It looks like they chose to use the "universal gravitational constant" "k" instead of Newton^s constant, "G": p.23, "k^2 = universal gravitational constant, 1.32452139x10^20, m^3/(sec^2)(sun mass units)"
But the value and unit of "k" given in the Wikipedia page is different. Do you know what NASA document means by "universal gravitational constant" in modern sense?
segfault99 · 44m ago
My first thought was to upload the PDF to Qwen3 and ask it to reimplement in Python using NumPy, Astropy, etc. Have to work on the day job, but could be some educational fun learning and Jupyter plots in my near future. Anyway, the generated code looks promising and contains the requisite green tick and bar graph emojis, so what's not to like?
kjellsbells · 2h ago
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?
jasperry · 2h ago
Yes, I believe they're drawn or stenciled in. Some amount of care has been taken here to produce a more professional-looking result, but you can find plenty of old typed papers where math is obviously handwritten in. Like John Nash's thesis: https://library.princeton.edu/sites/g/files/toruqf6021/files...
defrost · 20m ago
> how did authors handle symbols?
Mostly they didn't .. it was handballed to the secretaries of the math and physics typing pool who used stencils, high end typewriters, and other template mechanisms.
A good many such secretaries were reasonably talented math and physics graduates themselves who had limited opportunity to be hired to do "a man's work".
coderenegade · 2h ago
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.
defrost · 2h ago
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.
I think "k" was also known as "Gaussian gravitational constant" https://en.wikipedia.org/wiki/Gaussian_gravitational_constan...
But the value and unit of "k" given in the Wikipedia page is different. Do you know what NASA document means by "universal gravitational constant" in modern sense?
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?
Mostly they didn't .. it was handballed to the secretaries of the math and physics typing pool who used stencils, high end typewriters, and other template mechanisms.
A good many such secretaries were reasonably talented math and physics graduates themselves who had limited opportunity to be hired to do "a man's work".
Takes me back to when I lived and breathed such code for early geophysical and remote sensing work.