This is a lecture summarizing Taylor's Chapter 8 - Two-body Central-Force Problems. This is part of a series of lectures for Phys 311 & 312 Classical Mechanics I & II for physics majors taught at the University of Tennessee, Knoxville. This is from one cold take of a physics lecture and is not heavily edited.
If you would like to review these topics at an introductory level please see videos for introductory classical mechanics from 2023
https://www.youtube.com/playlist?list=PLb169AflJA0FmT7y9DgA5r0Safuzi9utq
or older videos from 2022
https://www.youtube.com/playlist?list=PLb169AflJA0FuePIIlFaopJMpN0AkpRmu
Both of those playlists follow the OpenStax University Physics textbook.