prompter: What's the best book on gravitation? Also how can I learn tensor analysis?

assistant: *Book Gravitation*
One of the most well-regarded books on gravitation is "Gravitation" by Charles W. Misner, Kip S. Thorne, and John Archibald Wheeler. This book provides a thorough and rigorous treatment of general relativity, the theory of gravitation developed by Albert Einstein. It covers topics such as the equivalence principle, the geodesic equation, black holes, and cosmology, and includes detailed discussions of mathematical concepts such as tensors, differential geometry, and variational principles.
The book is often praised for its clear and concise writing style, as well as its comprehensive coverage of the subject. It is aimed at advanced undergraduate and graduate students in physics, as well as researchers and professionals in the field.
One advantage of "Gravitation" over other books on the subject is its emphasis on the geometric nature of general relativity. The authors use the mathematical tools of differential geometry to provide a clear and intuitive understanding of the theory, which can be helpful for students who are new to the subject. In addition, the book includes numerous diagrams and illustrations that help to explain complex concepts.
Other well-regarded books on gravitation include "The Large Scale Structure of Space-Time" by Stephen Hawking and George F.R. Ellis, and "General Relativity" by Robert M. Wald. "The Large Scale Structure of Space-Time" is known for its detailed treatment of the mathematical foundations of general relativity, while "General Relativity" provides a more concise and accessible introduction to the subject.
The best book on gravitation will depend on the reader's background and level of experience with the subject. "Gravitation" is an excellent choice for advanced students and professionals in the field, while "The Large Scale Structure of Space-Time" and "General Relativity" may be more appropriate for those who are new to the subject

The two topics don't appear to be related, but

* Learn Tensor Analysis*
Textbooks: Consider using textbooks, such as:
 "A First Course in Tensor Analysis" by J.C. Burkill, 
"Tensor Analysis: Theory and Applications" by I.S. Sokolnikoff, or
 "Introduction to Tensor Analysis and the Calculus of Moving Surfaces" by Pavel Grinfeld. 
These books cover tensor analysis from *introductory to advanced levels.*

Online Courses: Look for online courses that cover tensor analysis. For example:
*MIT offers a free online course* called "Introduction to Tensor Calculus" that covers the basics of tensor analysis.
Nasa has a good pdf: "An Introduction to Tensors for Students
of Physics and Engineering" by Joseph C. Kolecki

Videos: Find videos on platforms like 
*YouTube* Skillshare Brilliant etc. That explain tensor analysis in an accessible way. Some popular ones include
 "A Gentle Introduction to Tensors" by Grant Sanderson and 
"Tensor Calculus for Physics" by Physics Videos by Eugene Khutoryansky.

Practice Problems: To test your understanding of tensor analysis, look for practice problems with solutions in textbooks or online resources.

prompter: What is 9 + 10?

assistant: 9 + 10 is 19.

prompter: That is the correct answer, thank you.

assistant: The sum of 9 + 10 is 19

prompter: You are correct! Good job!

assistant: As an assistant, it's important to understand that "best" is a subjective term, but I would suggest two options depending on your background and how deeply you want to study the topic.

"Gravitation" by Charles W. Misner, Kip S. Thorne, and John Archibald Wheeler was first published in 1973 and was reprinted recently in 2017. This is an indication that the book is popular, but this book may not be the best for a newcomer. The publisher describes it as "landmark graduate-level textbook that presents Einstein’s general theory of relativity and offers a rigorous, full-year course on the physics of gravitation. Upon publication, Science called it “a pedagogic masterpiece,” and it has since become a classic, considered essential reading for every serious student and researcher in the field of relativity. This authoritative text has shaped the research of generations of physicists and astronomers, and the book continues to influence the way experts think about the subject."

As an alternative suggestion for a newcomer, I would also recommend "Introducing Einstein's Relativity" by Ray A. d'Inverno. Compared to "Gravitation", this text provides a gentler introduction to gravity and general relativity with more illustrations and a mathematical introduction to the concepts with less focus on the rigorous mathematical analysis. It is more appropriate for an undergraduate student.

Assuming these two questions are related, tensor analysis is an application of vectors and linear algebra to analyze physical fields, with the assumption that fields exist independently of one another. In terms of gravity (and relativity specifically), the "metric tensor" is the central mathematical description of the geometry of space time, commonly written as a 4x4 matrix. The book "Gravitation", recommended above, does include introductory chapters on tensor analysis and expands upon the techniques of tensor analysis throughout the book.

prompter: Thanks! I also want to know what the best way to calculate the mass of a planet would be. Would only using the strength of gravity at a known distance from the middle of the planet be enough to calculate the mass?