I am interested in nineteenth-century astronomy and Laplace's Treatise of celestial mechanics is often mentioned as one of the most significant contributions to science in this period. The more than thousand pages long tomb is impenetrable to me. Most secondary literature just claims that it is a synthesis of the progress of eighteenth-century Newtonian science, but nobody goes into more detail.
Here is a list of some literature, but none really provides a detailed outline of Laplace's main work. Alas, there is no secondary literature of his main work as there is for figures like Galileo, Newton, Euler and Einstein.
I can understand why there is no secondary literature: you need to have a very strong mathematical background (problems like shape of earth, and lunar motion are complex) and in addition you also need to have much historical knowledge of empirical sciences on tides, lunar motions, astronomical data. This seems to be an extremely demanding skillset.
I was hoping somebody could fill the gap between the popularizing presentions and the technical subjects of the book. You may also refer to relevant secondary literature. Partial answers are also welcome. I don't expect a complete summary of his main work.
The main topics in the work can be read off the table of contents. The kind of questions I have are for example:
- what exactly did the book accomplish? What did Laplace himself said it accomplishes?
- what kind of (mathematical) methods and (theoretical) ideas are used to accomplish the main results?
- how to draw a distinction between his own contributions and his predecessors?
- was the book constructed according to some larger plan or does he just deal with different domains in each chapter?
- was some of his theory unsatisfactory? Were there errors in his reasoning or some problematic aspects?
- did Laplace's theoretical work resolve the needs of empirical science of his day (especially in astronomy)?
This is a non-exhaustive list of some questions (other contribution are also welcome).
p.s. the english translation of the four books is freely available online.