meeus

Overview ¶

Meeus implements algorithms from the book "Astronomical Algorithms" by Jean Meeus.

It follows the second edition, copyright 1998, with corrections as of August 10, 2009.

It requires Go 1.1 or later.

Library Goals ¶

Jean Meeus's book has long been respected as a broad-reaching source of astronomical algorithms, and many code libraries have been based on it. This library will be distinct in several respects, I hope.

First of all it is in the Go language, a programming language new enough that it well postdates the book itself. Go has many advantages for a large and diverse library such as this and it is a fine language for for scientific computations. I hope that a Go implementation will prove relevant for some time in the future.

Next, this library attempts fairly comprehensive coverage of the book. Each chapter of the book is addressed, and in the very few cases where there seems no code from the chapter that is applicable in Go, similar and more appropriate techniques are at least discussed in documentation. If meaningful, examples are given as well.

While this library attempts fairly comprehensive coverage of the book, it does not attempt to present a complete, well rounded, and polished astronomy library. Such a production-quality astronomy library would likely include some updated routines and data, routines and data from other sources, and would fill in various holes of functionality which Meeus elects to gloss over. Such a library could certainly be derived from this one, but it is beyond the scope of what is attempted here.

Thus, this library should represent a solid foundation for the development of a broad range of astronomy software. Much software should be able to use this library directly. Some software will need routines from additional sources. When the API of this library begins to present friction with that of other code, it may be time to fork or otherwise derive a new library from this one. Please feel free to do this, respecting of course the MIT license under which this software is offered.

Package Contents ¶

By Go convention, each package is in its own subdirectory. The "subdirectories" list of this documentation page lists all packages of of the library. Each package also corresponds to exacly one chapter of the book. The package documentation heading references the chapter number and a cross reference is given below of chapter numbers and package names.

Within a chapter of the book, Meeus presents explanatory text, numbered formulas, numbered examples, and other exercises. Within a package of this library, there are library functions and other codified definitions; there are Go examples which appear in documentation and which are also evaluated and verified to produce correct output by the go test feature; and there is test code which is neither part of the API nor the documentation but which verified by the go test feature.

The "API", or choice of functions to implement in Go, covers many of Meeus's numbered formulas and covers the algorithms needed to work most of the numbered examples. The correspondence is not one-to-one, but often "refactored" into functions that seem more idiomatic to Go. This is set as the limit of the API however, and thus the limit of the functionality offered by this library.

Each numbered example in the book is also translated to a Go example function. This typically shows how to use the implemented API to compute the results of the example. As the go test feature validates these results, the examples also serve as baseline tests of the correctness of the API code. Relevant "exercises" from the book are also often implemented as Go examples.

A few packages remain incomplete. A package is considered complete if it implements all major formulas and algorithms and if it implements all numbered examples. For incomplete packages, the package documentation will describe the ways in which it is incomplete and typically give reasons for the incompleteness.

In addition to the chapter packages, there is a package called "base". This contains a few definitions that are provided by Meeus but are of such general use that they really don't belong with any one chapter. The much greater bulk of base however, are functions which Meeus does not explicitly provide, but again are of general use. The nature of these functions is as helper subroutines or IO subroutines. The functions do not offer additional astronomy algorithms beyond those provided by Meeus.

Identifiers ¶

To more closely follow the book's use of Greek letters and other symbols, Unicode is freely used in the source code. Recognizing that these symbols are awkard to enter in many environments however, they are avoided for exported symbols that comprise the library API. The function Coord.EclToEq for example, returns (α, δ float64) but of course you can assign these return values to whatever variables you like. The struct Coord.Equatorial on the other hand, has exported fields RA and Dec. ASCII is used in this case to simplify using these symbols in your code.

Some identifiers use the prime symbol (ʹ). That's Unicode U+02B9, not the ASCII '. Go uses ASCII ' for raw strings and does not allow it in identifiers. U+02B9 on the other hand is Unicode category Lm, and is perfectly valid in Go identifiers.

Unit types ¶

An earler version of this library used the Go type float64 for most parameters and return values. This allowed terse, efficient code but required careful attention to the scaling or units used. Go defined types are now used for Time, RA, HourAngle, and general Angle quantities in the interest of making units and coversions more clear. These types are defined in the external package github.com/soniakeys/unit.

Sexagesimal formatting ¶

An earlier version of this library included routines for formatting sexagesimal quantities. These have been moved to the external package github.com/soniakeys/sexagesimal and use of this package is now restricted to examples and tests.

Meeus packages and the sexagesimal package both depend on the unit package. Meeus packages do not depend on sexagesimal, although the Meeus tests do.

Chapter Cross-reference ¶

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Chapter                                                 Package

1.  Hints and Tips                                      hints
2.  About Accuracy                                      accuracy
3.  Interpolation                                       interp
4.  Curve Fitting                                       fit
5.  Iteration                                           iterate
6.  Sorting Numbers                                     sort
7.  Julian Day                                          julian
8.  Date of Easter                                      easter
9.  Jewish and Moslem Calendars                         jm
10. Dynamical Time and Universal Time                   deltat
11. The Earth's Globe                                   globe
12. Sidereal Time at Greenwich                          sidereal
13. Transformation of Coordinates                       coord
14. The Parallactic Angle, and three other Topics       parallactic
15. Rising, Transit, and Setting                        rise
16. Atmospheric Refraction                              refraction
17. Angular Separation                                  angle
18. Planetary Conjunctions                              conjunction
19. Bodies in Straight Line                             line
20. Smallest Circle containing three Celestial Bodies   circle
21. Precession                                          precess
22. Nutation and the Obliquity of the Ecliptic          nutation
23. Apparent Place of a Star                            apparent
24. Reduction of Ecliptical Elements from one Equinox   elementequinox
    to another one
25. Solar Coordinates                                   solar
26. Rectangular Coordinates of the Sun                  solarxyz
27. Equinoxes and Solstices                             solstice
28. Equation of Time                                    eqtime
29. Ephemeris for Physical Observations of the Sun      solardisk
30. Equation of Kepler                                  kepler
31. Elements of Planetary Orbits                        planetelements
32. Positions of the Planets                            planetposition
33. Elliptic Motion                                     elliptic
34. Parabolic Motion                                    parabolic
35. Near-parabolic Motion                               nearparabolic
36. The Calculation of some Planetary Phenomena         planetary
37. Pluto                                               pluto
38. Planets in Perihelion and in Aphelion               perihelion
39. Passages through the Nodes                          node
40. Correction for Parallax                             parallax
41. Illuminated Fraction of the Disk and Magnitude      illum
    of a Planet
42. Ephemeris for Physical Observations of Mars         mars
43. Ephemeris for Physical Observations of Jupiter      jupiter
44. Positions of the Satellites of Jupiter              jupitermoons
45. The Ring of Saturn                                  saturnring
46. Positions of the Satellites of Saturn               saturnmoons
47. Position of the Moon                                moonposition
48. Illuminated Fraction of the Moon's Disk             moonillum
49. Phases of the Moon                                  moonphase
50. Perigee and apogee of the Moon                      apsis
51. Passages of the Moon through the Nodes              moonnode
52. Maximum declinations of the Moon                    moonmaxdec
53. Ephemeris for Physical Observations of the Moon     moon
54. Eclipses                                            eclipse
55. Semidiameters of the Sun, Moon, and Planets         semidiameter
56. Stellar Magnitudes                                  stellar
57. Binary Stars                                        binary
58. Calculation of a Planar Sundial                     sundial