ANALEMMA
Evaluating the Equation of Time

ANALEMMA is a FORTRAN77 program which evaluates the equation of time, based on a C program by Brian Tung.

The program can compute and plot the equation of time, the declination, and an analemma curve for various orbital parameters. The analemma is the curve traced by the position of the sun, measured at clock noon, over a year.

The program creates data and command files which must be processed by the GNUPLOT program:

        gnuplot < analemma_commands.txt
      

Usage:

analemma ecc lon obliq

• ecc, the eccentricity;
• lon, the perihelion longitude in degrees;
• obliq, the axial obliquity in degrees;

The program with no options uses the following default values:

• eccentricity = 0.01671;
• longitude of perihelion = 1.347 radians = 77.18 degrees;
• axial obliquity = 0.4091 radians = 23.44 degrees;

Licensing:

The computer code and data files described and made available on this web page are distributed under the GNU LGPL license.

Languages:

ANALEMMA is available in a C version and a C++ version and a FORTRAN90 version and a MATLAB version and a Python version.

Related Data and Programs:

CALENDAR_RD, a C++ program which computes the representation of a given date in a number of calendrical systems, by Edward Reingold, Nachum Dershowitz.

CALPAK, a FORTRAN90 library which makes various calendar calculations;

DATES, a dataset directory which contains lists of dates in various calendar systems.

GNUPLOT, FORTRAN77 programs which illustrate how a program can write data and command files so that gnuplot can create plots of the program results.

WEEKDAY, a FORTRAN77 library which determines the day of the week corresponding to a given date, such as 14 October 1066, Julian calendar, ... which was a Saturday.

Author:

Original C version by Brian Tung. FORTRAN77 version by John Burkardt.

Reference:

1. Brian Tung,
   Figure Eight in the Sky, a new perspective on an old fascination,
   Astronomical Games, August 2002,
   http://www.astronomycorner.net/games/analemma.html.

Source Code:

• analemma.f, the source code.
• analemma.sh, BASH commands to compile the source code.

Examples and Tests:

• analemma_data.txt the data file.
• analemma_commands.txt, the command file.
• analemma.png, the PNG file of the analemma, created by GNUPLOT.
• declination.png, the PNG file of the declination, created by GNUPLOT.
• eot.png, the PNG file of the equation of time, created by GNUPLOT.

List of Routines:

• MAIN is the main program for ANALEMMA.
• GET_UNIT returns a free FORTRAN unit number.
• S_TO_R8 reads an R8 value from a string.
• TIMESTAMP prints the current YMDHMS date as a time stamp.

You can go up one level to the FORTRAN77 source codes.