I was in highschool in the late 1960’s, and stories of Goddard’s team losing rocket after rocket were still main-stream rocket science. Your claim to be able to solve the multi-body equations Ms. Johnson would have had to do just struck me as quite a ... feat.
A) I didn't claim that; and
B) She didn't solve any multi-body equations so far as I can tell. (Two is not considered multi-body.)
The real problem is figuring out the effect of atmospheric drag; and from what I can tell they had data upon which to build their model.
Papers that include statements like:
for small angles x:... aren't real mathematical papers. They're intended to impress the unwashed.sin x = x
cos x = 1
ML/NJ