From: Subject: Sun's Daily Path over Griffith Observatory Date: Mon, 23 Nov 2009 12:19:02 -0800 MIME-Version: 1.0 Content-Type: multipart/related; type="text/html"; boundary="----=_NextPart_000_003A_01CA6C37.2454F8B0" X-MimeOLE: Produced By Microsoft MimeOLE V6.00.2900.3350 This is a multi-part message in MIME format. ------=_NextPart_000_003A_01CA6C37.2454F8B0 Content-Type: text/html; charset="iso-8859-1" Content-Transfer-Encoding: quoted-printable Content-Location: http://www.griffithobs.org/skyfiles/skysunspath.html Sun's Daily Path over Griffith Observatory

The Sun's Daily Path Across the Sky

Dinsmore Alter and Clarence Cleminshaw

Chapter 9 of Pictorial Astronomy
published = by the=20 Griffith Observatory, Los Angeles, =A91948

The changing position of the sun in the sky from hour to hour and = from day to=20 day is of interest to everyone, but especially to architects. They want = to know=20 the answers to such questions as, when and how far the sun will shine in = the=20 windows of different sides of a building. The accompanying diagrams at = the=20 bottom of this page show the sun's daily path across the sky at the = latitudes of=20 34=B0 and 42=B0 North. From these two diagrams, one can determine the = approximate=20 position of the sun with respect to the horizon of any place in the = United=20 States at any hour of the year.

The sun's position with reference to the horizon is expressed by = altitude and=20 azimuth. Altitude is the angular distance above the horizon measured=20 perpendicularly to the horizon. It has a maximum value of 90=B0 at the = zenith,=20 which is the point overhead. It is marked on the diagram at intervals of = 10=B0=20 along the vertical line in the center. That line represents the = celestial=20 meridian, which the sun crosses at noon. An altitude can be read at any = time of=20 the day by means of concentric circles which are 2=B0 apart.

Azimuth is the angular distance measured along the horizon in a = clockwise=20 direction. Astronomers measure it from the south point, navigators from = the=20 north point. In our diagrams which follow the navigators' rule, north is = 0=B0,=20 east is 90=B0, south is 180=B0, and west is 270=B0. Each degree of = azimuth is shown in=20 the circular band around the outside of the diagram, and numbers from 60 = to 300=20 indicate the azimuth at intervals of 10=B0. Lines radiating from the = center mark=20 the azimuth at intervals of 5=B0.

The sun's daily path across the sky on or about the 21st day of each = month is=20 indicated by means of seven curved lines. The upper one is for June and = the=20 lower one is for December. Each of the other five is for two months. For = instance, the path on March 21 is the same as on September 23.

Each path is divided into hours. Numbers along the upper and lower = paths show=20 the hours which would be indicated by a sundial. This is known as local = apparent=20 sun time. Standard time will differ from this, depending on the equation = of time=20 and the longitude. However, this uncertainty is not important for our = purpose,=20 which is to show the general course of the sun across the sky and not = its exact=20 position at any particular instant of time.

It is interesting to see how much the sunrise and sunset points move = during=20 the year. The azimuths of the extreme positions are as follows:

 =
    Date      Sunrise  Sunset
     June 21      61=B0    299=B0=20
     Dec. 21     119=B0    241=B0
     Difference   58=B0     58=B0

In other words, the sun rises 29=B0 south of east and sets 29=B0 = south of west on=20 December 21. This is for a latitude of 34=B0 N. The arc of the horizon = between the=20 east point and the sunrise point is called amplitude. On June 21 it is = 23-1/2=B0=20 at the equator, and increases to 90=B0 at the Arctic Circle, where the = sun is up=20 for 24 hours on that day. The value at a latitude of 42=B0 N. is = 32-1/2=B0.

On March 21 and September 23 the sun is on the celestial equator, = which=20 intersects the celestial meridian at a distance from the zenith equal to = the=20 latitude. At a latitude of 34=B0 N. On these dates the noon sun is 34=B0 = south of=20 the zenith. Its altitude is 56=B0, which is found by subtracting 34=B0 = from 90=B0.

On June 21 the sun is 23-1/2=B0 north of the celestial equator and = its maximum=20 altitude at noon is 79-1/2=B0, which is the sum of 56=B0 and 23-1/2=B0. = On December 21=20 the sun is 23-1/2=B0 south of the celestial equator and its noon = altitude is=20 32-1/2=B0, which is the difference between 56=B0 and 23-1/2=B0. Thus the = sun's=20 meridian altitude varies by 47=B0. This range is twice 23-1/2=B0 and is = the same for=20 all latitudes.

The approximate duration of sunlight can be estimated from the = diagram. The=20 upper curve for June 21 shows that the sun rises at about 4:45 A.M. and = sets at=20 about 7:15 P.M., giving a duration of 14-1/2 hours. On May 21 and July = 21 the=20 sun is up for 14 hours. The number for March and September is 12 hours. = There=20 are nearly 10 hours of sunshine on the shortest day.

The sun's daily path across the sky on or about the = 21st of each=20 month at latitude 34=B0 N.
All times are standard time (adjust for = daylight=20 time when in effect; remember, 9:00 standard time =3D 10:00 daylight = time).

The sun's daily path across the sky on or about the = 21st of each=20 month at latitude 42=B0 N.
All times are standard time (adjust for = daylight=20 time when in effect; remember, 9:00 standard time =3D 10:00 daylight = time).

[Precise sunrise and sunset times for Los Angeles are = given on=20 the Sky = Information page.]

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l.bmi_mapImage=3Dp.bmi_imgObj;p.bmi_imgObj.bmi_areaEl=3Del;return 1;}}=0A= return 0;}=0A= function bmi_resetTitle(el){if(!el)=0A= return;if(el.bmi_touched!=3D1)=0A= return;el.title=3D"";if(el.bmi_oldTitle){el.title=3Del.bmi_oldTitle;if(el= .bmi_oldAlt){el.alt=3Del.bmi_oldAlt;}}=0A= else if(el.bmi_oldAlt){el.alt=3Del.bmi_oldAlt;if(bmi_ie)=0A= el.title=3Del.alt;}=0A= if(el.bmi_gotOriginal){if(el.bmi_orig_mouseout){el.onmouseout=3Del.bmi_or= ig_mouseout;}}}=0A= function bmi_checkElement(el){var pwindow=3Dnull;if(el.bmi_gotOriginal)=0A= return;if(el.bmi_mapImage){if(el.bmi_mapImage.bmi_gotOriginal=3D=3D1){el.= bmi_gotOriginal=3D1;if(el.bmi_touched)=0A= bmi_resetTitle(el);return;}}=0A= if(el.bmi_touched!=3D1){bmi_setElementTitle(el);if(el.onmouseout){el.bmi_= orig_mouseout=3Del.onmouseout;el.onmouseout=3Dbmi_safeMouseOutEvents;}=0A= else{el.onmouseout=3Dbmi_safeMouseOutEvents;}}=0A= else{el.title=3Del.bmi_title;el.alt=3Del.bmi_alt;}=0A= if(el.bmi_mapImage)=0A= bmi_imageObjSelected=3Del.bmi_mapImage;else=0A= bmi_imageObjSelected=3Del;if(bmi_ie||bmi_opera)=0A= pwindow=3Ddocument.parentWindow;else if(bmi_nsonly||is_gecko)=0A= pwindow=3Ddocument.defaultView;else=0A= pwindow=3Dnull;if(pwindow&&(pwindow!=3Dpwindow.parent)){pwindow.focus();e= l.bmi_changedFocus=3D1;}=0A= return;}=0A= function bmi_setElementTitle(el){var = tmpAlt=3D"";if(el.alt){tmpAlt=3Del.alt;el.bmi_oldAlt=3Del.alt;el.bmi_alt=3D= "";el.alt=3D"";}=0A= if(el.title){el.bmi_oldTitle=3Del.title;el.title=3D"";}=0A= else{el.title=3DtmpAlt+"";}=0A= if(bmi_opera||bmi_firefox){el.title=3Dbmi_ffx_op_toolTip;el.bmi_touched=3D= 1;el.bmi_title=3Del.title;}=0A= else{el.title=3Del.title+bmi_toolTipSeperator+bmi_toolTip;el.bmi_touched=3D= 1;el.bmi_title=3Del.title;}=0A= return;}=0A= function bmi_checkInputType(type){if(!type)=0A= return 0;if(type.match("image")||type.match("Image")){return 1;}=0A= return 0;}=0A= function bmi_checkMIMEType(type){var typeStr=3Dnew String(type);var = find=3D/image\//gi;if(typeStr.search(find)!=3D-1)=0A= return 1;return 0;}=0A= function bmi_mouseOver(e){bmi_imageObjSelected=3Dnull;var = obj;if(document.bmi_onmouseover_original!=3Dnull)=0A= document.bmi_onmouseover_original(e);if(bmi_ie||bmi_opera){var = e=3Dwindow.event;obj=3De.srcElement;}=0A= else{obj=3De.target;}=0A= if(obj.bmi_gotOriginal)=0A= return;if(bmi_ImageElement(obj)){bmi_checkElement(obj);}=0A= return;}=0A= function bmi_safeMouseOutEvents(e){var = obj;if(bmi_ie||bmi_opera){e=3Dwindow.event;obj=3De.srcElement;}=0A= else{obj=3De.target;}=0A= bmi_resetTitle(obj);if(obj.bmi_changedFocus=3D=3D1){var = pwindow=3Dnull;if(bmi_ie||bmi_opera)=0A= pwindow=3Ddocument.parentWindow;else if(bmi_nsonly||is_gecko)=0A= pwindow=3Ddocument.defaultView;else=0A= pwindow=3Dnull;if(pwindow){pwindow.top.focus();obj.bmi_changedFocus=3D0;}= }=0A= if(obj.bmi_orig_mouseout){obj.bmi_orig_mouseout();}}=0A= function bmi_updateImageSrc(src)=0A= {var found=3D0;var find=3D/\?/g;var editUrl;var editIndex;var = editProto;var bmiSignIndex;var bmiSign;srcString=3Dnew = String(src);if(srcString.search(find)!=3D-1)=0A= {found=3D1;srcString=3DsrcString.concat("&"+bmi_concatStr+"=3D1");}=0A= else=0A= {var i=3DsrcString.lastIndexOf("/");var = newStr=3DsrcString.substring(i+1);srcString=3DsrcString.concat("/"+bmi_co= ncatStr+"/"+newStr);}=0A= if(bmi_htmlEdit){editIndex=3DsrcString.indexOf("://");if(editIndex!=3D-1)= {editProto=3DsrcString.substring(0,editIndex+3);editUrl=3DsrcString.subst= ring(editIndex+3);editIndex=3DeditUrl.indexOf("/");if(editIndex!=3D-1){ed= itUrl=3DeditUrl.substring(editIndex+1);bmiSignIndex=3DeditUrl.indexOf("/"= );if(bmiSignIndex!=3D-1){bmiSign=3DeditUrl.substring(0,bmiSignIndex);if(b= miSign=3D=3D"bmi"){editUrl=3DeditUrl.substring(bmiSignIndex+1);srcString=3D= editProto+editUrl;}}}}}=0A= return(srcString);}=0A= function bmi_replaceImages(array){if(!array)=0A= return;for(var = i=3D0;i=3Dmaps.length){return linked;}=0A= if(objs[i].useMap){var newStr=3Dnew String(objs[i].useMap);var = mapName=3DnewStr.substring(newStr.lastIndexOf("#")+1);if(bmi_ImageElement= (objs[i])!=3D1)=0A= continue;for(var = j=3D0;j=3Dmaps.length){return;}=0A= objs=3Dnull;objs=3Ddocument.getElementsByTagName("INPUT");if(objs){num+=3D= bmi_linkMapImages(maps,objs);}=0A= if(num>=3Dmaps.length){return;}=0A= objs=3Dnull;objs=3Ddocument.getElementsByTagName("OBJECT");if(objs){num+=3D= bmi_linkMapImages(maps,objs);}}=0A= return;}=0A= var bmi_orig_onLoad;function bmi_SafeAddOnload(f,urlStr,htmlEdit)=0A= {if(urlStr){bmi_concatStr=3DurlStr;}=0A= if(htmlEdit){bmi_htmlEdit=3DhtmlEdit;}=0A= if(bmi_ie4){window.onload=3Df;}=0A= else = if(window.onload){if(window.onload!=3Df){bmi_orig_onLoad=3Dwindow.onload;= window.onload=3Df;}}=0A= else{window.onload=3Df;}}=0A= ------=_NextPart_000_003A_01CA6C37.2454F8B0--