From NASA, 1963, by William C. Strack, Wilbur F. Dobson, and Vearl N. Huff

  As described herein, this code is designed to operate on an IBM 704 computer that has an 8000 word (8 K) memory and at least 1 K of drum. 

Even so constrained it includes means of changing coordinate base when approaching asymptotes inducing loss in numerical accuracy, variable step size control, etc.

Takes me back to when I lived and breathed such code for early geophysical and remote sensing work.

Love seeing stuff like this. The corrections for an oblate spheroid threw me for a loop at first, until I realized "yeah, of course". I've only ever played around with ideal bodies when simulating the n-body problem (sounds a bit raunchy...) so never even considered the fact that a rotating planet isn't perfectly spherical.

Idle question: in the days before TeX, when manuscripts like this were hammered out on Remington office typewriters, how did authors handle symbols?

In this manuscript for example you can see that power superscripts are really just regular numbers typed at an offset (perhaps rotating the paper around the platen one notch instead of the two that would be a whole line feed). But what about the vectors and the giant sigma? All hand drawn over the top of a typed manuscript?