Both these books are on my book shelf and are very good. Bate et. al. especially since it is a Dover book and very affordable.
The book that is always on my DESK is "Fundamentals of Astrodynamics and Applications" by Vallado. There is also a website with code from the book for Hohmann and Lambert transfers among other things. <self-promotion>This has been indispensable in creating my Unity Asset "Gravity Engine".</self-promotion>
The article mentions "few known exact solutions". There are actually quite a number. Most are from after 1950.
Cambridge University Press has two good books:
Exact Spacetimes in Einstein's General Relativity (Griffith & Podolsky)
- good readable (if you speak GR) account of the more common solutions
Exact Solutions of Einstein's Feild Equations (Stephani, Kramer, MacCallum, Hoenstelaers, Herlt)
- encyclopedic, authoritative and mathematical. In my case an aspirational purchase
L4 and L5 are stable when the smaller mass is less than about 0.0385 times the larger mass [1]. This means e.g. a typical binary star system would not have stable L4/L5 points. The reference [1] works through this in careful detail and is an excellent reference on this topic.
[1] Solar System Dynamics, Murray and Dermott, Cambridge University Press.
I've been on a Math journey since I retired a couple of years ago and I agree with all the books mentioned that I know and look forward to picking up some of the one I do not know. I agree baby Rudin is essential, but I find it tough going.
Some books I liked for self study because they have answers:
Introduction to Analysis, Mattock.
Elementary Differential Geometry, Pressley.
There is also recently Needham's Visual Differential Geometry and Forms, which is great.
There is Geometric Algebra for Physicists by Doran and Lasenby (2003). It recasts mechanics, E&M up to gauge theories and GR into geometric algebra. I stalled out at mechanics but I've now taken it off the Tsundoku pile and may give it another chance.
"The discovery still leaves much of the universe undetected. About 85 per cent of its matter is thought to be "dark matter" — that which is undetectable using ordinary methods."
If I understand the abstract, it reports finding "Ωb=0.051+0.021−0.025h−170 (95 per cent confidence; h70 = H0/(70 km s−1 Mpc−1) " which I think means 5% of the total (mass+dark matter+dark energy), since cosmology assumes Omega total = 1.0
My perception (as a lapsed PhD physicist) is the community takes on a new formalism when it has to i.e. there are new results that can only be derived with the new formalism. A formalism that allows slightly better derivation of existing results does not attract attention. Twistors, Clifford algebras and other things seem to have not met this hurdle so far.
I took that idea to its extreme and released "Geodesic Asteroids" on iOS (free) a couple of years ago. You can play on the 2D map or an embedded torus. There is also an old blog post I wrote at the time: http://nbodyphysics.com/blog/2015/03/06/asteroids-on-a-torus...
"It is certainly true that there are aspects of relativity that are counterintuitive, not only to retired engineers but also to many physicists."