University Of Oregon Sun Path
Sun path chart program (University of Oregon) SunPosition Calculator. The Sundial Primer. Last Modified: 2016, May. Mar 05, 2007 Sun path chart program This program creates sun path charts in Cartesian coordinates for: (1) 'typical' dates of each month (i.e.; days receiving about the mean amount of solar radiation for a day in the given month); (2) dates spaced about 30 days apart, from one solstice to the next; or (3) a single date you specify.
- University Of Oregon Sun Path Chart
- University Of Oregon Sun Path Chart
- University Of Oregon Sun Path
- University Of Oregon Sun Path Chart
Ptolemy and Regiomontanus shown on the frontispiece to Regiomontanus'Epitome of the Almagest, 1496. The Epitome was one of the mostimportant Renaissance sources on ancient astronomy.
Ptolemy:
Ptolemy, Latin in full Claudius Ptolemaeus (fl. AD 127-145,Alexandria), ancient astronomer, geographer, and mathematician whoconsidered the Earth the center of the universe (the 'Ptolemaicsystem'). Virtually nothing is known about his life.
Ptolemy's astronomical work was enshrined in his great book Hemathematike syntaxis ('The Mathematical Collection'), whicheventually became known as Ho megas astronomos ('The GreatAstronomer'). During the 9th century, however, Arab astronomers usedthe Greek superlative Megiste to refer to the book. When thedefinite article al was prefixed to the term, its title thenbecame known as the Almagest, the name still used today.
The Almagest is divided into 13 books, each of which deals withcertain astronomical concepts pertaining to stars and to objects inthe solar system (the Earth and all other celestial bodies thatrevolve around the Sun). It was, no doubt, the encyclopaedic natureof the work that made the Almagest so useful to later astronomers andthat gave the views contained in it so profound an influence. Inessence, it is a synthesis of the results obtained by Greekastronomy; it is also the major source of knowledge about the work ofHipparchus, most probably the greatest astronomer of antiquity.Although it is often difficult to determine which findings in thebook are those of Ptolemy and which are those of Hipparchus, Ptolemydid extend some of the work of Hipparchus through his ownobservations, apparently using somewhat similar instruments. Forexample, whereas Hipparchus had compiled a star catalog (the first ofits kind) containing 850 stars, Ptolemy expanded the number in hisown catalog to 1,022 stars.
On the motions of the Sun, Moon, and planets, Ptolemy again extendedthe observations and conclusions of Hipparchus--this time toformulate his geocentric theory, which is popularly known as thePtolemaic system. (See Ptolemy's theory of the solar system.) In thefirst book of the Almagest, Ptolemy describes his geocentric systemand gives various arguments to prove that, in its position at thecenter of the universe, the Earth must be immovable. Not least, heshowed that if the Earth moved, as some earlier philosophers hadsuggested, then certain phenomena should in consequence be observed.In particular, Ptolemy argued that since all bodies fall to thecenter of the universe, the Earth must be fixed there at the center,otherwise falling objects would not be seen to drop toward the centerof the Earth. Again, if the Earth rotated once every 24 hours, a bodythrown vertically upward should not fall back to the same place, asit was seen to do. Ptolemy was able to demonstrate, however, that nocontrary observations had ever been obtained. As a result of sucharguments, the geocentric system became dogmatically asserted inWestern Christendom until the 15th century, when it was supplanted bythe heliocentric (Sun-centered) system of Nicolaus Copernicus (q.v.),a Polish astronomer.
The Christian Aristotelian cosmos, engraving from Peter Apian'sCosmographia, 1524
Ptolemy accepted the following order for celestial objects in thesolar system: Earth (center), Moon, Mercury, Venus, Sun, Mars,Jupiter, and Saturn. He realized, as had Hipparchus, that theinequalities in the motions of these heavenly bodies necessitatedeither a system of deferents and epicycles or one of movableeccentrics (both systems devised by Apollonius of Perga, the Greekgeometer of the 3rd century BC) in order to account for theirmovements in terms of uniform circular motion.
In the Ptolemaic system, deferents were large circles centered on theEarth, and epicycles were small circles whose centers moved aroundthe circumferences of the deferents. The Sun, Moon, and planets movedaround the circumference of their own epicycles. In the movableeccentric, there was one circle; this was centered on a pointdisplaced from the Earth, with the planet moving around thecircumference. These were mathematically equivalent schemes. Evenwith these, all observed planetary phenomena still could not be fullytaken into account. Ptolemy therefore exhibited brilliant ingenuityby introducing still another concept. He supposed that the Earth waslocated a short distance from the center of the deferent for eachplanet and that the center of the planet's deferent and the epicycledescribed uniform circular motion around what he called the equant,which was an imaginary point that he placed on the diameter of thedeferent but at a position opposite to that of the Earth from thecenter of the deferent--i.e., the center of the deferent was betweenthe Earth and the equant. He further supposed that the distance fromthe Earth to the center of the deferent was equal to the distancefrom the center of the deferent to the equant. With this hypothesis,Ptolemy could better account for many observed planetary phenomena.In the Ptolemaic system, the plane of the ecliptic is that of theSun's apparent annual path among the stars. The planes of thedeferents of the planets were believed to be inclined at small anglesto the plane of the ecliptic, while the planes of their epicycleswere inclined by equal amounts to those of the deferents, so that theplanes of the epicycles would always parallel that of the ecliptic.The planes of the deferents of Mercury and Venus were assumed tooscillate above and below the plane of the ecliptic, and likewise theplanes of their epicycles were thought to oscillate with respect tothe planes of the deferents.All this was necessary to explain retrograde motion, the apparentbackwards track of the outer planets against the background of stars.
Although Ptolemy realized that the planets were much closer to theEarth than the 'fixed' stars, he seems to have believed in thephysical existence of crystalline spheres, to which the heavenlybodies were said to be attached. Outside the sphere of the fixedstars, Ptolemy proposed other spheres, ending with the primum mobile('prime mover'), which provided the motive power for the remainingspheres that constituted his conception of the universe.As a geometrician of the first order, Ptolemy performed importantwork in mathematics. He devised new geometrical proofs and theorems;and, in a book entitled Analemma (Greek Peri analemmatos; Latin Deanalemmate), he discussed the details of the projection of points onthe celestial sphere (an imaginary sphere extending outward from theEarth for an infinite distance and on whose surface the objects inspace appear to be located) onto three planes at right angles (90) toeach other--the horizon, the meridian, and the prime vertical. Inanother book, the Planisphaerium, Ptolemy is concerned withstereographic projection--the delineation of the forms of solidbodies on a plane--and here he used the south celestial pole as hiscenter of projection.
Ptolemy also prepared a calendar that gave, in addition to weatherindications, the risings and settings of the stars in the morning andevening twilight. Other mathematical publications include a work, intwo books, entitled Hypotheseis ton planomenon ('PlanetaryHypothesis') and two separate geometrical works, one of which isconcerned with proving that there cannot be more than threedimensions of space; the other contains an attempted proof for apostulate on parallel lines that had been devised by Euclid.According to one authority, Ptolemy wrote three books on mechanics;another authority, however, credits him with only one mechanicalwork, Peri ropon ('On Balancing').
Ptolemy's work on optical phenomena appeared in Optica, the originaledition of which consisted of five books. In the last book, he dealswith a theory of refraction (the change in direction of light andother energy waves when they pass obliquely from a medium of onedensity into a medium of different density), and he discusses therefraction suffered by light from celestial bodies at variousaltitudes. This is the first recorded attempt at a solution of thisobservational problem. Ptolemy also wrote a three-book treatise onmusic known as the Harmonica.
As a geographer, Ptolemy's reputation rests mainly on his Geographikehyphegesis (Guide to Geography), which was divided into eight books;it included information on how to construct maps and lists of placesin Europe, Africa, and Asia tabulated according to latitude andlongitude. There were, however, many errors in the Guide--e.g., theEquator was placed too far north, and the value used for thecircumference of the Earth was nearly 30 percent less than a moreaccurate value that had already been determined--as well as somecontradictions between the text and maps. Moreover, as a whole, theGuide cannot be considered 'good geography'; it does not mentionanything about the climate, natural products, inhabitants, orpeculiar features of the countries with which it deals, and Ptolemy'streatment of the geographical importance of such factors as riversand mountain ranges is careless and of little use.
In spite of its faults, the Guide is an important work from ahistorical point of view because, like the Almagest, it exerted agreat influence on later generations. Christopher Columbus, forexample, used it to strengthen his belief that Asia could be reachedby travelling westward because Ptolemy had indicated that Asiaextended much farther east than it actually does. Even as late as1775, it was believed that the Indian Ocean was bounded by a southerncontinent, as Ptolemy had suggested; the return voyage from theSouthern Hemisphere of Capt. James Cook in July of that year provedotherwise.
Excerpt from the Encyclopedia Britannica without permission.
Great Circles:To explore the solar system, one first needs a coordinate system, a map. For gettingaround town, a flat map works fine with four directions, north, east, south, west.However, the sky appears to look like a sphere, so spherical coordinates areneeded.
The shortest path between two points on a plane is a straight line. Onthe surface of a sphere, however, there are no straight lines. Theshortest path between two points on the surface of a sphere is given bythe arc of the great circle passing through the two points. A great circleis defined to be the intersection with a sphere of a plane containing thecenter of the sphere.
Two great circles
If the plane does not contain the center of the sphere, its intersectionwith the sphere is known as a small circle. In more everyday language, ifwe take an apple, assume it is a sphere, and cut it in half, we slicethrough a great circle. If we make a mistake, miss the center and hencecut the apple into two unequal parts, we will have sliced through a smallcircle.
Two small circles
Spherical Triangles:
If we wish to connect three points on a plane using the shortest possibleroute, we would draw straight lines and hence create a triangle. For asphere, the shortest distance between two points is a great circle. Byanalogy, if we wish to connect three points on the surface of a sphereusing the shortest possible route, we would draw arcs of great circles andhence create a spherical triangle. To avoid ambiguities, a triangle drawnon the surface of a sphere is only a spherical triangle if it has all ofthe following properties:
- The three sides are all arcs of great circles.
- Any two sides are together greater than the third side.
- The sum of the three angles is greater than 180°.
- Each spherical angle is less than 180°.
University Of Oregon Sun Path Chart
The figure below shows a spherical triangle, formed by three intersectinggreat circles, with arcs of length (a,b,c) and vertexangles of (A,B,C).
Note that the angle between two sides of a spherical triangle is definedas the angle between the tangents to the two great circle arcs, as shownin the figure below for vertex angle B.
Earth's Surface:
University Of Oregon Sun Path Chart
The rotation of the Earth on its axis presents us with an obvious means ofdefining a coordinate system for the surface of the Earth. The two pointswhere the rotation axis meets the surface of the Earth are known as thenorth pole and the south pole and the great circle perpendicular to therotation axis and lying half-way between the poles is known as theequator. Great circles which pass through the two poles are known asmeridians and small circles which lie parallel to the equator are known asparallels or latitude lines.
The latitude of a point is the angular distance north or south of theequator, measured along the meridian passing through the point. A relatedterm is the co-latitude, which is defined as the angular distance betweena point and the closest pole as measured along the meridian passingthrough the point. In other words, co-latitude = 90° - latitude.
Distance on the Earth's surface is usually measured in nautical miles,where one nautical mile is defined as the distance subtending an angle ofone minute of arc at the Earth's center. A speed of one nautical mile perhour is known as one knot and is the unit in which the speed of a boat oran aircraft is usually measured.
Horizon System:
Humans perceive in Euclidean space -> straight lines and planes.But, when distances are not visible (i.e. very large) than theapparent shape that the mind draws is a sphere -> thus, we use aspherical coordinate system for mapping the sky with the additionaladvantage that we can project Earth reference points (i.e. NorthPole, South Pole, equator) onto the sky. Note: the sky is not reallya sphere!
From the Earth's surface we envision a hemisphere and mark the compasspoints on the horizon. The circle that passes through the south point,north point and the point directly over head (zenith) is called themeridian.
This system allows one to indicate any position in the sky by tworeference points, the time from the meridian and the angle from thehorizon. Of course, since the Earth rotates, your coordinates willchange after a few minutes.
The horizontal coordinate system (commonly referred to as the alt-azsystem) is the simplest coordinate system as it is based on the observer'shorizon. The celestial hemisphere viewed by an observer on the Earth isshown in the figure below. The great circle through the zenith Z and thenorth celestial pole P cuts the horizon NESYW at the north point (N) andthe south point (S). The great circle WZE at right angles to the greatcircle NPZS cuts the horizon at the west point (W) and the east point (E).The arcs ZN, ZW, ZY, etc, are known as verticals.
The two numbers which specify the position of a star, X, in this systemare the azimuth, A, and the altitude, a. The altitude of X is the anglemeasured along the vertical circle through X from the horizon at Y to X.It is measured in degrees. An often-used alternative to altitude is thezenith distance, z, of X, indicated by ZX. Clearly, z = 90 - a. Azimuthmay be defined in a number of ways. For the purposes of this course,azimuth will be defined as the angle between the vertical through thenorth point and the vertical through the star at X, measured eastwardsfrom the north point along the horizon from 0 to 360°. This definitionapplies to observers in both the northern and the southern hemispheres.
It is often useful to know how high a star is above the horizon and inwhat direction it can be found - this is the main advantage of the alt-azsystem. The main disadvantage of the alt-az system is that it is a localcoordinate system - i.e. two observers at different points on the Earth'ssurface will measure different altitudes and azimuths for the same star atthe same time. In addition, an observer will find that the star's alt-azcoordinates changes with time as the celestial sphere appears to rotate.Despite these problems, most modern research telescopes use alt-az mounts,as shown in the figure above, owing to their lower cost and greater stability.This means that computer control systems which can transform alt-azcoordinates to equatorial coordinates are required.
Celestial Sphere:
The celestial sphere has a north and south celestial pole as well as acelestial equator which are projected reference points to the samepositions on the Earth surface. Right Ascension and Declination serve asan absolute coordinate system fixed on the sky, rather than a relativesystem like the zenith/horizon system. Right Ascension is the equivalentof longitude, only measured in hours, minutes and seconds (since the Earthrotates in the same units). Declination is the equivalent of latitudemeasured in degrees from the celestial equator (0 to 90). Any point ofthe celestial (i.e. the position of a star or planet) can be referencedwith a unique Right Ascension and Declination.
The celestial sphere has a north and south celestial pole as well as acelestial equator which are projected from reference points from the Earthsurface. Since the Earth turns on its axis once every 24 hours, the starstrace arcs through the sky parallel to the celestial equator. Theappearance of this motion will vary depending on where you are located onthe Earth's surface.
Note that the daily rotation of the Earth causeseach star and planet to make a daily circular path around the northcelestial pole referred to as the diurnal motion.
Equatorial Coordinate System :
Because the altitude and azimuth of a star are constantly changing, it isnot possible to use the horizontal coordinate system in a catalog ofpositions. A more convenient coordinate system for cataloging purposes isone based on the celestial equator and the celestial poles and defined ina similar manner to latitude and longitude on the surface of the Earth. Inthis system, known as the equatorial coordinate system, the analog oflatitude is the declination, δ.The declination of a star is its angular distance in degrees measured fromthe celestial equator along the meridian through the star. It is measurednorth and south of the celestial equator and ranges from 0° at thecelestial equator to 90° at the celestial poles, being taken to be positivewhen north of the celestial equator and negative when south. In the figure below,the declination of the star X is given by the angle between Y and X.
The analog of longitude in the equatorial system is the hour angle, H(you may also see the symbol HA used). Defining the observer's meridianas the arc of the great circle which passes from the north celestial polethrough the zenith to the south celestial pole, the hour angle of a staris measured from the observer's meridian westwards (for both northern andsouthern hemisphere observers) to the meridian through the star (from 0° to360°). Because of the rotation of the Earth, hour angle increases uniformlywith time, going from 0° to 360° in 24 hours. The hour angle of a particularobject is therefore a measure of the time since it crossed the observer'smeridian - hence the name. For this reason it is often measured in hours,minutes and seconds of time rather than in angular measure (just likelongitude). In figure above, the hour angle of the star X is given by theangle Z-NCP-X. Note that all stars attain their maximum altitude above thehorizon when they transit (or attain upper culmination on, in the case ofcircumpolar stars) the observers meridian.
The declination of a star does not change with time. The hour angle does,and hence it is not a suitable coordinate for a catalogue. This problem isovercome in a manner analogous to the way in which the Greenwich meridianhas been (arbitrarily) selected as the zero point for the measurement oflongitude. The zero point chosen on the celestial sphere is the firstpoint of Aries, γ, and theangle between it and the intersection of the meridian through a celestialobject and the celestial equator is called the right ascension (RA) of theobject. Right ascension is sometimes denoted by the Greek letter αand is measured from 0h to24h along the celestial equator eastwards (in the direction of aright-handed screw motion about the direction to the north celestial pole)from the first point of Aries, that is, in the opposite direction to thatin which hour angle is measured. Like the definition of hour angle, thisconvention holds for observers in both northern and southern hemispheres.In above figure, the right ascension of the star X is given by the angle-NCP-Y.
Most modern research telescopes do not use equatorial mounts due to theirhigher cost and lower stability. This is at the expense of the simplicityof telescope tracking - an equatorially-mounted telescope need only moveits right ascension axis in order to track the motion of the celestialsphere. The figure above shows an example of an equatorially-mountedtelescope.
The above diagram displays the typical motion of a star or planet in the sky, withthe relevant angles marked. The star, X, crosses the horizon at L and V, travelingfrom L through U on the meridian, down to V. H is the hour angle of the star, whichwill equal the arc BT, but not the arc XU.Constellations:
Drawn onto the celestial sphere are imaginary shapes calledconstellations, Latin for `group of stars'. Due to the nature of the Earth'ssurface, the sky is divided into the northern and southern sky as seen from eachhemisphere.
The origin of the names of particular constellations is lost with time,dating back before written records. The ancient Greeks were the first torecord the oral legends. But the boundaries of the constellations werefixed by the International Astronomical Union in 1928. For many of theconstellations it is easy to see where they got their names. For example,
In all, there are 88 constellationnames cataloged by Hipparchus in 100 B.C. To find out more about yourfavorite constellation, goto Constellationof the Month. Since the boundaries are fixed, a star will always remain in aconstellation unless its proper motion moves it into another.
Star Names:
Hipparchus also developed a simply method of identifying the stars in thesky by using a letter from the Greek alphabet combined with theconstellation name.
So, for example, the brightest star in the constellation Orion is AlphaOrion, the second brightest star is Beta Orion, and so on. When theletters run out, we use a number 33 Orion, 101 Orion, etc. Some of thevery brightest stars have their own names due to their importance to earlynavigators. For example, Alpha Canis Major is Sirius, the Dog Star.
About 6000 stars are visible with the naked eye on a dark, moonlessnight. However, there are over 1013 stars in the whole MilkyWay galaxy were the solar system resides. Thus, we only see a very smallfraction of the closest and brightest stars with our eyes. The first star catalogwas published by Ptolemy in the 2nd century. It contained the positions of 1025 ofthe brightest stars in the sky. The first modern star catalog was the BonnerDurchmusterung by Argelander in 1860, containing 320,000 stars.
Since the Earth's axis is tilted 23 1/2 degrees from the plane of ourorbit around the Sun, The apparent motion of the Sun through the skyduring the year is a circle that is inclined 23 1/2 degrees from thecelestial equator. This circle is called the ecliptic and passesthrough 12 of the 88 constellations that we call the zodiac.
Equinox and Solstice:
The projection of the Sun's path across the sky during the year iscalled the ecliptic. The points where the ecliptic crosses thecelestial equator are the vernal and autumnal equinox's. The pointwere the Sun is highest in the northern hemisphere is called thesummer solstice. The lowest point is the winter solstice.
Days are longest in the summer for the northern hemisphere due to tiltof the Earth's axis allowing for more sunlight to be projected ontosurface. Note also the reason for the 'midnight' sun at the North Polein summer. Longest day of the year is at the summer solstice
For opposite reasons, days are short and nights long in the winter.
Seasons:
The seasons are caused by the angle the sun's rays make with the ground.Higher Sun angle means more luminosity per square meter. Low Sun angleproduces fewer rays per square meter. More intensity means more heat and,therefore, higher temperatures.
Note that, due to the fact that our oceans store heat, the actual changesin mean Earth temperature are delayed by several weeks, i.e. the hottestdays of summer are usually in late July, over a month from the summersolstice.
Sidereal and Synodic time:
A `day' is defined by the rotation of object in question. For example,the Moon's `day' is 27 Earth days.
A `year' is defined by the revolution of object in question. Forexample, the Earth's year is 365 days divided into months; whereas, Pluto's `year' is 248.6 Earthyears.
Typical we use synodic time, which means with respect to the Sun, inour everyday life. For example, noon, midnight, twilight are allexamples of synodic time based on where the Sun is in the sky (e.g.directly overhead on the equator for noon). Astronomers often usesidereal time, which means time with respect to the stars, for theirmeasurements.
Since the Earth moves around the Sun once every 365 days, the Sun'sapparent position in the sky changes from day to day.
Note, in the above diagram, we see that the Earth's synodic day is 4mins longer than its sidereal day.Phases of the Moon:
The Moon is tidally locked to the Earth, meaning that one side alwaysfaces us (the nearside), whereas the farside is forever hidden from us.In addition, the Moon is illuminated on one side by the Sun, the otherside is dark (night).
Which parts are illuminated (daytime) and which parts we see from theEarth are determined by the Moon's orbit around the Earth, what is calledthe phase of the Moon (click here for the currentphase of the Moon).
As the Moon moves counterclockwise around the Earth, the daylight sidebecomes more and more visible (i.e. we say the Moon is `waxing'). After full Moon isreached we begin to see more and more of the nighttime side (i.e. we saythe Moon is `waning'). This whole monthly sequence is called the phases of the Moon.
University Of Oregon Sun Path
Eclipses:
On rare occasions the Moon comes between the Earth and the Sun (a solar eclipse) or the Moonenters the Earth's shadow (a lunar eclipse).
University Of Oregon Sun Path Chart
Eclipses only occur when the line of nodes is aligned with the Sun (2to 5 times a year). All solar eclipses occur at new moon with a duration of only 4 to 7 mins.The path of shadow across surface of the Earth determines who gets to seeit.All lunar eclipses occur at full moon and everyone on nightside of Earthis able to observe lunar eclipses. The deep red color during the eclipsecomes from light refracted through Earth's atmosphere (i.e. redsunset's)