Was Keplers version of the equation too inaccurate to use for problems in the book?
No, for your last homework problems, Kepler’s version is fine, although some problems explicitly call for Newton’s generalized form. Usually it will be clear from context which one to use. It’s hard to tell when you’re looking for an “exact” answer (i.e. the orbit changes a little) vs. a general answer (i.e. the change in orbit is very small and therefore negligible). Usually you can tell from context what accuracy of answer is called for, but indeed sometimes there may be (usually unintended) ambiguities. If in doubt on a test about what’s needed, state your assumptions. If your answer is correct based on your assumptions, you will get full points.
