
<HTML><HEAD>

<TITLE>Length of the day calc</TITLE>

<SCRIPT>

function toRadian(str) {

         return parseFloat(str) * 2.0 * Math.PI /

                   360.0;

}


 function earth(f) {

          var radius = 6371.0;  // km

          var radius1 = 3959.6;  // miles

          var radius2 = 3440.1;  // nautical miles

          var radius3 = 6366.134;  // km per radian

	  var radius4 = 1.0;  // constant1

	  var radius5 = 360.0;  // constant2

	  var radius6 = 60.0;  // constant3

	  var radius7 = 15.0;  // constant4

          var a = toRadian(f.lat_a.value);

          var b = toRadian(f.lat_a.value);

          var c = toRadian(f.lat_d.value -

                      f.lat_d.value);

          var d = toRadian(f.lat_d.value);



          with (Math) {



              f.length2.value = parseInt((radius4 * acos(-tan(a) * 
                                tan(d)) * radius5 / (Math.PI) /
				radius7),10);


		f.length3.value =parseInt((radius4 * acos(-tan(a) * 
                                tan(d)) * radius5 / (Math.PI) /
				radius7   -
				parseInt((radius4 * acos(-tan(a) * 
                                tan(d)) * radius5 / (Math.PI) /
				radius7),10))*radius6,10);


                  f.distance3.value = parseInt((radius *

                    acos(cos(a) * cos(a) * cos(c) + 

                    sin(a) * sin(a) )),10);


                  f.distance4.value = parseInt((radius3 *

                    cos(a) * acos(cos(c) )),10);

 
            }

}


</SCRIPT>

</HEAD>

<BODY BGCOLOR="#99FF" TEXT="#5000FF" LINK="#FF00FF">



</BODY>

<P><TD WIDTH="100%"><DT><IMG SRC="globe3.gif" BORDER=0 WIDTH=100 ALIGN=right></DT></TD></P>




<CENTER><P><TD WIDTH="100%"><DT><IMG SRC="length.jpg" BORDER=0 WIDTH=700 ALIGN=CENTER></DT></TD></P></CENTER>
<H1><B>A. <TD WIDTH="100%"><DT><IMG SRC="noatmosref.jpg" BORDER=0 WIDTH=250 ALIGN=CENTER></DT></TD> - </B></H1>
<FORM NAME="ecalc">

<TABLE>

<TR><TD>Latitude of the city of your choice (31.75N for Jerusalem)<TD><INPUT NAME="lat_a"> = a, (minus sign for Southern Latitudes.)

<TR><TD>Declination of the sun (any value between +23.5 and -23.5. Use <A HREF="declination.gif"> the declination curve vs. the day # of the year.</A> )<TD><INPUT NAME="lat_d"> = delta

</TABLE>


<HR>



<INPUT TYPE="BUTTON" VALUE="calculate"

onClick="earth(this.form)">

<p>

The length of the day from sunrise to sunset is 


<INPUT NAME="length2" > hours, and  <INPUT NAME="length3" >  minutes. Note that when you do not get a numerical value, the day length is 24 hours. 



<CENTER><P><TD WIDTH="100%"><DT></DT></TD></P></CENTER>

</FORM>



<P>
The length of the day was calculated by doubling the equation for the Hour Angle H between a transit of the sun and sunset: 
<p>
    H (of sunset) = arccos ( - tan(a)*tan(delta) ) .
<p>
<H1><B>B. <TD WIDTH="100%"><DT><IMG SRC="withatmosref.jpg" BORDER=0 WIDTH=400 ALIGN=CENTER></DT></TD> - </B></H1>

<SCRIPT>

function toRadian(str) {

         return parseFloat(str) * 2.0 * Math.PI /

                   360.0;

}


 function earth1(f) {

          var radius = 6371.0;  // km

          var radius1 = 3959.6;  // miles

          var radius2 = 3440.1;  // nautical miles

          var radius3 = 6366.134;  // km per radian

	  var radius4 = 1.0;  // constant1

	  var radius5 = 360.0;  // constant2

	  var radius6 = 60.0;  // constant3

	  var radius7 = 15.0;  // constant4

	  var zenith1 = 90.8333;  // constant5

          var z3 = -0.0145439; // constant6


          var a1 = toRadian(f.lat_a1.value);


          var d1 = toRadian(f.lat_d1.value);





          with (Math) {



              f.length4.value = parseInt((radius4 * acos(
				( z3 - sin(a1)*sin(d1))/
				(cos(a1) * cos(d1))) * radius5 / (Math.PI) /
				radius7),10);

		f.length5.value =parseInt((( radius4 * acos((
				z3 - sin(a1)*sin(d1))/(cos(a1) * 
                                cos(d1))) * radius5 / (Math.PI) /
				radius7 -
				parseInt((radius4 * acos(
				( z3 - sin(a1)*sin(d1))/
				(cos(a1) * cos(d1))) * radius5 / (Math.PI) /
				radius7),10)) * radius6),10);
 
            }

}


</SCRIPT>


<FORM NAME="ecalc1">
<TABLE>

<TR><TD>Latitude of the city of your choice<TD><INPUT NAME="lat_a1"> = a, (minus sign for Southern Latitudes.)

<TR><TD>Declination of the sun (any value between +23.5 and -23.5)<TD><INPUT NAME="lat_d1"> = delta

</TABLE>


<HR>



<INPUT TYPE="BUTTON" VALUE="calculate"

onClick="earth1(this.form)">

<p>

The length of the day from the apparent sunrise to the apparent sunset becomes 


<INPUT NAME="length4" > hours, and  <INPUT NAME="length5" >  minutes.  



<CENTER><P><TD WIDTH="100%"><DT></DT></TD></P></CENTER>

</FORM>



<P>
The length of the day was calculated by doubling the equation for the Hour Angle H between a transit of the sun and the apparent sunset (or sunrise): 
<p>
    H (of sunset) = arccos (( cos (z) - sin(a)*sin(delta)) / (cos(a)*cos(delta)) ) .
<p>
<CENTER><P>&nbsp;<FONT SIZE=+2><A HREF="gallery.html">Return to the Main Page.</A></P></CENTER>

<H1><B>C. <TD WIDTH="100%"><DT><IMG SRC="lengthofday.jpg" BORDER=0 WIDTH=600 ALIGN=CENTER></DT></TD> - </B></H1>

<SCRIPT>

function toRadian(str) {

         return parseFloat(str) * 2.0 * Math.PI /

                   360.0;


}


 function earth2(f) {

          var radius = 6371.0;  // km

          var radius1 = 3959.6;  // miles

          var radius2 = 3440.1;  // nautical miles

          var radius3 = 6366.134;  // km per radian

	  var radius4 = 1.0;  // constant1

	  var radius5 = 360.0;  // constant2

	  var radius6 = 60.0;  // constant3

	  var radius7 = 15.0;  // constant4

	  var zenith1 = 90.8333;  // constant5

          var z3 = -0.0145439; // constant6

          var z4 = 0.3987491; // constant7


          var z5 = 0.0172024; // constant8

          var z6 = 4.36511505; // constant9

          var z7 = 30.061602; // constant10

          var z8 = 0.98562628; // constant11

          var z9 = 0.01; // constant12

          var a2 = toRadian(f.lat_a2.value);

          var d2y = toRadian(f.lat_d2y.value);
          var d2m = toRadian(f.lat_d2m.value);

          var d2d = toRadian(f.lat_d2d.value);



          with (Math) {

 

              f.length6.value = parseInt((radius4 * acos(
				( z3 - sin(a2)*z4*sin(z6+z7*d2m+z8*d2d))/
				(cos(a2)*cos(asin(z4*sin(z6+z7*d2m+z8*d2d))))) * radius5 / (Math.PI) /
				radius7),10);

		f.length7.value =parseInt(((radius4 * acos(
				( z3 - sin(a2)*z4*sin(z6+z7*d2m+z8*d2d))/
				(cos(a2)*cos(asin(z4*sin(z6+z7*d2m+z8*d2d))))) * radius5 / (Math.PI) /
				radius7 -
				parseInt((radius4 * acos(
				( z3 - sin(a2)*z4*sin(z6+z7*d2m+z8*d2d))/
				(cos(a2)*cos(asin(z4*sin(z6+z7*d2m+z8*d2d))))) * radius5 / (Math.PI) /
				radius7),10)) * radius6),10);
 
            }

}


</SCRIPT>


<FORM NAME="ecalc2">
<TABLE>

<TR><TD>Latitude of the city of your choice<TD><INPUT NAME="lat_a2"> = a, (minus sign for Southern Latitudes.)
<TR><TD>Type 4 digits for the year : <TD><INPUT NAME="lat_d2y"> ,
<TR><TD>type 1 or 2 digits for the month : <TD><INPUT NAME="lat_d2m"> ,
<TR><TD>and type 1 or 2 digits for the day of the month : <TD><INPUT NAME="lat_d2d"> .

</TABLE>


<HR>



<INPUT TYPE="BUTTON" VALUE="calculate"

onClick="earth2(this.form)">

<p>

The length of the day from the apparent sunrise to the apparent sunset becomes 


<INPUT NAME="length6" > hours, and  <INPUT NAME="length7" >  minutes.  



<CENTER><P><TD WIDTH="100%"><DT></DT></TD></P></CENTER>

</FORM>



<P>
<CENTER><P><TD WIDTH="100%"><DT></DT></TD></P></CENTER>
 <HR>
<p>



<P>

<center><FONT SIZE=4 COLOR=#6000FF>Other Cities</FONT><BR>





<TABLE BORDER bgcolor=SILVER><TR BGCOLOR=PLUM>

<TD WIDTH=100 ALIGN="center" NOWRAP>CITY</TD>

<TD WIDTH=100 ALIGN="center" NOWRAP>LATITUDE (N)</TD>

<TD width=100 ALIGN="center" NOWRAP>LONGITUDE (E)</TD>

</TR>



<TD>London</TD>

<TD>51



</TD>

<TD>0</TD>

</TR>

</TR>



<TD>Tel Aviv</TD>

<TD>32



</TD>

<TD>35</TD>

</TR>

<TR>

<TD>Cairo</TD>

<TD>

30

</TD>

<TD>31</TD>

</TR>
<TR>

<TD>Wien</TD>

<TD>

48

</TD>

<TD>16</TD>

</TR>



<TR>

<TD>New York</TD>

<TD>

41

</TD>

<TD>-74 (74W)</TD>

</TR>



<TR>

<TD>Tokyo</TD>

<TD>

35

</TD>

<TD>140</TD>

</TR>



<TR>

<TD>Singapore</TD>

<TD>

1

</TD>

<TD>104</TD>

</TR>

<TR>

<TD>Manila</TD>

<TD>

14

</TD>

<TD>121</TD>

</TR>



<TR>

<TD>Bangkok</TD>

<TD>

13

</TD>

<TD>100</TD>

</TR>







<TR>

<TD>Anchorage (ALASKA)</TD>

<TD>

61.2

</TD>

<TD>-150</TD>

</TR><TR>

<TD>Tucson</TD>

<TD>
32.25

</TD>

<TD>-110.95</TD>

</TR>
<TR>

<TD>Addis Ababa</TD>

<TD>

9

</TD>

<TD>39</TD>

</TR>
<TR>

<TD>Phoenix</TD>

<TD>

33.5

</TD>

<TD>-112.05</TD>

</TR></TABLE></center>

<p>
<CENTER><P>&nbsp;<FONT SIZE=+2><A HREF="gallery.html">Return to the Main Page.</A></P></CENTER>

<p>
<CENTER><P><TD WIDTH="100%"><DT></DT></TD></P></CENTER>
 <HR>
<p>





Prepared by A.C. from the <IMG SRC="hujianimation.gif" ALIGN=CENTER>
<p>
<CENTER><P><TD WIDTH="100%"><DT></DT></TD></P></CENTER>
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<p>
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