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This text is published under the Creative Commons license CC-BY-ND.

Copyright (c) 2017 Jean Forget. All rights reserved.

The text is often (but irregularly) updated on Github. There are a French version and an English version. Since I am more at ease discussing astronomical subjects in French, the English version will lag behind the French one.

This text is an integral part of the module's distribution package. So you can read it on web pages generated from CPAN (http://search.cpan.org, https://metacpan.org, etc). But it is not used during the module installation process. So, I guess it will not appear in .deb or .rpm packages.

Why This Text? For Whom?

The main purpose of this text is to explain how the sunrises and sunsets are computed. These explanations are much too long to be included into the module's POD section.

For Whom? For Me

You may be surprised that the main person for whom I write this is myself. I write this text to remember which problems I have encountered while maintaining this module and how I fixed them. But mainly, I write this to build a detailed description of the precise iterative algorithm, because Paul Schlyter's explanations are not detailed enough for my taste and there is no compilable source available to check this algorithm (unlike the simple version without iteration.

For Whom? For The Next Module Maintainer

The second person for whom I write is the next module maintainer. I have read Neil Bowers' message about the module authors pledge. I agree with him and I declare that should I stop maintaing my modules for whatever reason, I accept that any volunteer can take charge of them.

What Neil did not explain, is that the new maintainer must obey a few criteria and must have three available resources to take over a module maintenance: be competent in Perl programming, have enough available time to work on the module and be enthusiastic enough to get around to it.

In the case of astronomical module, the competence in Perl programming is not enough, you must also be competent in astronomy. So, if you think you might maintain this module, first read the present text. If you understand why I bother about such and such question, if you can follow my train of thought with being lost, then you are competent enough. If you think I am playing Captain Obvious and if you have instant answers to my questions, then you are the ideal person which could maintain this module. If you do not understand what all this is about, and if sines and cosines put you off, do not consider working on this module's innards.

For Whom? For Bug Reporters

This text is also for those who think they have found a bug in the module or who want to offer an idea to improve the module. Maybe the bug is already known and is waiting for a fix. Maybe the bug was found and the fix is not successful. Maybe the proposed improvement contradicts some other functionality of the module.

For Whom? For Curious Users

Lastly, this text is aimed at any person curious enough to learn a few astronomical facts. I tried to steer away from overly complicated computations. Their place is in the Perl source, not in this text. Yet, you will find here simple computations and mathematical reasoning.

Remarks About The Style

Some chunks of this text appear as a series of questions and answers. This is not a FAQ. Rather, this is a elegant way to give a progressive explanation of some subject. This method has already been used by many other writers, especially Plato, Galileo and Douglas Hofstadter.

Other Remarks

In my explanations, I usually take the point of view of a person living in the Northern hemisphere, between the Tropic of Cancer and the Arctic Circle. For example, I will write that at noon, the sun is located exactly southward, although any schoolboy from Australia, New Zealand, South Africa, Argentina and similar countries perfectly know that at noon, the sun is northward.

In a similar way, 21st of March is called the vernal equinox or the spring equinox, even if it pinpoints the beginning of autumn in the Southern hemisphere.

But using politically correct sentences would yield convoluted phrases, which hinders the pedagogical purpose of the text and the understanding of the described phenomena.

Sources

I will give here only the sources that provide lists of numerical values. Books and articles with only a literary description of the subject are too many to be listed here.

Unused Sources

Some sources provide a list of sunsets and sunrises, but I did not use them because they do not explain which algorithm they use or because I cannot control the parameters.

The Almanach Du Facteur

In France, it is (or rather it was) customary to buy almanachs from the postman each year. In each almanach, you find a page giving the sunrise and sunset times for all the days of the year. Unfortunately, the times are given in HH:MM syntax, not including the seconds. In addition, even if you buy a provincial edition, the sunrise and sunset times are given for Paris. Lastly, the algorithm is not specified.

The Institut de Mécanique Céleste et de Calcul des Éphémérides (IMCCE, Institute of Celestial Mechanics and Ephemerides Computation)

This site (also available in english) used to give an HTML form to generate a table giving the sunrise and sunset times for a location and a time span of your choosing. Unfortunately, this webpage disappeared.

There is an available webservice to give the same functionality, but I did not try it.

Used Sources

Paul Schlyter's Website

This site provides a C program ready to compile and use, giving the sunrise and sunset times. This is the basis of the simple algorithm used in Astro::Sunrise. Its precision, as stated by the author, is oneor two minutes, but it can be much less precise depending on the location and date, especially when we are close to the beginning or the end of the period when the midnight sun is visible.

Paul Schlyter's website includes also many informations about computing the position of various celestial bodies. This website is very interesting, but I preferred writing my own version, describing the computation of only the sun and not bothering with other celestial bodies.

The U.S Naval Observatory

The US Naval Obseravtory gives a HTML form to compute the sunrise and sunset times. These times are given in HH:MM format. I would have preferred HH:MM:SS, but I will have to deal with just HH:MM.

This website gives also very interesting informations about celestial computations, but without restricting itself to the sun, like I am doing here.

Stellarium

Stellarium is a PC app to simulate a night sky. If you do not bother with the main view giving a real time sky simulation, you can use it to obtain the coordinates of a given celestial body at a given time when seen from a given Earth location.

To be completed

Heliocentrism Or Geocentrism?

From those two assertions below, which one is true and which one is false?

A

The Sun goes around the Earth.

B

The Earth goes around the Sun.

Assertion A is false, everyone agrees. But assertion B is false too.

Oh yes indeed, will you answer, it should read actually:

C

The Earth runs along an elliptic orbit with the Sun located on one focus of the ellipsis.

This assertion is false too. Each one of the following assertions is nearer to the truth than assertions B and C (and A).

D

The center of mass of the Earth-Moon binary system runs along an elliptic orbit with the center of mass of the Solar System located on a focus of the ellipsis.

And I will point that the center of mass of the Sun is not the same as the center of mass of the Solar System. There are even times when the center of mass of the Solar System is outside the surface of the Sun. The webpage about an HP-41 program states that on 15th March 1983, the distance between both centers of mass was nearly 2.1 Sun radii.

E

The Earth runs along an orbit around the Sun, with noticeable perturbations caused by the Moon, Jupiter, Saturn, etc.

Which is a formulation equivalent to assertion D.

F

The movement of the Earth with the Solar System is a n-body problem, with n ≥ 3. Therefore, there is no analytical solution.

G

The Solar System is a chaotic system. Even if we can predict with a reasonable accuracy what the various orbits will look like within the next hundred million years, this prediction is no longer possible for an interval of one milliard years (one billion years for US).

H

The Earth moves in the general direction of the Hercules constellation with a approximate speed of 220 km/s.

I

The Earth runs along an orbit around the center of the Milky Way, with noticeable perturbations caused by the Sun, the Moon, Jupiter, Saturn, etc.

Assertions B and C are what Terry Pratchett, Jack Cohen and Ian Stewart call lies to children (Science of Discworld, chapter 4, pages 38 and 39). These are false assertions, but simple enough to be understood by a child and which, even if false, leads children to a better understanding of the described phenomena and brings them closer to truth. You cannot tell assertion C to a child and expect him to understand it without telling him first assertion B. And it is worse with assertions D and next.

Moreover, these are lies to adults. In the beginning, people would consider that the aim of Physics was to build a mathematical representation of the real world, getting closer and closer to the ultimate truth. Then, there was de Broglie's work with the duality of wave and particle and the Copenhagen interpretation. Is the ultimate nature of the electron (for example) a wave? No. Is it a particle? No. So what? We do not care about the ultimate nature of the electron. The aim of Physics is to no longer to provide a mathematical representation of the real world, but to build several mathematical models of the real world. We know that intrinsically all models are false, but each one has it usefulness to lead to make computations about the real world.

Please note that I was talking about scientific methods. I was not dealing with electoral campaigns and advertisements. Every sane adult knows for sure that these are ridden with lies.

Other lies to adults you will find in the following: the light propagates instantly from one place to another, the celestial bodies outside the Solar System are motionless, they are located on a sphere call the Celestial Sphere, UTC time is equal to GMT time and, as I have already stated, all interesting locations on Earth are between the Tropic of Cancer and the Arctic Circle.

Conclusion

All this to explain that in the following text, I will not refrain from using the geocentric model where the Sun turns around the Earth in 24 hours or the geocentric model where the Sun turns arount the Earth in 365.25 days.

"It is not necessary that the following hypothesis be true or even resemble the truth. One thing is for sure that they provide calculations in accordance with the actual observations"

Excerpt from Osiander's preface to Copernic's book. This excerpt was reused by Jean-Pierre Petit as a foreword to Cosmic Story. In Copernic's time, Osiander wanted to have heliocentrism accepted by people who were certain that geocentrism was the one and only truth. It is ironical that I use the same quotation to have geocentrism accepted by people who believe that heliocentrism is the one and only truth.

Earth / Sun Movements

Basic Movements

In an heliocentric system pointing at fixed stars, Earth orbits around the Sun in one year. In other words, in a geocentric system, the Sun orbits around the Earth in one year, with an average speed of 0.986 degrees per day.

Also, the Earth spins around itself, making one turn in 23h 56mn 4s, with a speed of 4.178e-3 degrees per second, that is, 360.986 degrees per day.

Q: I thought that the Earth was spinning in 24h!

A: While the Earth spins, the Sun orbits around it. And what we see is the combination of both movements, which gives a combined speed of 360 degrees per day. What the commoner is interesting in is to find the Sun at the same place in the sky at regular times day after day. Only after this is achieved, the commoner becomes a learned person and is interested in knowing the position of the Moon, the stars and the planets.

Q: And why did you say "average" two or three times?

A: Because the angular speed of the Sun is not constant. We will get back to this question later.

Coordinates

The ecliptic if the plane where the Earth's orbit around the Sun is located (when using an heliocentric model) or where the Sun's orbit around the Earch is located (when using a geocentric model). We define also the equatorial plane, the plane which contains the Earth's equator. These two planes intersect with a 23° 26' angle. The intersection is a line, named line of nodes. In some cases, it is more convenient to use a half-line than a line. In this case, the line of nodes is a half line starting at the Earth center and aiming at the Pisces constellation.

Other Movements

Weather And Climate

Equinox Precession

Nutation

Perihelion Precession

Other Drifts And fluctuations

The Equation Of Time And The Analemma

cpanm Astro::Sunrise

perl -MCPAN -e shell
install Astro::Sunrise