Astronomy

Is sundial time entirely dependent on solar azimuth?

Is sundial time entirely dependent on solar azimuth?


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I've visited several "how sundials work" sites and can't seem to get a clear answer to this: is "sundial time" just a linear function of solar azimuth? More specifically:

  • When the sun is due south (northern hemisphere), it is sundial noon. All sites I've visited agree on this.

  • When the sun is due west (azimuth 270 degrees), I say the sundial time is 6pm, a quarter turn/day from noon. However, I can't find a site that actually says this, and some sites seem to disagree with this. Same for it being 6am sundial time when the sun is due east.

I know there are different types of sundials, but had always assumed they would give the same sundial time. Is that not true?

As a note, the sundial I describe above can be fairly inaccurate at times, which makes me question whether I'm correct.

EDIT (to clarify question): Forgetting entirely about clock time for a moment, suppose I build a sundial. When the sun is due west, my sundial reads 6pm. When the sun is due east, my sundial reads 6am. When the sun is due south, my sundial reads noon. My question: have I built my sundial correctly? The type of answer I'm hoping to get:

  • No. When you build a sundial, it should read (something else) when the sun is due west.

  • There are many different types of sundials. Depending on type, your sundial may or may not read 6pm when the sun is due west.

  • It depends on your latitude: sundials are latitude-specific. There's no such thing as a global sundial.

  • Yes, your understanding of a sundial is correct. Sundials can be off by as much as (some number/formula) from mean solar time, depending on your latitude. They can be as much as (some number/formula) from clock time, depending on your longitude and time zone.


Any sundial that gives the same result as this is correct and any other is wrong (but sometimes close enough):

_ /############ /| /############# skewer / /############## (central) v / /############### | north /################ | (S in S. /################# | hmsphre) /################## ________|________ /################### hoop | /##### LEVEL ####### (from the | side) /###### GROUND ####### | /####### (SOIL) ####### latitude--|- /####################### (use || /######################## protractor)| /######################### |V /########################## | /########################### |/############################ j############################# ,|############################# /#|############################# /##|############################# /###|############################# /####|############################# /#####|############################# /######|############################# /#######|############################# /########V############################# /####################################### ########################################

write noon on hoop's inside closest to ground, midnight opposite, 6 pm on the east side, 9 pm midway between the last two, and so on (hours only occurring in darkness optional).

If your sundial reads 6 pm at due west all the time then you're doing it wrong. Let's say I put a vertical stick in the ground, draw a 24 hour clock face around it, put noon poleward and think it's a sundial. In New York City, it could literally be saying 6 am when a genuine sundial says 9 am. That's just middle latitudes. At the equator on the equinox, it would read 6 am all morning and 6pm all afternoon at the equator. If you go 1 mile south of where the next noon, summer solstice and Tropic of Cancer coincide, it would say about 4:30am at sunrise, go forwards at first, then backwards, finally showing the middle 6 hours of the night passing in 7 seconds. Backwards. At noon. Then it will run forwards again until it reaches 7:30pm at sunset. If you place the stick right, you can even make it stay between 4:30a and 6a all morning, stop at 6 am at the instant of noon then instantly become midnight, run infinity years per second backwards for an infinitely short amount of time, go almost 6 hours backwards in seconds, then later forwards again very slowly until it shows about 7:30pm at sunset. This is why sundials cannot be made that way.

(of course, this is theoretical, there are no infinitely thin, vertical, and straight sticks, shadows are fuzzy, they can be too short to see, the Earth wobbles a bit, the speed of light is not infinite, this would only be true if only the Sun and Earth existed, even a flea jumping in Russia moves the Earth etc.)

And yes, the sundial time can be up to 16 minutes away from mean solar time (the equation of time), easily noticeable, but if you wanted correct local clock time instead of correct sundial time then you could put as many dates as needed on another dial and rotate the hour scale until the arrows point at the current time of year. The shadow then shows mean solar time.

That should be close enough to mean solar time that you wouldn't care for a number of centuries, certainly a century if you're real picky. As for clock time, what sundial disagreements are possible is limited only by the whims of man. The sundial is several hours wrong in West China. Cause they use the zone that's good for Shanghai (or Tokyo when daylight savings).

And all sundials without moving parts are latitude specific. Some are adjustible, though. Some designs are more suited for some latitudes or even become impossible in some places, like the kind with a wedge or rod on a level face. They will also not work on days with polar night. Though you could use a moondial if it's also not polar moon's below the horizon for days or weeks. Yes, moondials exist! You need to correct for moon phase and time of year or they're useless.


The sundial translates the position of the sun to the time of day, so it depends on the path the sun takes across the sky, this is called the ecliptic.

Because the earth's rotation is tilted with respect to its orbit around the sun, the ecliptic shifts across the sky during the year, which is also the cause of seasonal change on earth. Yet the highest altitude of the ecliptic will always be due south, which means noon is well defined every day of the year.

Now to answer the question; if the day length (from sun-rise to sun-down) is exactly 12 hours, the sun will rise at an azimuth of 90 degrees and set at 270 degrees. However, this happens only twice a year, namely at the vernal equinox (first day of spring) and the autumnal equinox (first day of fall).

At the longest day, the summer solstice, both sun-rise and sun-down azimuths will be at their highest shift northward. On the other hand, during the shortest day, the winter solstice, the azimuth-shift will be maximally southward. This last bit applies to the northern hemisphere, for the southern hemisphere the seasons and therefore day lengths are reversed.

So in short, you have to account for what place on earth your sundial is at and what time of year it is.


The sun is not on the same Azimuth for the same hour (not even at noon!). You need to take the analema figure (http://en.wikipedia.org/wiki/Equation_of_time) into your accounts. If you do not, your clock will be exact only 4 times a year.


The shadow of a vertical stick would show the Sun's azimuth, but that's not really a sundial. A proper sundial's gnomon is aligned with the celestial poles so that the shadow indicates the Sun's hour angle. Then the great circle of hour angle $pm$90$^circ$ is projected onto the sundial plane as an east-west line; the shadow falls on that line at 6am or 6pm local apparent solar time regardless of the Sun's declination. Unless the sundial is an equatorial type, the other hour marks are spaced closer together around noon and farther apart around 6am and 6pm.


North American Sundial Society

He may be wheelchair bound, but that doesn't diminish Tom Laidlaw's enthusiasim for sundials. In front of his house on Carolina Lane is the Vancouver Heights neighborhood landmark - a sundial garden. And what has he planted?

There is a bright circular equatorial sundial that shows the time from 4am to 8pm (and even an offset for daylight saving time). On the grass is an analemmatic sundial sundial marking time from 6am to 6pm for anyone who wants to stand to the plywood walkway. On a table near the house are a series of globe, equatorial and horizontal sundials as well as other sundial types that he will gladly explain. For example, Tom has turned a skate board into a polar dial by adding a "T" gnomon in the middle. And then there is a model of the Jefferson dial where you swing the gnomon around a globe to cast only a thin line shadow

Katie Gillespie, of the Columbian, reports "The 80-year-old retired electrician has always been a 'do-it-yourself kind of guy,' he said. For a while, it was skateboards he fancied, and bookshelves, and a Benjamin Franklin chair that transforms from a chair into a stepladder. He’s self-taught, he said, researching new projects online, then diving in. 'It’s fun to watch him talk to people about it,' said Debra Brouhard, Laidlaw’s daughter and neighbor."

His latest obsession is sundials. As a member of the North American Sundial Society, Tom now designs a multitude of sundials. Visitors see his yard dotted with all types of sundials. They come in all sizes: big and small. His analemmatic sundial on the lawn always draws attention. Nearby, a plumb bob dangles from a beam. allowing Tom to tell time solar noon. when the shadow draws a line on the lawn pointing due north.

Gillespie found that, "Laidlaw’s passion for sundials began in 2009, when his grandson, Doug Brouhard, stuck a stick in the ground while they were camping. Doug Brouhard was about 12 at the time, and the dial didn’t quite work, Laidlaw said. It was the right idea, though, and a new hobby was born. 'I still have the stick that started it all,' Doug Brouhard said."

Read more of Katie Gillespie's article and see more photos of Tom Laidlaw and his sundials at http://www.columbian.com/news/2017/aug/30/sundial-garden-shines-in-vancouver-heights/


Sundials: Design, Construction, and Use (Springer Praxis Books Popular Astronomy)

Dr Denis Savoie De´partement Astronomie-Astrophysique Palais de la De´couverte Avenue Franklin D. Roosevelt 75008 Paris France Original French edition: Les cadrans solaires Published by # E´ditions Belin – Paris 2003 Ouvrage publie´ avec le concours du Ministe`re franc¸ais charge´ de la culture – Centre national du livre This work has been published with the help of the French Ministe`re de la Culture – Centre National du Livre Translator: Bob Mizon, 38 The Vineries, Colehill, Wimborne, Dorset, UK

SPRINGER–PRAXIS BOOKS IN POPULAR ASTRONOMY SUBJECT ADVISORY EDITOR: John Mason B.Sc., M.Sc., Ph.D.

ISBN: 978-0-387-09801-2 Springer Berlin Heidelberg New York Springer is a part of Springer Science + Business Media (springer.com) Library of Congress Control Number: 2008934753 Apart from any fair dealing for the purposes of research or private study, or criticism or review, as permitted under the Copyright, Designs and Patents Act 1988, this publication may only be reproduced, stored or transmitted, in any form or by any means, with the prior permission in writing of the publishers, or in the case of reprographic reproduction in accordance with the terms of licences issued by the Copyright Licensing Agency. Enquiries concerning reproduction outside those terms should be sent to the publishers. # Copyright, 2009 Praxis Publishing Ltd. The use of general descriptive names, registered names, trademarks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. Cover design: Jim Wilkie Translation editor: Dr John W. Mason Project management: Originator Publishing Services, Great Yarmouth, Norfolk Printed in Germany on acid-free paper

A little astronomy . . . . . . . . . . . . . . . . . . . . . . . . . . 1.1 The moving Earth . . . . . . . . . . . . . . . . . . . . . . . 1.2 Geographical coordinates . . . . . . . . . . . . . . . . . . 1.3 The Celestial Sphere and the local Celestial Sphere. 1.4 The Sun’s annual motion . . . . . . . . . . . . . . . . . . 1.5 The Sun’s diurnal motion . . . . . . . . . . . . . . . . . . 1.6 The hour angle of the Sun . . . . . . . . . . . . . . . . . 1.7 The equation of time . . . . . . . . . . . . . . . . . . . . .

An introduction to sundials . . . . . . . . . . . . . 2.1 A brief history of sundials . . . . . . . . . . . 2.2 A brief history of time. . . . . . . . . . . . . . 2.3 The general principle of the sundial . . . . . 2.4 The conversion of solar time to clock time 2.5 Finding the local meridian . . . . . . . . . . .

Equatorial sundials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.1 The principle of the equatorial sundial . . . . . . . . . . . . . . . . . 4.2 Marking out the classic equatorial sundial. . . . . . . . . . . . . . .

gnomon . . . . . . . . . . . . . The first gnomons. . . . . . Determining local latitude The solar calendar. . . . . . A seasonal indicator . . . .

Uses of the equatorial sundial . . . . . . . . . . . . . . . . . . . . . . . Determining the meridian . . . . . . . . . . . . . . . . . . . . . . . . . The armillary equatorial sundial . . . . . . . . . . . . . . . . . . . . .

Horizontal sundials . . . . . . . . . . . . . . . . . . . . . . . . . . 5.1 The principle of the horizontal sundial . . . . . . . . . . 5.2 Marking out, using the equatorial sundial . . . . . . . . 5.3 Trigonometrical marking . . . . . . . . . . . . . . . . . . . 5.4 Indicating the dates of the equinoxes . . . . . . . . . . . 5.5 Indicating noon for a different location. . . . . . . . . . 5.6 Marking out a horizontal sundial without calculation 5.7 Babylonian and Italic time . . . . . . . . . . . . . . . . . .

Polar sundials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.1 The principle of the polar sundial . . . . . . . . . . . . . . . . . . . . 6.2 Marking out the sundial . . . . . . . . . . . . . . . . . . . . . . . . . .

Vertical sundials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.1 Vertical sundials . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.2 Making a vertical direct south sundial . . . . . . . . . . . . . 7.3 Making a vertical direct north sundial . . . . . . . . . . . . . 7.4 Making vertical direct west and direct east sundials . . . . 7.5 Making a reflection sundial . . . . . . . . . . . . . . . . . . . . 7.6 Making a sundial on a plane surface without calculation.

Horizontal analemmatic sundials . . . . . . . . . . . . . . . . . . . . . 8.1 The analemmatic sundial . . . . . . . . . . . . . . . . . . . . . . . 8.2 Marking out the analemmatic sundial . . . . . . . . . . . . . . 8.3 Demonstration of the principle of the analemmatic sundial 8.4 Making a solar compass. . . . . . . . . . . . . . . . . . . . . . . . 8.5 The circular analemmatic sundial. . . . . . . . . . . . . . . . . .

Altitude sundials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9.1 The principle of the altitude sundial . . . . . . . . . . . . . . . . . . 9.2 The Saint Rigaud Capuchin sundial . . . . . . . . . . . . . . . . . . .

A little test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Hour lines. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

10 Sundials in the tropics . . . . . . . . . 10.1 Sundials in the tropics . . . . . . 10.2 Sundials north of the Equator . 10.3 Sundials south of the Equator .

The equation of time and the Sun’s declination . Formulae for diurnal motion . . . . . . . . . . . . . Demonstrations . . . . . . . . . . . . . . . . . . . . . . Small problems in gnomonics . . . . . . . . . . . . . Practicalities of constructing a sundial . . . . . . . Mottoes on sundials . . . . . . . . . . . . . . . . . . .

1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 1.10 1.11 1.12 1.13 1.14 1.15 1.16 1.17 1.18 2.1 2.2 2.3 2.4 2.5 2.6 2.7 2.8 2.9 2.10a

The Earth’s orbit and axis of rotation . . . . . . . . . . . . . . . . . . . . . . . . . . . . The surface of the Earth with its parallels and meridians. . . . . . . . . . . . . . Latitude j and longitude l of a place on the surface of the Earth . . . . . . . The Celestial Sphere . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . The local Celestial Sphere . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . The apparent annual path of the Sun across the Celestial Sphere . . . . . . . . Characteristic quantities for the position of the Sun on the ecliptic . . . . . . The signs of the Zodiac on the Celestial Sphere . . . . . . . . . . . . . . . . . . . . . The azimuth of the Sun . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . The apparent path of the Sun and altitude h . . . . . . . . . . . . . . . . . . . . . . . The semi-diurnal arc H0 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . The path of the Sun in one day across the Celestial Sphere . . . . . . . . . . . . The Sun’s hour angle H. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Reduction to the Equator. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Kepler’s Second Law . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Differences in longitudes between the fictitious Sun and the true Sun . . . . The variation of the equation of time in one year . . . . . . . . . . . . . . . . . . . The evolution of day length for the latitude of Paris . . . . . . . . . . . . . . . . . The Tower of the Winds in Athens (1st century BC) . . . . . . . . . . . . . . . . . . A scaphe dial with eyelet (Louvre Museum, 1st–2nd century AD) . . . . . . . A Graeco-Roman dial (Timgad, Algeria) . . . . . . . . . . . . . . . . . . . . . . . . . . A canonical sundial (Coulgens, Charente) . . . . . . . . . . . . . . . . . . . . . . . . . An Arab-Islamic sundial in the Museum of Islamic Art in Cairo, Egypt. . . The frontispiece of Gnomonics (18th century) by Bedos de Celles . . . . . . . . A vertical me´ridienne showing mean time on the town hall at Aumale (SeineMaritime) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . A map showing the distribution of sundials across France . . . . . . . . . . . . A vertical sundial in the courtyard of the Hoˆtel des Invalides in Paris. . . . The meridians are projected onto the horizontal sundial from the hour lines

1 2 3 4 5 6 8 10 11 12 14 15 16 19 20 21 22 23 26 27 28 29 30 31 31 32 36 38

2.10b The meridians in the equatorial plane can be projected onto variably inclined planes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.11 When the Sun is in the plane of the meridian, the direction of the shadow of the polar style does not vary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.12 A me´ridienne by Chavin at Serres (Hautes-Alpes) . . . . . . . . . . . . . . . . . . . . 2.13 The equal shadows method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.14 The meridian passage method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.1 The principle of measuring latitude . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2 To draw the meridian, we observe the position of the shadow of the tip of the gnomon. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.3 The annual variation of the length of the shadow of the gnomon when the Sun culminates. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.4 Example of a diagram for a seasonal indicator . . . . . . . . . . . . . . . . . . . . . 4.1 The north face of an equatorial sundial (Chaˆteaubernard, Charente) . . . . . 4.2 The orientation of an equatorial sundial . . . . . . . . . . . . . . . . . . . . . . . . . . 4.3 The annual evolution of the shadow of the style . . . . . . . . . . . . . . . . . . . . 4.4 Hour lines on an equatorial sundial. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.5 The construction of an equatorial sundial . . . . . . . . . . . . . . . . . . . . . . . . . 4.6 The shadow of the tip of the style in the course of a day. . . . . . . . . . . . . . 4.7 The principle of the equatorial dial showing local time . . . . . . . . . . . . . . . 4.8 An armillary sundial (Cognac, Charentes) . . . . . . . . . . . . . . . . . . . . . . . . . 4.9 The principle of the armillary sundial . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.1 The horizontal sundial. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.2 The horizontal sundial and the Celestial Sphere . . . . . . . . . . . . . . . . . . . . 5.3 A horizontal sundial at Vaire´ in the Vende´e . . . . . . . . . . . . . . . . . . . . . . . 5.4 Diagram for a horizontal sundial. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.5 The variation of the Sun’s hour angle in the equatorial and horizontal planes 5.6 A horizontal sundial with a triangular style . . . . . . . . . . . . . . . . . . . . . . . 5.7 Drawing the hour lines for a thick style . . . . . . . . . . . . . . . . . . . . . . . . . . 5.8 The equinoctial . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.9 A sundial in the park of the town hall in Chaˆteaubernard (Charente) . . . . 5.10 Hour lines on a horizontal sundial indicating Italic hours and Babylonian hours . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.11 A dial showing Babylonian and Italic hours . . . . . . . . . . . . . . . . . . . . . . . 6.1 A polar sundial in the park of the town hall in Chaˆteaubernard (Charente) 6.2 A polar dial. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.3 Hour lines on a polar dial . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.4 A polar dial at the winter solstice (a), the summer solstice (c), and at the equinoxes (b). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.5 The law of tangents. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.6 The construction of a polar sundial . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.1 A declining vertical sundial at Mondovie (Italy) . . . . . . . . . . . . . . . . . . . . 7.2 A meridional dial . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.3 Drawing the hour lines on a vertical meridional sundial . . . . . . . . . . . . . . 7.4 The construction of a meridional sundial . . . . . . . . . . . . . . . . . . . . . . . . . . 7.5 A vertical dial on the convent at Cimiez (Nice) . . . . . . . . . . . . . . . . . . . . . 7.6 Vertical (slightly) declining sundial at the Hoˆpital Lae¨nnec in Paris . . . . . . 7.7 A septentrional dial. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.8 A septentrional sundial . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

39 40 41 43 45 49 50 53 54 57 58 58 59 60 62 63 65 66 67 68 69 70 71 73 74 75 76 79 79 82 83 83 85 86 86 90 91 92 92 93 94 96 97

7.9 7.10 7.11 7.12 7.13 7.14 7.15 7.16 7.17 8.1 8.2 8.3 8.4 8.5 8.6 8.7 8.8 8.9 8.10 9.1 9.2 9.3 9.4 9.5 9.6 10.1 10.2 10.3 10.4 10.5

The construction of a septentrional sundial . . . . . . . . . . . . . . . . . . . . . . . . Drawing the hour lines on a septentrional sundial. . . . . . . . . . . . . . . . . . . Direct west (a) and direct east (b) sundials . . . . . . . . . . . . . . . . . . . . . . . . Vertical sundial, facing approximately east, at Peveragno (Italy) . . . . . . . . Making a direct west dial . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Making a direct east sundial . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Five sundials on a cube, four vertical and one horizontal . . . . . . . . . . . . . Direct south reflection sundial . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Determining the polar axis for any surface . . . . . . . . . . . . . . . . . . . . . . . . Gnomonic, stereographic and orthographic projections . . . . . . . . . . . . . . . Horizontal analemmatic sundial . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . The ‘‘gardeners’ method’’ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Analemmatic sundial on the Promenade du Peyrou in Montpellier (He´rault) Positions of hour points. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . The scale of dates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Analemmatic sundial at Gruissan (Aude) . . . . . . . . . . . . . . . . . . . . . . . . . An equatorial armillary dial made from an embroidery hoop . . . . . . . . . . A solar compass . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . A circular analemmatic sundial . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Cylindrical altitude sundial (shepherd’s dial) in Chaˆteaubernard (Charente) The Saint Rigaud Capuchin sundial. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Drawing the table of hours . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Drawing the scale of dates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . An example of the complete diagram on an A4-sized board . . . . . . . . . . . How a Saint Rigaud Capuchin sundial works . . . . . . . . . . . . . . . . . . . . . . Between the Tropic of Cancer and the Equator, the Sun passes through the local zenith twice a year . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . A solar calendar with a gnomon at the Equator . . . . . . . . . . . . . . . . . . . . An equatorial sundial between the Tropic of Cancer and the Equator . . . . Hour lines on a horizontal dial at latitude þ16 . . . . . . . . . . . . . . . . . . . . Between the Equator and the Tropic of Capricorn, the Sun passes through the local zenith twice a year . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

98 99 100 101 102 103 105 108 109 111 112 113 114 115 116 117 119 120 122 126 127 128 129 130 131 134 135 135 136 138

They will merely scorn sundials: no longer used, of course. But they are, notwithstanding their obvious social role over many centuries, an excellent exercise for the student who takes no pleasure in verbiage. So, for heaven’s sake, start by learning the theory of sundials! Then you can go on to discuss the history of astronomical thought to your heart’s content! Begin at the beginning: by far the most difficult course. H. Bouasse, Astronomie The´orique et Pratique, Paris, 1928 This book is an introduction to the construction of sundials, and to the calculations involved in that construction. It is aimed at all devotees of astronomy who wish to know more about sundials. It is also written for teachers of physics and technology, and for students in teacher training. Those teaching in primary schools will also find material for simple and amusing applications to do with light and shadow. Many new educational programmes for schoolchildren may, in fact, contain projects on sundials or on the measurement of time. Although there are many books on the subject of sundials, they are unfortunately of mixed quality, and often too elementary or too complicated. Some will be difficult to find, and some are by authors who have not mastered the subject. Sundials are of course an excellent introduction to astronomy, but first of all it is necessary to delve into cosmography (the study of the visible universe that includes geography and astronomy) in order to understand the way they work. This is the burden of the first chapter, and it may seem hard going compared with the rest of the book, which is more practical but useful concepts will have been established. Too often, this first stage is neglected in works on sundials, meaning that students cannot absorb all the notions involved. Moreover, we must recognize that some of those notions are difficult. For example, it is not immediately obvious why an equatorial sundial has two faces.

And how do we explain to the novice why an analemmatic sundial is so called, and why it is elliptical and its style movable? How can we convey to students the notion of the two components of the equation of time? Knowing how the Sun moves through the sky in the course of a year as seen from your observing site is the best introduction to the workings of a sundial. The best way to learn about this is undoubtedly by attending planetarium shows: beneath the artificial sky-vault, practically all the movements of the Earth can be simulated. This will increase your understanding of the nature of, for example, the ecliptic, the local meridian, the phenomenon of the seasons, and the inclination of the Earth’s axis of rotation. It is so much harder to convey these things on a blackboard! A sundial is not just a theoretical instrument. Making a working model is a source of great satisfaction, as theory is turned into reality. Often, having set up a sundial and seen it tell the hour and the date, we come to understand certain things which were hitherto unclear. This book deals only with classic sundials, easy to make from wood or card with compasses, a protractor, a ruler and a calculator. Only plane trigonometry is used, and each formula is demonstrated. Fact boxes, often of a historical nature, occur throughout the chapters, sometimes with an indication of the appropriate academic level, and there are web-based exercises. With our insistence on the practical and observational aspects of sundials, we hope that readers will be able to create a sundial, and in their own way, using their own particular modifications and improvements. Most of these ideas have been tested out at summer camps, by young people with no previous knowledge of astronomy. Finally, this book deals with sundials in tropical and southern hemisphere regions, but this is a subject which, if fully explored, would need a book of its own! There is one formula which is not demonstrated here: the equation for the tip of the shadow of a gnomon, since the study of conics belongs to higher and special mathematics. However, in the form in which it is given, it may easily be employed by sixth-form students and may be applied in that form to equatorial, horizontal, polar or vertical sundials in either hemisphere. For those who wish to go further into the calculations involved in sundials, the bibliography will direct them towards further reading. I must express my very grateful thanks to two of my colleagues in the Sundial Commission: to Serge Gre´gori, the most accomplished sundial ‘hunter’ I know, for supplying the marvellous photos which embellish this book and to Olivier Escuder, the ‘systematist’ of sundial mottoes, for his selection of original examples. Finally, I would also like to thank my friend and colleague Marc Goutaudier, of the Palais de la De´couverte, for his invaluable help. He took on the heavy task of proofreading and checking all the calculations in the original French language edition, and I am very grateful to him. Denis Savoie Paris, France December 2008

A full understanding of the apparent motion of the Sun is the necessary starting point for the understanding of the workings of a sundial. The cosmographical ideas in this chapter will be of use throughout the book, in understanding the characteristics of different types of sundials. 1.1

It is useful to recall first of all that the Earth moves in three principal ways: it rotates on its axis, it revolves about the Sun, and its rotational axis precesses. We are concerned only with the first two of these motions when discussing sundials. An observer studying the Earth from a distance of a few million kilometers would see our planet rotating from west to east in about 24 hours. Also, the Earth would be moving around the Sun in the ecliptic plane in a little over 365 days (Figure 1.1). The Earth’s axis always leans in the same direction relative to the ecliptic plane. For our external observer, the consequences of these two motions would be obvious: it would soon become apparent that, on Earth, there is a succession of days and nights and a sequence of seasons. Now, to an observer on Earth, the combination of these two motions is much less obvious. This observer has the impression that the Earth is motionless and that

Figure 1.1 The Earth rotates on its axis every 24 hours approximately, and orbits the Sun, in the plane of the ecliptic, in just over 365 days. The angle between the axis of the Earth’s rotation and the vertical to the plane of the ecliptic is currently 23 26 0 .

the heavenly bodies are moving: so, on Earth, we talk about the apparent motion of the heavens. In particular, if we discuss sundials, we tend to think of the apparent motion of the Sun rather than of the real motion of the Earth. 1.2

The way in which we construct sundials depends on our geographical location. So we must define the various terms used to specify our position on the surface of the Earth.

Parallels and meridians Assuming the Earth to be perfectly spherical, we first of all determine an imaginary straight line PP 0 around which our planet rotates (Figure 1.2). This line is known as the Earth’s axis, or its axis of rotation. It encounters the Earth’s surface at two points, the North Pole (P) and the South Pole (P 0 ). The longest circular parallel which is perpendicular to the axis of rotation is known as the Equator, dividing the Earth into the northern and southern hemispheres. The smaller circles parallel to the Equator are known as parallels of latitude, the most important among them situated 23 26 0 north of the Equator (the Tropic of Cancer), and 23 26 0 south of the Equator (the Tropic of Capricorn). The importance of these two Tropics derives from the fact that only in locations between these two lesser parallels can the Sun be at the zenith. The parallels lying at 66 34 0 N and 66 34 0 S are respectively the Arctic and

Figure 1.2 The surface of the Earth with its parallels and meridians.

1.2 Geographical coordinates

Antarctic Circles. In latitudes greater than these, the ‘‘midnight sun’’ is observed, i.e. the phenomenon of the Sun being above the horizon at local midnight. The semicircles between the poles are known as meridians. The meridian passing through the Royal Greenwich Observatory is known as the prime (or international) meridian. Latitude and longitude In order to describe a location on the Earth’s surface, we use geographical coordinates of latitude and longitude (Figure 1.3). The latitude of a place (c) is the angle between the Equator and the vertical at that place. It is expressed in degrees from the Equator (with positive sign in the northern hemisphere, 0 to þ90 , and negative sign in the southern hemisphere, 0 to 90 ). For example, France extends from around latitude 41 55 0 N (Ajaccio) to 50 57 0 N (Calais). One degree of latitude represents approximately 111.11 km on the ground. The longitude l of a place is the dihedral angle between the local meridian and the Greenwich Meridian (longitude zero), from 0 to þ180 westwards, and from 0 to 180 eastwards (following the sign convention of astronomy). Longitude is expressed either in degrees, minutes and seconds ( , 0 , 00 ) or in hours, minutes and seconds (h, m, s). Note that 15 ¼ 1 h. The longitude of the Paris Observatory is 2 20 0 15 00 (2 20 0 15 00 E), or 0 h 9 m 21 s.

Figure 1.3 Latitude c and longitude l of a place on the surface of the Earth. The Equator is the parallel of reference for latitude, and the Greenwich meridian the meridian of reference for longitude.

Conversion of degrees into hours: see Appendix G, page 165.

The Celestial Sphere and the local Celestial Sphere

The Celestial Sphere For an observer on the Earth’s surface, our planet seems motionless while the spherical vault of the heavens seems to move around it. Since the radius of the Earth is negligible compared with the distance to the heavenly bodies, including the Sun, we can consider the Earth to lie exactly at the center of this sphere. Now this imaginary sphere, of great and arbitrary size compared with the size of the Earth, is known as the Celestial Sphere, and it is centered upon the center of the Earth. Observation of the night sky will show that the stars seem to travel from east to west around an imaginary axis which encounters the inner surface of the Celestial Sphere close to the Pole Star (Figure 1.4). We observe exactly the same principle in a planetarium. The imaginary axis is the rotational axis of the Earth, passing through the Celestial Sphere at two opposite points, the North Celestial Pole and the South Celestial Pole. By analogy with the Earth, we also define a Celestial Equator.

Figure 1.4 The Celestial Sphere.

1.4 The Sun’s annual motion

Figure 1.5 The local Celestial Sphere. The Celestial Sphere is referred to when discussing apparent annual motions, while the local Celestial Sphere is used for apparent diurnal and nocturnal paths.

The local observer’s Celestial Sphere For any point on the Earth’s surface, we can define a local Celestial Sphere (Figure 1.5). On this sphere, it is possible to represent the movement of heavenly bodies using two fixed references: the vertical at the observer’s location, which can be determined by using a plumb line and the horizon, which is a great circle at right angles to the vertical. It is on this horizon that the cardinal points (north, east, south and west) are defined. The observer’s vertical passes through a unique point, the zenith, 90 from the horizon. Through the North and South Poles passes a great circle, the local meridian. This passes through the zenith of the observer’s location and indicates geographical north and south. The altitude in degrees of the North Celestial Pole is the same as the observer’s latitude.

The ecliptic Since the publication in 1543 of Nicolaus Copernicus’ De Revolutionibus, in which he affirmed, among other things, that the Earth rotates and moves around the Sun, it has been recognized that the motion of the ‘day-star’ is an apparent motion. Not only is the Sun carried from east to west through the sky because of the Earth’s rotation (diurnal motion), but it also seems to move throughout the year relative to the stars (annual motion). So, if it were possible to observe the Sun and the stars at

the same time, it would become obvious that the Sun moves about one degree per day eastwards against the starry Celestial Sphere. By noting the Sun’s position every day, we can verify that, a year later on the same date, it returns to the same point against the backdrop of the stars. Therefore, in the course of a year, the center of the Sun describes a great circle, known as the ecliptic, on the Celestial Sphere. The Sun’s path is so called because solar and lunar eclipses can occur only when the center of the Moon is very near the plane of the ecliptic. The inclination of the ecliptic relative to the Celestial Equator is known as the obliquity of the ecliptic (e): this is also the angle between the equatorial polar axis PP 0 and the ecliptic polar axis P P 0 (Figure 1.6). At present, the value of the

Figure 1.6 The apparent annual path of the Sun across the Celestial Sphere. In the course of a year, the Sun describes a great circle (the ecliptic) on the Celestial Sphere.

1.4 The Sun’s annual motion

obliquity of the ecliptic is 23 26 0 , and it is decreasing by about 1 0 per century. The value of 23 27 0 given in many books refers to the obliquity at the beginning of the twentieth century. Noteworthy points The ecliptic cuts the Celestial Equator at two points, g and g 0 . These are known as the nodes. g is a particularly important point, being the ascending node (vernal equinox). The Sun crosses this point at the spring equinox around 20 March, moving from the southern into the northern hemisphere. g 0 is the descending node (autumnal equinox). Here, the Sun crosses the ecliptic at the autumnal equinox around 23 September, moving from the northern into the southern hemisphere. The other two notable points on the ecliptic are points E and E 0 , at opposite ends of a diameter perpendicular to the line of the nodes: these are the points of the Sun’s passage through the solstices. The mean interval between two passages of the Sun through the vernal equinox is known as the tropical year, its current value being 365 d 5 h 48 m 45 s. Note that the dates of the spring equinox, summer solstice, autumnal equinox and winter solstice quoted here, and in subsequent paragraphs, refer to the northern hemisphere. In the southern hemisphere, the seasons are reversed. Solar longitude Solar longitude, written as ,0 (not to be confused with the longitude of a place), is the angle between the vernal point g and the Sun (Figure 1.7). It is measured along the ecliptic in the direct (west-east) sense, and is expressed in degrees from 0 to 360 . The Sun moves approximately one degree eastwards every day along the ecliptic. When the longitude of the Sun is zero, the Sun is at point g, i.e. the vernal equinox, on 20 March. At 90 , the Sun reaches its greatest angular distance above the equator (þ23 26 0 ). This is the summer solstice on 21 June. At 180 , the Sun crosses point g 0 . This is the autumnal equinox, on 23 September. Finally, at 270 , the Sun reaches its greatest angular distance below the equator (23 26’). This is the winter solstice, on 21 December. The seasons In astronomy, a season is the time taken by the Sun to traverse each of the quadrants between points g, E, g 0 and E 0 (Figure 1.7): spring corresponds to the arc gE summer corresponds to the arc Eg 0 autumn corresponds to the arc g 0 E 0 winter corresponds to the arc E 0 g. The seasons are not all of equal length. Currently, the shortest (in the northern hemisphere) is winter and the longest is summer. This inequality is due to the fact that the movement of the Sun in longitude is not uniform. The Sun stays in the northern hemisphere for 186 days, and in the southern for 179 days in other

Figure 1.7 Characteristic quantities for the position of the Sun on the ecliptic: longitude l0 , right ascension a and declination d.

words, in Europe and North America, spring and summer combined are longer than autumn and winter. The reverse is true for locations in the southern hemisphere. The declination of the Sun The movement of the Sun in longitude corresponds to a variation in its angular distance from the Equator. This is known as the declination of the Sun, and is written as d (Figure 1.7). At the spring equinox (20 March) this declination is zero. Its value increases thereafter until the summer solstice of 21 June, to a maximum of þ23 26 0 . Then it decreases to zero at the autumnal equinox (23 September), and the value becomes negative after this date. It reaches a minimum value of 23 26 0 on

1.4 The Sun’s annual motion

21 December, at the winter solstice. Lastly, the declination increases, to become zero once again on 20 March. To sum up, the value for the declination of the Sun increases between the winter solstice and the summer solstice, and decreases between the summer solstice and the winter solstice. Right ascension As well as the Sun’s movement in declination, there is its movement in right ascension, written as a. This is the projection onto the Celestial Equator of the Sun’s longitude. Right ascension is measured in hours from 0 h to 24 h, from point g, in the direct sense. Right ascension is zero at the spring equinox, 6 h at the summer solstice, 12 h at the autumnal equinox and 18 h at the winter solstice. Table 1.1 brings together the values expressing the position of the Sun at the equinoxes and solstices. The declination d of the Sun and its right ascension a are linked to the solar longitude l0 thus: tan a ¼ cos e tan l0 sin d ¼ sin e sin l0 e being the obliquity of the ecliptic. At the end of this book there is a table giving the declination of the Sun for each day of the year at 12 h ut (Appendix C, page 148). In gnomonics (the study of sundials), it is normally assumed that the Sun’s declination does not vary in the course of a day, though in reality there is a slight change in its value. At the equinoxes this variation reaches a maximum value of almost 1 0 per hour. Moreover, as the Earth moves round the Sun in one year, with its axis inclined and pointing towards the Pole Star, the altitude of the Sun varies throughout the year as seen from every point on the surface of the globe. The ecliptic is represented on the Celestial Sphere and not on the local Celestial Sphere (Figure 1.6). In effect, the annual motion of the Sun is independent of its diurnal motion, a fact well worth remembering! Table 1.1 Values of longitude, right ascension and declination of the Sun at the equinoxes and solstices. Spring equinox


Is sundial time entirely dependent on solar azimuth? - Astronomy

Four megalithic sundials: geometrical
and astronomical analyses

More recently, Brennan has found that early Celtic explorers even made their way to western North America 2000 years ago, where they carved Ogham or Gaelic characters onto the rocks to mark a spring equinox (see "Martin Brennan at Anubis Cave equinox" on video.google.com/videoplay?docid=-1856547827596216006). .

N.L. Thomas has carefully interpreted many different stone inscriptions from Knowth or other megalithic sites, as described in his 1989 book, Irish symbols of 3500 BC. .

Finally, as an important addendum to such previous work, C. Knight and R. Lomas in their book Uriel's Machine (1999) argue that the ancient Book of Enoch was written somewhere in the British Isles just before the Flood (ca. 3100 BC). It describes a large megalithic observatory similar to the ones described above, except where each quarter of the year (91 days) had been divided into three parts rather than four or eight. Thus, every full year of 365 days would have contained 12 months rather than 16 or 32.

Some people believe that the ancient British Isles could have been a remote outpost of a more advanced Sumerian civilization. For example, "Shamsiel" in Enoch taught "signs of the Sun", while "Shamash" in Sumeria was a "god of the Sun". Furthermore, certain recovered cylinder seals from ancient Sumeria show star-like symbols which suggest that two kinds of calendar, using either 12 or 16 months, may have been in use at the time (see "Shamash" or "Annunaki" on Wikipedia).

Might some of those modern crop pictures be coming from the megalith builders themselves?

In light of these new geometrical and astronomical analyses, it has become clear that the four crop pictures discussed above: Avebury 2003, Oliver's Castle 2007, Hackpen Hill 2003 and Avebury 2005, could not plausibly have been made by local human fakers.

Some of the astronomical crop pictures discussed above seem refer to latitudes near 51-53 N, where Avebury and Knowth are located whereas others seem to refer to a more northern range of 60-62 N, which might correspond to southern Norway. Likewise, Hackpen Hill seems to refer to a distant time in the past around 3000 to 2000 BC, when Knowth was first being built.

One long-time student of the Tuatha de' Danaan, a retired geologist called Tim O'Brien, has argued that the legendary term "Achaia" might refer to "Accad" in northern Sumeria (www.goldenageproject.org.uk/whodunit.html) where a group of advanced scientists once lived. After the collapse of that city in 2100 BC, did those scientists migrate elsewhere?

Just after the Flood (ca. 3100 BC), a frantic period of mound building began in low-lying areas all around the world, so that people would have somewhere safe to go if the flood waters returned. Silbury Hill was built for example during that period. By legend, Ireland was swept clear of any inhabitants for 300 years. Only by 2800 AD did a series of "invaders" once again begin to inhabit Ireland, as documented in the Lebor Gabala Erren. The Tuatha de' Danaan ("People of Anu") were supposedly the fourth of these, sometime around 2000 BC. Having left Accad in Sumeria after its fall (or perhaps Achaia in Greece), they would have had to travel first over land to Norway, and then later across the sea to Scotland and Ireland. It may have seemed logical for them to migrate to a relative place of safety such as the ancient British Isles, since their own ancestors ("Uriel" and "Shamsiel") seem to have had bulit megalithic sites there, one thousand years earlier.

Now the Tuatha de' Danaan who emigated to Ireland were reportedly tall, fair-skinned blondes or redheads with blue or green eyes. They dramatically upgraded the local Irish gene pool by interbreeding, so as to create the Celtic-Gaelic race we see today. St. Patrick recorded how one of their pure-bred women married an Irish king in 400 AD. They made the golden torc, and could move heavy stones with ease. But where did they come from originally? How did they reach Ireland by air? What kinds of technology might they have brought with them? And why do so many modern crop pictures appear near their ancient sites of settlement, often showing Celtic or even sundial-type astronomical motifs?


Answer Desk

The difference between meteorites, meteors, and meteoroids is one of altitude relative to a celestial surface: in space, it's a meteoroid in the atmosphere, it's a meteor and on the surface, it's a meteorite. (See here and here for more information.)

The International Astronomical Union (IAU) defined the term Small Solar System Body (SSSB) in 2006 with Resolution B5 as


(3) All other objects³,except satellites, orbiting the Sun shall be referred to collectively as "Small Solar System Bodies".

[Footnote 3] "These currently include most of the Solar System asteroids, most Trans-Neptunian Objects (TNOs),comets, and other small bodies."


And, although this official definition clearly states, "All other objects . orbiting the Sun", I'm not sure how verbatim this definition is meant to be treated.

What I mean by this is, well, for example, in Law, all definitions are, by default, unless previously stated, treated in an context of exactness. But although science is oftentimes based on specificity, it is not always, and the degree thereof in this context is thus not wholly clear to me.


Answer Desk

This is known as spectroscopy. Every molecule and atom in the universe emits and absorbs light at specific frequencies. This is a result of the quantization of the energy levels (for electrons) in an atom. Although there are lots of complicating factors, such as redshift, to account for, the patterns are usually so distinctive that the complications can be accounted for, and do not prevent scientists from figuring out chemical compositions (and even, to some extent, how abundant each chemical is).

For example, here are the emission spectra of several common atoms at rest (with respect to the observer):

Absorption spectra, on the other hand, appear as darker regions in the band. Here's an example of an absorption spectra, which identities several elements by knowing that it is distinguished by absorbing light at specific wavelengths that others do not:

For exoplanets with significant atmospheres, we can only expect to see the spectra for its upper atmosphere. All other signals will be muted out by the rest of the atmosphere. We will not be able to tell what the surface looks like, or what it is made of.


A Gnomon is called a watch, but if to speak more precisely, it's just part of them, namely the object casting the shadow. Often &ndash it is a triangle. The geographical latitude determines the angle of it. The gnomon is always directed to the North. The exact hours two gnomon. One face is a curved contour.

It is Made with the purpose to avoid confusion, for some of the faces to measure the time, and it looks pretty aesthetically pleasing. Also, for aesthetics you can make the gnomon is slightly bent. Most importantly, face for the recording time was direct.


Solar Thermal Systems: Components and Applications

B. Hoffschmidt , . O. Kaufhold , in Comprehensive Renewable Energy , 2012

3.06.3.3.4 Specific control components

Tracking of parabolic trough mirrors is usually controlled by solar position algorithms assisted by sensors which can be used for fine-tuning the tilt angle in such a way that the optical axis is in line with the direction of sunlight. Figure 13 shows a characteristic sensor for fine-tuning of mirror tilt angle.

Figure 13 . Sensor for fine-tuning of mirror tilt angle.

On the other hand, the control system must be fail-safe in the case of an electricity failure. Either centralized or decentralized power backup systems must be installed in order to defocus the troughs or move the focus away from the receiver in the case of an emergency.


Solar activity

the aggregate of phenomena observed on the sun and associated, for example, with the formation of sun-spots, faculae, flocculi, filaments, and prominences, with the occurrence of solar flares and disturbances in the solar corona, and with an increase in ultraviolet, X- , and corpuscular radiation. Such phenomena are usually observed in a limited region, called an active region, on the sun&rsquos surface. The region may exist for a few days to several months.

When an active region arises, flocculi appear they correspond to an increase in the brightness of the absorption lines of hydrogen and ionized calcium. After some time, usually a few days, small sunspots appear. The number and size of the sunspots gradually increase, and the intensity of other manifestations of solar activity become more pronounced.

The radiation excess in the hydrogen and calcium lines that characterizes the active region increases markedly when solar flares occur. Solar flares arise in the vicinity of developing or decaying sunspot groups and show up in the sudden appearance of emission in strong absorption lines (for example, the Ha and Hp lines of hydrogen or the H and K lines of ionized calcium) and in the increase in intensity of ultraviolet, X-, and corpuscular radiation. The level of emission in the radio-frequency region also increases. Small flares are observed almost daily in large sunspot groups large flares occur comparatively rarely. Flares may last from a few minutes to several hours. The strength of the magnetic field in sunspots reaches several thousand oersteds.

The intensity of solar activity is described by such quantities as the relative sunspot number (Wolf number), the sunspot area, and the area and brightness of faculae, flocculi, filaments, and prominences. The mean annual values of these quantities vary in a periodic manner. The Wolf number, for example, has an average period of approximately 11 years the length of the period ranges from 7.5 to 16 years. The value of the maximum of the 11-year cycle varies with a period of approximately 80 years.

Active regions are distributed on the sun&rsquos disk in two belts that run parallel to the equator, on either side of it. The distance of the belts from the equator also varies periodically. At the beginning of the 11-year cycle, the active regions lie at their greatest distance from the solar equator. They gradually draw closer to the equator, and by the end of the cycle their average helio-graphic latitude is ±8°.


Contents

The 4 distinct instruments within the observatory of Jantar Mantar in New Delhi: the Samrat Yantra, the Jayaprakash, Rama Yantra and the Misra Yantra.

  • Samrat Yantra: The Samrat Yantra, or Supreme Instrument, is a giant triangle that is basically an equal hour sundial. It is 70 feet high, 114 feet long at the base, and 10 feet thick. It has a 128-foot ih-long (39 m) hypotenuse that is parallel to the Earth's axis and points toward the North Pole. On either side of the triangle is a quadrant with graduations indicating hours, minutes, and seconds. At the time of the Samrat Yantra's construction, sundials already existed, but the Samrat Yantra turned the basicihuj sundial into a precision tool for measuring declination and other related coordinates of various heavenly bodies. The Vrihat Samrat yantra can calculate the local time at an accuracy of up to two seconds and is considered the worlds largest sundial. [1]
  • Jaya Prakash Yantra: The Jaya Prakash consists of hollowed out hemispheres with markings on their concave surfaces. Crosswires were stretched between points on their rim. From inside the Ram, an observer could align the position of a star with various markings or a window's edge. This is on of the most versatile and complex instruments that can give the coordinates of celestial objects in multiple systems- the Azimuthal-altitude stytem and the Equatorial coordinate system. This allowed for the easy conversation of the popular celestial system. [3]
  • Rama Yantra: Two large cylindrical structures with open top, used to measure the altitude of stars based on the latitude and the longitude on the earth.
  • Misra Yantra: The Misra Yantra (literally mixed instrument) is a composition of 5 instruments designed as a tool to determine the shortest and longest days of the year. It could also be used to indicate the exact moment of noon in various cities and locations regardless of their distance from Delhi. The Misra yantra was able to indicate when it was noon in various cities all over the world and was the only structure in the observatory not invented by Jai Singh II.
  • Shasthansa Yantra: Using a pinhole camera mechanism, it has been built within the towers that support the quadrant scales. It is used to measure specific measurements of the sun such as the zenith distance, declination, and diameter of the sun. [3]
  • Kapala Yantra: Built on the same principle as the jai Prakash, the instrument is used more as a demonstration to indicate the transformation of one coordinate system to another. Not used for active celestial observation. [3]
  • Rasivalya Yantra: Twelve of these structure where built, each referring to the zodiacal constellations by measuring the latitude and longitude of a celestial object at the very moment the celestial object crosses the meridian. [3]

Between 1727 and 1734 Jai Singh II built five similar observatories in west-central India, all known by the name Jantar Mantar. They are located at

While the purpose of the Jantar Mantar was astronomy and astrology (Jyotish), they are also a major tourist attraction and a significant monument of the history of astronomy.


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