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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]

#21

Post by mr_mitm »

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".

When I was a grad student at the Institute for Theoretical Physics in Heidelberg in 2014, they still had a few of these secretaries who would type out handwritten manuscripts by professors who couldn't or wouldn't write LaTeX. Maybe they still do.

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

#22

Post by keepamovin »

ddahlen wrote: post #19

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. Sou…

That is cool! I encourage you to post as a Show HN with a comment explaining more if you want

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

#23

Post by adrian_b »

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…

The code appears to use in some places GK2M, which is the Newtonian constant of gravity, and in other places SQRDK, which is inappropriately described as a "gravitational constant", but it actually is the mass of the Sun expressed in some special units.

Newton's constant is known only with a very high uncertainty, i.e. a very low precision.

For the great bodies of the Solar System, e.g. the Sun and the planets, one knows with a high accuracy the product between their mass and Newton's constant, because that can be measured by the force with which they attract a body of known mass, e.g. an artificial satellite or an interplanetary probe.

Computing their mass in kilograms would be pointless in most cases, because that would introduce great uncertainties in the computations. So for the Sun and the planets one expresses their masses by the products between their mass and Newton's constant, whenever that is possible, i.e. whenever one needs to compute their attraction force exerted upon a small object.

Wikipedia names the product mass-Newtonian constant as "the standard gravitational parameter of a body", but I believe that this is a misleading name, because this product is just the mass of the body expressed in different (non-SI) units. Expressing a mass by its product with the Newtonian constant is not different from expressing the mass in pounds instead of kilograms. Using the Newtonian constant instead of some random unit conversion factor just has the advantage of removing the uncertainties from some expressions computing forces of gravity.

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

#24

Post by wiz21c »

ddahlen wrote: post #19

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. Sou…

I'm interested. Could you give examples ?

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

#25

Post by ddahlen »

wiz21c wrote: post #24
ddahlen wrote: post #19

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. Sou…

I'm interested. Could you give examples ?

https://www.cambridge.org/core/journals/international-astron...

Here is a heavily used method in astronomy, this involves a higher order polynomial expansion than RK4.

This method has been extended a few times, my code uses a variation of it, and I know of several other projects which are also descended from it.

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