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A general Fortran code for solutions of problems in space mechanics [pdf]

jonathanadams.pro

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Re: A general Fortran code for solutions of problems in space mechanics [pdf]

#11

Post by jahewson »

defrost wrote: post #7
kjellsbells wrote: post #4

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 sig…

> 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".

Non-secretary women were not in short supply at NASA at this time though. The work of Virginia E. Morrell and Bonnie J. McBride a few years earlier, at this same research center springs to mind.

Re: A general Fortran code for solutions of problems in space mechanics [pdf]

#12

Post by scellus »

segfault99 wrote: post #6

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?

The combination of Fortran and AI here starts to be close to 2001. ;)

Re: A general Fortran code for solutions of problems in space mechanics [pdf]

#13

Post by ekelsen »

nyc111 wrote: post #8

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)" 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…

I think it's just units. From wikipedia: "and its value in radians per day follows by setting Earth's semi-major axis (the astronomical unit, au) to unity, k:(rad/d) = (GM)0.5·au−1.5."

the value given in the paper assumes the distance in meters I think.

Re: A general Fortran code for solutions of problems in space mechanics [pdf]

#14

Post by AIPedant »

nyc111 wrote: post #8

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)" 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…

It's just regular old G, defined in mass-of-sun units: https://en.m.wikipedia.org/wiki/Gravitational_constant (fourth item in the first table: NASA also uses meters whereas Wiki uses km)

Gauss's constant k is defined as sqrt(G), but for a while the international standard was to define k and then compute G as k^2, which is why NASA refers to it that way.

Re: A general Fortran code for solutions of problems in space mechanics [pdf]

#15

Post by fuzzfactor »

scellus wrote: post #12
segfault99 wrote: post #6

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?

The combination of Fortran and AI here starts to be close to 2001. ;)

You mean 2001 of 1969?

The X-files AI episodes of the '90's are about as close to 1969 as to today.

All anybody could do then was to use their imagination, but is it all that much different today?

Re: A general Fortran code for solutions of problems in space mechanics [pdf]

#16

Post by jensgk »

kjellsbells wrote: post #4

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 sig…

After the Remington era, I once used this :-) IBM Selectric typewriter math fonts, I found this description: https://www.duxburysystems.org/downloads/library/texas/apple...

Re: A general Fortran code for solutions of problems in space mechanics [pdf]

#17

Post by defrost »

jahewson wrote: post #11
defrost wrote: post #7

Earlier quoted context omitted.

> 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".

Non-secretary women were not in short supply at NASA at this time though. The work of Virginia E. Morrell and Bonnie J. McBride a few years earlier, at this same research center springs to mind.

There were some to be sure .. I wouldn't imply otherwise, none the less many existed that were not hired and most STEM heavy companies and institutions were very male biased.

(With the few and obvious exceptions such as Dame Vera Stephanie "Steve" Shirley's ventures)

FWiW I learnt a wee bit from Cheryl Praeger, Cathleen Morawetz, Robyn Owens, et al.

Re: A general Fortran code for solutions of problems in space mechanics [pdf]

#18

Post by fuzzfactor »

tiu wrote: post #9
kjellsbells wrote: post #4

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 sig…

Godement in his analysis exposition briefly talks about this, it was all hand drawn.

These look like the fonts from the IBM Selectric with the changeable typeballs.

When you needed a greek letter you had to stop there, change typeballs, type the greek letter, then put the regular typeball back on.

On the equations the big stuff would be drawn in by hand from stencils.

On a diagram it could be a mechanical (assisted) drawing that was labeled by typing the same font size, like sketch (a).

When you get to sketch (b) though, this one is a reduced photocopy of the original page that was typed on when labeling the mechanical drawing to begin with.

You can see the way that all of the equations and illustrations could very well be place-held in the text draft until a perfect equation or diagram could then be added later by cutting the proper size horizontal strip of paper containing the original drawing, and "pasting" it over the blank spot in the text where the figure goes. Before photocopying to arrive at the priceless original like this where you couldn't always tell where it was cut-and-pasted.

The Fortran printouts from the IBM line printer look like they could be pasted in both at full-size and photoreduced, on one page at page 20.

But a good typist could avoid that for most equations, they could blaze through the text but when an equation came up it took more time to get one equation right than to type many more pages of text.

As can be seen, it was obviously worth it :)

Re: A general Fortran code for solutions of problems in space mechanics [pdf]

#19

Post by ddahlen »

It is neat to see some of the old work done in the field, this looks like a pretty classic treatment of the topic. It looks like they were using a fourth-order Runge-Kutta integrator, which would likely limit long term integrations accuracy (though looks sufficient for their use case). Many algorithms I have seen typically use much higher order integration methods to beat down the accumulation of numerical error.

Source: Working on my PhD in orbital mechanics of asteroids/comets, here are my open source (python/rust) orbital integration tools: https://github.com/dahlend/kete

Re: A general Fortran code for solutions of problems in space mechanics [pdf]

#20

Post by mr_mitm »

segfault99 wrote: post #6

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?

Scipy implements similar algorithms, but delegates the heavy lifting to - you guessed it - Fortran. Example: https://github.com/scipy/scipy/blob/v1.16.1/scipy/integrate/...
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