This book is a tool for our own teaching and an opportunity to rethink and reorganize the results of our own research. However, I think such a book can be useful to others, for two main reasons. First, spaceflight is no longer the privilege of the few superpowers, but is becoming available to many nations and agencies. Orbit determination is an essential knowhow, both in the planning phase of mission analysis and in the operations of space missions. Thus its mathematical tools need to become widely available.

Second, the knowledge and skill used in orbit determination, for both natural and artificial celestial bodies, was available only among a restricted group of specialists. The prevailing attitude was a proprietary one: the knowledge and the software were protected by formal copyright and/or by secrecy, although protecting in this way the pure mathematical theory is, in the long run, impossible. This attitude might have been justified under the conditions of the world of 30–40 years ago, in the critical phases of the competition to achieve space firsts. Now it is time to teach and disseminate this knowledge, allowing the formation of a wider group of specialists.

I know that many of the rules of thumb and practical advice contained in this book will be rated as well known, even obvious, by the few experts, but this is not the point. Even well-known results may need to be presented in a rational, rigorous, and didactically effective new way, together with the outcome of recent innovative research.