Two Body Problem Differential Equation help

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I was watching the video linked below. I am confused around part 32:50. The differential is being rewritten as the derivatives of two other quantities. This is where I get confused. What is the point of rewriting terms in a differential equation as derivatives of something else? I understand in the video how he rewrote the first term, but for the second term he introduces a quantity that I don't understand. Can anyone help?

Link: https://www.youtube.com/watch?v=Yc3l1MEvkO0&t=1985s