Some of my Programs in Physics and Astronomy, and more

Astronomy Programs

Sun, Moon, and Planets

These programs are based on the VSOP87 theory, Variations séculaires des orbites planétaires. VSOP was developed and is maintained (updated with the latest data) by the scientists at the Bureau des Longitudes in Paris.

NEW: Here you can run the programs interactively: Interactive Astro Programs.

hvfSunMoonPlanets.zip is a collection of Python3-programs to show data for Sun, Moon, the Planets, Solstices, Perihels, Moon Phases and Perigees.
Longitude, latitude, right ascension, declination, altitude, azimut, hour angle, time of rising, transition, and setting and other data are calculated for Sun, Moon, and the planets.
It contains the following Python files:

• SunMoonLBR-TZ.py displays the data for Sun and Moon and a given location, date, time, and timezone. It implements the full set of parameters of VSOP87C in LBR representation for the Earth (and therefore the Sun) and the parameters in Jean Meeus' book Astronomical Algorithms, first edition 1991, for the Moon. The difference deltaT between Terrestrial Time TT (or TDT) and Universal Time Coordinated (UTC) is taken into account.
  VSOP87C shows the parameters for heliocentric longitude, latitude (both in degrees), and radius (in Astronomical Units).
  For known locations, the local timezone is used including the automatic change between standard time and daylight saving time where applicable.
  The timezones for the stored known locations are included. For other locations, either a timezone or a Zone offset (in hours East of Greenwich) can be speficied. A list of the known timezones can be produced on request. The new options are shown here: Show SunMoonLBR-TZ.py help .
  
  
• SunMoonXYZ-TZ.py displays the same data as SunMoonLBR-TZ.py but it uses the full set of parameters of VSOP87D in XYZ representation. The results of both programs are identical. Here is the output for an arbitrary day like Easter Sunday 2021 at noon CEST in Zurich: Easter Sunday 2021
  
  
• SunPlanetsLBR-TZ.py displays the data as SunMoonLBR-TZ.py and in addition the data for the 7 Planets (Mercury, Venus, Mars, Jupiter, Saturn, Uranus, Neptune) including the angular distances between the Sun and all Planets, based on the VSOP87C LBR parameters.
  Here is the output for the Great Conjunction of December 21, 2020 at 1720h CET.
  
  
• SunPlanetsXYZ-TZ.py displays the same data as SunPlanetsLBR-TZ.py but uses the VSOP87D XYZ parameter set.
  
  

Sun Solstices and Perihelions

• Solstice.py displays date and time of the four solstices and equinoxes for the year(s) given as parameter, either as UTC or TDT.
  Here are the values for 2021 and 2022: Solstices in 2021 and 2022
  
  
• Perihel.py shows dates, times and radius (au, km) of the Sun perihelions and aphelions of the year(s) given as parameters in UTC.
  Years can be specified as single years, 2021, or as a range of years, 2021-2030. The allowed range is 1601 through 2500.
  In the years before 1900, the perihelion occurs either at the end of December or the beginning of January. We stick to a consistent time scale such that each year starts with January, and perihelions in December show date and time in the preceding year. Aphelions are always in the specified year.
  Here are the values for 2021 and 2022:
  

  $ Perihel.py 2021 2022
  
  ./Perihel.py Version 1.0 hvf 30.03.2021 based on VSOP87 Ephemerides
  
   Perihelion UTC                          Aphelion   UTC
   Date       Time  Radius(au) Radius(km)  Date       Time  Radius(au) Radius(km) 
   2021-01-02 13:51 0.98325706 147093162   2021-07-05 22:27 1.01672922 152100525
   2022-01-04 06:54 0.98333654 147105052   2022-07-04 07:10 1.01671536 152098453
                  

  And here the values for 1896 until 1900; we see that the perihelion date meanders between December and January - the calendar years 1896 and 1898 have two perihelions, whereas in 1897 and 1899 there is none. But each year has one aphelion, of course.
  

  $ Perihel.py  1896-1900
  
  ./Perihel.py Version 1.0 hvf 30.03.2021 based on VSOP87 Ephemerides
  
   Perihelion UTC                          Aphelion   UTC
   Date       Time  Radius(au) Radius(km)  Date       Time  Radius(au) Radius(km) 
   1896-01-01 18:16 0.98321777 147087285   1896-07-03 20:50 1.01675230 152103978
   1896-12-31 10:15 0.98327822 147096327   1897-07-02 03:38 1.01676740 152106237
   1898-01-02 12:14 0.98326597 147094495   1898-07-02 15:02 1.01670900 152097502
   1898-12-31 22:03 0.98323968 147090562   1899-07-04 08:57 1.01678777 152109284
   1900-01-02 06:25 0.98326336 147094105   1900-07-02 13:23 1.01679003 152109622
                  

  Here is the complete list of all perihelions and aphelions from 1601 (i.e. December 1600) until 2500: Perihelions and Aphelions from 1601 until 2500.
  

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Moon Phases, Perigees, Ascending and Descending Nodes, and Maximum Declinations

• MoonPhases.py shows dates and times of all moon phases of the year(s) given as parameters, either as UTC or TDT. A second table shows the dates and times of New Moon and Full Moon together with the distance from the Earth (center to center) and an indicator for Super Moon, ++, (distance less than 360'000 km) and Mini Moon, --, (distance greater than 405'000 km).
  Here are the values for 2021 and 2022: Moon Phases in 2021 and 2022
  

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• MoonPeri.py shows dates, times and distance (km) of all moon perigees and apogees of the year(s) given as parameters, either as UTC or TDT.
  An indicator for Super Moon, ++, (distance less than 360'000 km) and Mini Moon, --, (distance greater than 405'000 km) is also shown.
  Here are the values for 2021 and 2022: Moon Perigees and Apogees in 2021 and 2022
  

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• MoonNodes.py shows dates and times when the Moon passes through the Ascending and Descending Nodes of the year(s) given as parameters, either as UTC or TDT.
  Here are the values for 2021 and 2022: Moon Asscending and Descending Nodes in 2021 and 2022
  

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• MoonDecli.py shows dates and times when the Moon reaches its Maximum Declination (North and South) of the year(s) given as parameters, either as UTC or TDT.
  Here are the values for 2021 and 2022: Moon Maximum Declinations in 2021 and 2022
  

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• MoonSynopsis.py combines the output of the four preceding programs into one list, sorted by date and time of the events: Full Moon and New Moon, Perigee and Apogee, Ascending and Descending Nodes (passing the Ecliptic, Latitude zero), and Maximum Declination (angle to the Equator) North and South.
  Here are the values for 2021 and 2022: Moon Synopsis for 2021 and 2022
  

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Planet Events: Conjunctions, Oppositions, Elongations

• Planets.py shows dates and times of events of a set of specified or all planets. Events are Inferior Conjunction (minimal distance to Earth) for Mercury and Venus, Superior Conjunction (planet behind the Sun, maximal distance to Earth), Opposition (for the outer planets, minimal distance to Earth), and Maximum Elongation for Mercury and Venus (maximum angle between Sun and planet), where Eastern Elongation means that the planet is visible in the evening, and Western Elongation for the morning.
  Here are the values for 2021, 2022, and 2023: Planet Events for 2021 until 2023
  

Programs in Physics

Nfold coupled pendulum

The harmonic oscillator is a standard problem in elementary physics, and a simple pendulum is a populaar application of the harmonic oscillator as long as the amplitude is small such that non-linear effects can still be neglected.
The problem of two or more pendulums hanging on each other is far more complicated. Analytical solutions, even for small amplitudes, are hard to find.
My program Nfold-pendulum.py solves this problem numerically. Using the Lagrange formalism, numerical integration of the equation of motion is performed and a graphical display is produced. The point masses are connected with massless rods. Units are kg for the masses, meter for the rods, and degrees for the angles and degrees/sec for the angular velocities.
The number of pendulums, N, is unlimited.
The gravitational constant g is set to 10 m/s².
The total energy shown on the display stays constant, this means that the calculations do not lose precision.

Nfold-pendulum.zip contains the code.

This video shows the standard case

        $ Nfold-pendulum.py 2 2 1 1 2 180 -90 0 0
        

And here is a more complicated case with six coupled pendulums

        $ Nfold-pendulum.py 6 2 1 2 1 2 1 1 1 1 1 1 1 180 180 180 180 180 -90 0   0   0   0   0   0
                              <- arms  -> <- masses-> <-      angles       -> <- angular veloc.  ->

        

FEHASHMAC

fehashmac is a collection of 52 publicly known hash algorithms integrated into a command-line utility. FEHASHMAC also contains a set of known test vectors and results for each algorithm such that the correct implementation for each hardware platform and compiler version can directly be verified.

See the README for more information. The current release is also available here.

SUDOKU

Sudoku is a well-known pastime that appealed to my penchant for recursive algorithms. I therefore started in 2005 to write a sudoku PERL script that will be capable to solve any square sudoku problem with either square or rectangular subsets or subsets of any shape. The maximum dimension is limited to 26x26.
Diagonals are also supported.

The script is written in PERL5. Once the input parameters are verified, a Postscript file may be produced with the input configuration for printout, possibly later converted to PDF.