position versus time; orbit determination; impulsive maneuvers and transfers; relative motion and rendezvous; the two-point transfer problem; interplanetary trajectories and gravity assists; orbital perturbations and decay; numerical propagation; rocket performance and launch; and the restricted three-body problem with its libration points.
Who it is for: It is written for upper-level undergraduate and early graduate students in aerospace and mechanical engineering, and for practicing engineers who want a rigorous refresher. It assumes calculus, vectors and matrices, and elementary particle dynamics, and builds everything particular to orbits from there.
Open the book and begin developing the knowledge to approach any orbit problem with clarity and confidence, from the first derivation to the final number.