One of the interesting things about Mercury, is that general relativity has a non-negligible effect on its dynamics (the famous "perihelion precession" that Einstein explained). What the authors did in this paper is run a number of long term simulations of the Solar System with general relativity --- but then they switched it off at a random time. What they find is that after switching off general relativity the Solar System goes unstable shortly thereafter. So the stability of the Solar System is highly dependent on general relativity.
As a side note, the second author on the paper is Hanno Rein, who wrote Rebound [2], which is a very cool state of the art gravitational simulator. If you ever want to play around with gravitational dynamics, that's what I'd recommend using. (And that's what they use in this paper.)
[1]: This is not terribly surprising because it turns out that nearly every dynamical system with more than three bodies is only marginally stable on a timescale of order its own lifetime.
https://github.com/hannorein/rebound
One of my all-time favorite figures is Fig. 1 of this paper of theirs describing one of the integrators used in Rebound:
It's a well established fact that numerical integration methods either gain or lose energy (in particular, the Runge-Kutta family is known to lose energy over time). For celestial mechanics simulations, a special class of numerical integration methods called "symplectic integrators" are used and their purpose is to conserve energy and angular momentum.
> but if you do any adjustments to correct it, that is a kind of fudge not based in true physics.
When you are numerically integrating differential equations that model physical phenomena, you're not doing "true physics" but an approximation thereof.
And an approximation that makes Earth drift 70 km per year or Saturn's moons drift out of orbit in a few hundred years is a very bad approximation by scientific standards.
The methods used for celestial mechanics calculations need to be precise over thousands to millions of years. And the way they work is to "fudge" with the numerical methods to preserve energy and angular momentum. It's a much better approximation of "true physics" than your toy simulation.
Your assumption that the issues are due to floating point errors is incorrect. 64 bit double precision is millimeter accurate to the orbit of Neptune. That's good enough for scientific applications.
If you're interested in this, you could take a look at this scientific grade N-body simulator and the methods it uses: https://github.com/hannorein/rebound
https://github.com/hannorein/rebound
There's some tutorials that come with it. It can also read data from JPL's ephemerides to calculate orbits of various planets and minor bodies in the Solar System. It has a couple of different integrators (some symplectic, some not), but one of them (IAS15) is new and (as far as I know) the best for long-term integrations of Solar-System-like systems.
Also if you're interested in studying the long-term evolution of hierarchical triples, I wrote a Python package to study that:
https://github.com/joe-antognini/kozai
As far as star charts, you can do things like that with AstroPy. If you want the coordinates of stars, look into astropy.vo, and then if you want to plot them, you can do that with some of the functions in astropy.wcs.
# curl https://www.chillingeffects.org/notices/10275257 | grep github
https://help.github.com/articles/dealing-with-non-fast-forward-errors/
https://github.com/Zizzamia/ng-tasty
https://github.com/zen-kernel/zen-kernel
https://github.com/yahoo/pure/releases/
https://github.com/yahoo/pure
https://github.com/YabataDesign/afterglow-theme
https://github.com/wet-boew/wet-boew
https://github.com/wearefractal/glob-watcher
https://github.com/wanderlust/wanderlust
https://github.com/thombergs/wicked-charts
https://github.com/Thibauth/python-pushover
https://github.com/tcnksm/vagrant-pushover
https://github.com/substack/pushover
https://github.com/SteveSanderson/knockout-es5
https://github.com/sps/pushover4j
https://github.com/sensu/sensu-community-plugins/blob/master/handlers/notification/pushover.rb
https://github.com/schneems/wicked/wiki/Testing-Wicked-with-RSpec
https://github.com/schneems/wicked
https://github.com/satyr/coco
https://github.com/satyr
https://github.com/sampsyo/beets/issues/546
https://github.com/rust-lang/cargo
https://github.com/rniemeyer/knockout-delegatedEvents
https://github.com/rniemeyer/knockout-amd-helpers
https://github.com/qbit/node-pushover
https://github.com/openSUSE/wicked/issues/432
https://github.com/openSUSE/wicked
https://github.com/Nuku/Flexible-Survival/blob/master/Stripes/Candy
https://github.com/Netflix/Lipstick
https://github.com/nemomobile/lipstick
https://github.com/mrmrs/colors
https://github.com/mirage
https://github.com/mileszs/wicked_pdf/issues/78
https://github.com/LubosD/darling
https://github.com/laprice/pushover
https://github.com/kryap/php-pushover
https://github.com/krisselden/broccoli-sane-watcher
https://github.com/Knockout-Contrib/Knockout-Validation
https://github.com/knockout/knockout
https://github.com/knockout
https://github.com/kirang20/wgxp-java-rosa
https://github.com/jreese/znc-push/blob/master/doc/pushover.md
https://github.com/jnwatts/pushover.sh
https://github.com/jfinkels/flask-restless/
https://github.com/jasonlewis/resource-watcher
https://github.com/huxi/lilith
https://github.com/hannorein/rebound
https://github.com/gregghz/Watcher
https://github.com/feuerbach/tasty
https://github.com/facebook/rebound-js
https://github.com/facebook/rebound
https://github.com/erniebrodeur/pushover
https://github.com/entertailion/Fling/blob/master/README.md
https://github.com/enkydu/raspi_runner
https://github.com/dyaa/Laravel-pushover
https://github.com/danesparza/Pushover.NET
https://github.com/crazed
https://github.com/callmenick/css-loaders-spinners-2/tree/master/js
https://github.com/callmenick/css-loaders-spinners-2
https://github.com/allure-framework/allure-core
https://github.com/abrt/satyr
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