<description/> <author>Robert Mutel</author> <company/> <keywords/> <revisedBy>Robert Mutel</revisedBy> </userData> <identityInfo> <revision>1</revision> <documentID>a5d72f4a-cbd2-4b9c-88ad-65d14e28a393</documentID> <versionID>c12f3dea-e61e-42b6-b3eb-dde3ff8d0692</versionID> <parentVersionID>00000000-0000-0000-0000-000000000000</parentVersionID> <branchID>00000000-0000-0000-0000-000000000000</branchID> </identityInfo> </metadata> <settings> <presentation> <textRendering> <textStyles> <textStyle name="Normal"> <blockAttr margin-left="0" margin-right="0" text-indent="inherit" text-align="left" list-style-type="inherit" tabs="inherit"/> <inlineAttr font-family="Arial" font-charset="0" font-size="10" font-weight="normal" font-style="normal" underline="false" line-through="false" vertical-align="baseline"/> </textStyle> <textStyle name="Heading 1"> <blockAttr margin-left="0" margin-right="0" text-indent="inherit" text-align="left" list-style-type="inherit" tabs="inherit"/> <inlineAttr 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</results> </mathRendering> <pageModel show-page-frame="false" show-header-frame="true" show-footer-frame="false" header-footer-start-page="1" paper-code="1" orientation="portrait" print-single-page-width="false" page-width="450" page-height="600"> <margins left="86.4" right="86.4" top="86.4" bottom="86.4"/> <header use-full-page-width="false"> <left>{\rtf1\ansi\ansicpg1252\deff0\deflang1033{\fonttbl{\f0\fswiss\fprq15 Arial;}{\f1\fswiss\fprq15\fcharset0 Arial;}} \viewkind4\uc1\pard\f0\fs18\{n\}\f1 of \{nn\}\f0\par } </left> <center>{\rtf1\ansi\ansicpg1252\deff0\deflang1033{\fonttbl{\f0\fswiss\fprq15\fcharset0 Arial;}{\f1\fswiss\fprq15 Arial;}} \viewkind4\uc1\pard\qc\f0\fs18\par \f1\par } </center> <right>{\rtf1\ansi\ansicpg1252\deff0\deflang1033{\fonttbl{\f0\fswiss\fprq15\fcharset0 Arial;}{\f1\fswiss\fprq15 Arial;}} \viewkind4\uc1\pard\qr\f0\fs18 Saved: \f1\{fd\}\par } </right> </header> <footer use-full-page-width="true"> <center>{\rtf1\ansi\deff0\deflang1033{\fonttbl{\f0\fswiss 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exclude-large-results="false" save-text-images="false" screen-dpi="96"/> <miscellaneous> <handbook handbook-region-tag-ub="1581" can-delete-original-handbook-regions="true" can-delete-user-regions="true" can-print="true" can-copy="true" can-save="true" file-permission-mask="4294967295"/> </miscellaneous> </settings> <regions> <region region-id="132" left="12" top="14.25" width="351.75" height="36" align-x="12" align-y="24" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <f family="Arial" charset="0"> <inlineAttr line-through="false">Verification of JAVA Celestial Navigation paper calculation: 3 star solution</inlineAttr> </f> RLM 29 Jan 2004 </text> </region> <region region-id="757" left="456" top="32.25" width="151.5" height="12" align-x="456" align-y="42" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <c val="#00f">JD given y,m,d,ut (Meeus p. 61-62)</c> </text> </region> <region region-id="758" left="468" top="63" width="202.5" height="110.25" align-x="531" align-y="72" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:function> <ml:id xml:space="preserve">JD</ml:id> <ml:boundVars> <ml:id xml:space="preserve">y</ml:id> <ml:id xml:space="preserve">m</ml:id> <ml:id xml:space="preserve">d</ml:id> <ml:id xml:space="preserve">ut</ml:id> </ml:boundVars> </ml:function> <ml:program> <ml:ifThen> <ml:apply> <ml:lessThan/> <ml:id xml:space="preserve">m</ml:id> <ml:real>3</ml:real> </ml:apply> <ml:localDefine> <ml:id xml:space="preserve">y</ml:id> <ml:apply> <ml:minus/> <ml:id xml:space="preserve">y</ml:id> <ml:real>1</ml:real> </ml:apply> </ml:localDefine> 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xml:space="preserve">c</ml:id> <ml:apply> <ml:minus/> <ml:apply> <ml:minus/> <ml:apply> <ml:plus/> <ml:id xml:space="preserve">d</ml:id> <ml:apply> <ml:div/> <ml:id xml:space="preserve">ut</ml:id> <ml:real>24</ml:real> </ml:apply> </ml:apply> <ml:real>13</ml:real> </ml:apply> <ml:real>1524.5</ml:real> </ml:apply> </ml:localDefine> <ml:localDefine> <ml:id xml:space="preserve">jd</ml:id> <ml:apply> <ml:plus/> <ml:apply> <ml:plus/> <ml:id xml:space="preserve">a</ml:id> <ml:id xml:space="preserve">b</ml:id> </ml:apply> <ml:id xml:space="preserve">c</ml:id> </ml:apply> </ml:localDefine> </ml:program> </ml:define> </math> <rendering item-idref="1"/> </region> <region region-id="134" left="12" top="68.25" width="246.75" height="12" align-x="24.75" align-y="78" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <f family="Arial" charset="0"> <inlineAttr line-through="false">Define ancilliary variables, function definitions, constants</inlineAttr> </f> </text> </region> <region region-id="3" left="24" top="92.25" width="96" height="13.5" align-x="56.25" align-y="102" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:function> <ml:id xml:space="preserve">a</ml:id> <ml:boundVars> <ml:id xml:space="preserve">λ</ml:id> <ml:id xml:space="preserve">δ</ml:id> </ml:boundVars> </ml:function> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:id xml:space="preserve">cos</ml:id> <ml:id xml:space="preserve">λ</ml:id> </ml:apply> <ml:apply> <ml:id xml:space="preserve">cos</ml:id> <ml:id xml:space="preserve">δ</ml:id> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="2"/> </region> <region region-id="7" left="138" top="92.25" width="94.5" height="13.5" align-x="171" align-y="102" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:function> <ml:id xml:space="preserve">b</ml:id> <ml:boundVars> <ml:id xml:space="preserve">λ</ml:id> <ml:id xml:space="preserve">δ</ml:id> </ml:boundVars> </ml:function> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:id xml:space="preserve">sin</ml:id> <ml:id xml:space="preserve">λ</ml:id> </ml:apply> <ml:apply> <ml:id xml:space="preserve">cos</ml:id> <ml:id xml:space="preserve">δ</ml:id> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="3"/> </region> <region region-id="11" left="276" top="92.25" width="51.75" height="12" align-x="276" align-y="102" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> Equation 11 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<ml:boundVars> <ml:id xml:space="preserve">ζ</ml:id> </ml:boundVars> </ml:function> <ml:apply> <ml:id xml:space="preserve">cos</ml:id> <ml:id xml:space="preserve">ζ</ml:id> </ml:apply> </ml:define> </math> <rendering item-idref="5"/> </region> <region region-id="762" left="186" top="116.25" width="53.25" height="13.5" align-x="198" align-y="126" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">κ</ml:id> <ml:real>1.002738</ml:real> </ml:define> </math> <rendering item-idref="6"/> </region> <region region-id="238" left="12" top="158.25" width="154.5" height="12" align-x="12" align-y="168" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <f family="Arial" charset="0"> 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</ml:apply> </ml:parens> <ml:real>0.5</ml:real> </ml:apply> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="7"/> </region> <region region-id="360" left="168" top="194.25" width="109.5" height="12" align-x="174" align-y="204" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> xyz to geocentric latitude </text> </region> <region region-id="760" left="444" top="194.25" width="151.5" height="12" align-x="444" align-y="204" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <sp/> <c val="#00f">GMST (radians)<sp count="2"/>at 0h UT (AA B6)</c> </text> </region> <region region-id="759" left="456" top="219" width="239.25" height="204" align-x="517.5" align-y="228" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:function> <ml:id xml:space="preserve">GST0</ml:id> <ml:boundVars> <ml:id xml:space="preserve">y</ml:id> <ml:id xml:space="preserve">m</ml:id> <ml:id xml:space="preserve">d</ml:id> </ml:boundVars> </ml:function> <ml:program> <ml:localDefine> <ml:id xml:space="preserve">j</ml:id> <ml:apply> <ml:id xml:space="preserve">JD</ml:id> <ml:sequence> <ml:id xml:space="preserve">y</ml:id> <ml:id xml:space="preserve">m</ml:id> <ml:id xml:space="preserve">d</ml:id> <ml:real>0</ml:real> </ml:sequence> </ml:apply> </ml:localDefine> <ml:localDefine> <ml:id xml:space="preserve">t</ml:id> <ml:apply> <ml:div/> <ml:apply> <ml:minus/> <ml:id xml:space="preserve">j</ml:id> <ml:real>2451545.0</ml:real> </ml:apply> <ml:real>36525</ml:real> </ml:apply> </ml:localDefine> <ml:localDefine> <ml:id xml:space="preserve">a</ml:id> <ml:apply> <ml:mult 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<ml:mult style="default"/> <ml:id xml:space="preserve">b</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> </ml:apply> <ml:apply> <ml:mult style="default"/> <ml:id xml:space="preserve">c</ml:id> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">t</ml:id> <ml:real>2</ml:real> </ml:apply> </ml:apply> </ml:apply> <ml:apply> <ml:mult style="default"/> <ml:id xml:space="preserve">e</ml:id> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">t</ml:id> <ml:real>3</ml:real> </ml:apply> </ml:apply> </ml:apply> </ml:localDefine> <ml:localDefine> <ml:id xml:space="preserve">gst</ml:id> <ml:apply> <ml:id xml:space="preserve">mod</ml:id> <ml:sequence> <ml:id xml:space="preserve">gst</ml:id> <ml:apply> <ml:mult style="default"/> <ml:real>86400</ml:real> <ml:id xml:space="preserve">sec</ml:id> </ml:apply> </ml:sequence> </ml:apply> </ml:localDefine> <ml:ifThen> <ml:apply> <ml:lessThan/> <ml:id xml:space="preserve">gst</ml:id> <ml:apply> <ml:mult style="default"/> <ml:real>0</ml:real> <ml:id xml:space="preserve">sec</ml:id> </ml:apply> </ml:apply> <ml:localDefine> <ml:id xml:space="preserve">gst</ml:id> <ml:apply> <ml:plus/> <ml:id xml:space="preserve">gst</ml:id> <ml:apply> <ml:mult style="default"/> <ml:real>86400</ml:real> <ml:id xml:space="preserve">sec</ml:id> </ml:apply> </ml:apply> </ml:localDefine> </ml:ifThen> <ml:localDefine> <ml:id xml:space="preserve">gst</ml:id> <ml:apply> <ml:mult style="default"/> <ml:id xml:space="preserve">gst</ml:id> <ml:apply> <ml:div/> <ml:apply> <ml:mult style="default"/> <ml:real>2</ml:real> <ml:id xml:space="preserve">π</ml:id> </ml:apply> <ml:apply> <ml:mult style="default"/> <ml:real>86400</ml:real> <ml:id xml:space="preserve">sec</ml:id> </ml:apply> </ml:apply> </ml:apply> </ml:localDefine> </ml:program> </ml:define> </math> <rendering item-idref="8"/> </region> <region region-id="358" left="30" top="236.25" width="93.75" height="13.5" align-x="73.5" align-y="246" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:function> <ml:id xml:space="preserve">Λ</ml:id> <ml:boundVars> <ml:id xml:space="preserve">x</ml:id> <ml:id xml:space="preserve">y</ml:id> <ml:id xml:space="preserve">z</ml:id> </ml:boundVars> </ml:function> <ml:apply> <ml:id xml:space="preserve">atan2</ml:id> <ml:sequence> <ml:id xml:space="preserve">x</ml:id> <ml:id xml:space="preserve">y</ml:id> </ml:sequence> </ml:apply> </ml:define> </math> <rendering item-idref="9"/> </region> <region region-id="359" left="174" top="236.25" width="69" height="12" align-x="180" align-y="246" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> xyz to longitude </text> </region> <region region-id="574" left="6" top="272.25" width="211.5" height="12" align-x="18.75" align-y="282" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <f family="Arial" charset="0"> <inlineAttr line-through="false">Define some handy functions at right (GST0, JD)</inlineAttr> </f> </text> </region> <region region-id="764" left="18" top="301.5" width="194.25" height="28.5" align-x="102.75" align-y="318" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:function> <ml:id xml:space="preserve">hmsrad</ml:id> <ml:boundVars> <ml:id xml:space="preserve">hh</ml:id> <ml:id xml:space="preserve">mm</ml:id> <ml:id xml:space="preserve">ss</ml:id> </ml:boundVars> </ml:function> <ml:apply> <ml:mult style="default"/> <ml:parens> <ml:apply> <ml:plus/> <ml:apply> <ml:plus/> <ml:parens> <ml:id xml:space="preserve">hh</ml:id> </ml:parens> <ml:apply> <ml:div/> <ml:id xml:space="preserve">mm</ml:id> <ml:real>60</ml:real> </ml:apply> </ml:apply> <ml:apply> <ml:div/> <ml:id xml:space="preserve">ss</ml:id> <ml:real>3600</ml:real> </ml:apply> </ml:apply> </ml:parens> <ml:apply> <ml:div/> <ml:id xml:space="preserve">π</ml:id> <ml:real>12</ml:real> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="10"/> </region> <region region-id="831" left="18" top="349.5" width="284.25" height="28.5" align-x="102.75" align-y="366" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:function> <ml:id xml:space="preserve">dmsrad</ml:id> <ml:boundVars> <ml:id xml:space="preserve">dd</ml:id> <ml:id xml:space="preserve">mm</ml:id> <ml:id xml:space="preserve">ss</ml:id> </ml:boundVars> </ml:function> <ml:apply> <ml:mult style="default"/> <ml:parens> <ml:apply> <ml:plus/> <ml:apply> <ml:plus/> <ml:parens> <ml:id xml:space="preserve">dd</ml:id> </ml:parens> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:id xml:space="preserve">sign</ml:id> <ml:id xml:space="preserve">dd</ml:id> </ml:apply> <ml:apply> <ml:div/> <ml:apply> <ml:absval/> <ml:id xml:space="preserve">mm</ml:id> </ml:apply> <ml:real>60</ml:real> </ml:apply> </ml:apply> </ml:apply> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:id xml:space="preserve">sign</ml:id> <ml:id xml:space="preserve">dd</ml:id> </ml:apply> <ml:apply> <ml:div/> <ml:apply> <ml:absval/> <ml:id xml:space="preserve">ss</ml:id> </ml:apply> <ml:real>3600</ml:real> </ml:apply> </ml:apply> </ml:apply> </ml:parens> <ml:apply> <ml:div/> <ml:id xml:space="preserve">π</ml:id> <ml:real>180</ml:real> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="11"/> </region> <region region-id="1045" left="12" top="386.25" width="193.5" height="12" align-x="13.5" align-y="396" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <f family="Arial" charset="0"> <inlineAttr line-through="false">Epoch of observation: 19 Feb 2004 at 20 UT</inlineAttr> </f> </text> </region> <region region-id="1046" left="18" top="410.25" width="234" height="13.5" align-x="48" align-y="420" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">GHAγ</ml:id> <ml:apply> <ml:id xml:space="preserve">mod</ml:id> <ml:sequence> <ml:apply> <ml:plus/> <ml:apply> <ml:id xml:space="preserve">GST0</ml:id> <ml:sequence> <ml:real>2004</ml:real> <ml:real>2</ml:real> <ml:real>19</ml:real> </ml:sequence> </ml:apply> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:id xml:space="preserve">hmsrad</ml:id> <ml:sequence> <ml:real>20</ml:real> <ml:real>0</ml:real> <ml:real>0</ml:real> </ml:sequence> </ml:apply> <ml:id xml:space="preserve">κ</ml:id> </ml:apply> </ml:apply> <ml:apply> <ml:mult style="default"/> <ml:real>2</ml:real> <ml:id xml:space="preserve">π</ml:id> </ml:apply> </ml:sequence> </ml:apply> </ml:define> </math> <rendering item-idref="12"/> </region> <region region-id="1052" left="282" top="410.25" width="77.25" height="13.5" align-x="311.25" align-y="420" show-border="false" show-highlight="true" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">GHAγ</ml:id> <ml:unitOverride> <ml:id xml:space="preserve">deg</ml:id> </ml:unitOverride> <result xmlns="http://schemas.mathsoft.com/math20"> <unitedValue> <ml:real>89.116718450249451</ml:real> <unitMonomial xmlns="http://schemas.mathsoft.com/units10"> <unitReference unit="degree"/> </unitMonomial> </unitedValue> </result> </ml:eval> </math> <rendering item-idref="13"/> </region> <region region-id="1047" left="18" top="440.25" width="96.75" height="13.5" align-x="57.75" align-y="450" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:function> <ml:id xml:space="preserve">SHA</ml:id> <ml:boundVars> <ml:id xml:space="preserve">α</ml:id> </ml:boundVars> </ml:function> <ml:apply> <ml:minus/> <ml:apply> <ml:mult style="default"/> <ml:real>360</ml:real> <ml:id xml:space="preserve">deg</ml:id> </ml:apply> <ml:id xml:space="preserve">α</ml:id> </ml:apply> </ml:define> </math> <rendering item-idref="14"/> </region> <region region-id="1048" left="168" top="440.25" width="46.5" height="12" align-x="186" align-y="450" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> Equation 1 </text> </region> <region region-id="1049" left="18" top="464.25" width="159.75" height="13.5" align-x="58.5" align-y="474" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:function> <ml:id xml:space="preserve">GHA</ml:id> <ml:boundVars> <ml:id xml:space="preserve">α</ml:id> </ml:boundVars> </ml:function> <ml:apply> <ml:id xml:space="preserve">mod</ml:id> <ml:sequence> <ml:apply> <ml:plus/> <ml:id xml:space="preserve">GHAγ</ml:id> <ml:apply> <ml:id xml:space="preserve">SHA</ml:id> <ml:id xml:space="preserve">α</ml:id> </ml:apply> </ml:apply> <ml:apply> <ml:mult style="default"/> <ml:real>2</ml:real> <ml:id xml:space="preserve">π</ml:id> </ml:apply> </ml:sequence> </ml:apply> </ml:define> </math> <rendering item-idref="15"/> </region> <region region-id="1079" left="198" top="464.25" width="110.25" height="13.5" align-x="223.5" align-y="474" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:function> <ml:id xml:space="preserve">λ</ml:id> <ml:boundVars> <ml:id xml:space="preserve">α</ml:id> </ml:boundVars> </ml:function> <ml:apply> <ml:minus/> <ml:apply> <ml:mult style="default"/> <ml:real>360</ml:real> <ml:id xml:space="preserve">deg</ml:id> </ml:apply> <ml:apply> <ml:id xml:space="preserve">GHA</ml:id> <ml:id xml:space="preserve">α</ml:id> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="16"/> </region> <region region-id="1054" left="18" top="488.25" width="60" height="12" align-x="25.5" align-y="498" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <f family="Arial" charset="0"> <inlineAttr line-through="false">Star positions</inlineAttr> </f> </text> </region> <region region-id="1070" left="96" top="489" width="32.25" height="12.75" align-x="104.25" align-y="498" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">i</ml:id> <ml:range> <ml:real>0</ml:real> <ml:real>3</ml:real> </ml:range> </ml:define> </math> <rendering item-idref="17"/> </region> <region region-id="1581" left="156" top="488.25" width="177.75" height="24" align-x="156" align-y="498" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <f family="Arial" charset="0"> <inlineAttr line-through="false">Zenith angles derived from test case: </inlineAttr> </f> <f family="Symbol" charset="2" size="10"> <inlineAttr font-style="normal" underline="false" line-through="false">F</inlineAttr> </f> <f family="Arial" charset="0"> <inlineAttr line-through="false"> = 35.000N, </inlineAttr> </f> <inlineAttr font-style="normal" underline="false" line-through="false"> <f family="Symbol" charset="2" size="10"> l </f> </inlineAttr> <f family="Arial" charset="0"> <inlineAttr line-through="false"> = 75.000E</inlineAttr> </f> </text> </region> <region region-id="1066" left="12" top="530.25" width="87.75" height="82.5" align-x="40.5" align-y="546" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">α</ml:id> <ml:id xml:space="preserve">i</ml:id> </ml:apply> <ml:sequence> <ml:apply> <ml:id xml:space="preserve">hmsrad</ml:id> <ml:sequence> <ml:real>6</ml:real> <ml:real>45</ml:real> <ml:real>19.08</ml:real> </ml:sequence> </ml:apply> <ml:apply> <ml:id xml:space="preserve">hmsrad</ml:id> <ml:sequence> <ml:real>7</ml:real> <ml:real>39</ml:real> <ml:real>30.24</ml:real> </ml:sequence> </ml:apply> <ml:apply> <ml:id xml:space="preserve">hmsrad</ml:id> <ml:sequence> <ml:real>4</ml:real> <ml:real>36</ml:real> <ml:real>8.52</ml:real> </ml:sequence> </ml:apply> <ml:apply> <ml:id xml:space="preserve">hmsrad</ml:id> <ml:sequence> <ml:real>7</ml:real> <ml:real>45</ml:real> <ml:real>33.18</ml:real> </ml:sequence> </ml:apply> </ml:sequence> </ml:define> </math> <rendering item-idref="18"/> </region> <region region-id="1076" left="126" top="530.25" width="93" height="82.5" align-x="154.5" align-y="546" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">δ</ml:id> <ml:id xml:space="preserve">i</ml:id> </ml:apply> <ml:sequence> <ml:apply> <ml:id xml:space="preserve">dmsrad</ml:id> <ml:sequence> <ml:real>-16</ml:real> <ml:real>43</ml:real> <ml:real>12.1</ml:real> </ml:sequence> </ml:apply> <ml:apply> <ml:id xml:space="preserve">dmsrad</ml:id> <ml:sequence> <ml:real>5</ml:real> <ml:real>12</ml:real> <ml:real>58.8</ml:real> </ml:sequence> </ml:apply> <ml:apply> <ml:id xml:space="preserve">dmsrad</ml:id> <ml:sequence> <ml:real>16</ml:real> <ml:real>31</ml:real> <ml:real>6</ml:real> </ml:sequence> </ml:apply> <ml:apply> <ml:id xml:space="preserve">dmsrad</ml:id> <ml:sequence> <ml:real>28</ml:real> <ml:real>01</ml:real> <ml:real>5.4</ml:real> </ml:sequence> </ml:apply> </ml:sequence> </ml:define> </math> <rendering item-idref="19"/> </region> <region region-id="1077" left="246" top="530.25" width="46.5" height="82.5" align-x="267" align-y="546" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">ζ</ml:id> <ml:id xml:space="preserve">i</ml:id> </ml:apply> <ml:sequence> <ml:apply> <ml:mult style="default"/> <ml:real>78.83</ml:real> <ml:id xml:space="preserve">deg</ml:id> </ml:apply> <ml:apply> <ml:mult style="default"/> <ml:real>54.22</ml:real> <ml:id xml:space="preserve">deg</ml:id> </ml:apply> <ml:apply> <ml:mult style="default"/> <ml:real>84.64</ml:real> <ml:id xml:space="preserve">deg</ml:id> </ml:apply> <ml:apply> <ml:mult style="default"/> <ml:real>40.90</ml:real> <ml:id xml:space="preserve">deg</ml:id> </ml:apply> </ml:sequence> </ml:define> </math> <rendering item-idref="20"/> </region> <region region-id="1078" left="342" top="528" width="67.5" height="84.75" align-x="350.25" align-y="546" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">Star</ml:id> <ml:id xml:space="preserve">i</ml:id> </ml:apply> <ml:sequence> <ml:str xml:space="preserve">Sirius</ml:str> <ml:str xml:space="preserve">Procyon</ml:str> <ml:str xml:space="preserve">Aldebaran</ml:str> <ml:str xml:space="preserve">Pollux</ml:str> </ml:sequence> </ml:define> </math> <rendering item-idref="21"/> </region> <region region-id="584" left="12" top="650.25" width="301.5" height="12" align-x="12" align-y="660" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <f family="Arial" charset="0"> <inlineAttr line-through="false">1. </inlineAttr> </f> <f family="Arial" charset="0"> <inlineAttr line-through="false">Positions, observed zenith angles for three stars from Megastar</inlineAttr> </f> </text> </region> <region region-id="1080" left="18" top="681" width="24.75" height="12.75" align-x="30.75" align-y="690" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">i1</ml:id> <ml:real>0</ml:real> </ml:define> </math> <rendering item-idref="22"/> </region> <region region-id="1081" left="72" top="681" width="24.75" height="12.75" align-x="84.75" align-y="690" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">i2</ml:id> <ml:real>1</ml:real> </ml:define> </math> <rendering item-idref="23"/> </region> <region region-id="1455" left="120" top="681" width="24.75" height="12.75" align-x="132.75" align-y="690" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">i3</ml:id> <ml:real>2</ml:real> </ml:define> </math> <rendering item-idref="24"/> </region> <region region-id="1456" left="6" top="705" width="73.5" height="18" align-x="33.75" align-y="714" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">Star</ml:id> <ml:id xml:space="preserve">i1</ml:id> </ml:apply> <result xmlns="http://schemas.mathsoft.com/math20"> <ml:str 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item-idref="58"/> </region> <region region-id="1563" left="30" top="1070.25" width="90.75" height="13.5" align-x="72.75" align-y="1080" show-border="false" show-highlight="true" is-protected="true" z-order="0" background-color="#ffffc6" tag=""> <math optimize="false" disable-calc="false"> <ml:eval xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:apply> <ml:id xml:space="preserve">Φ</ml:id> <ml:sequence> <ml:id xml:space="preserve">x</ml:id> <ml:id xml:space="preserve">y</ml:id> <ml:id xml:space="preserve">z</ml:id> </ml:sequence> </ml:apply> <ml:unitOverride> <ml:id xml:space="preserve">deg</ml:id> </ml:unitOverride> <result xmlns="http://schemas.mathsoft.com/math20"> <unitedValue> <ml:real>34.993347126550567</ml:real> <unitMonomial xmlns="http://schemas.mathsoft.com/units10"> <unitReference unit="degree"/> </unitMonomial> </unitedValue> </result> </ml:eval> </math> <rendering item-idref="59"/> </region> <region region-id="1580" left="174" top="1083" width="93" height="18" align-x="201.75" align-y="1092" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">Star</ml:id> <ml:id xml:space="preserve">i3</ml:id> </ml:apply> <result xmlns="http://schemas.mathsoft.com/math20"> <ml:str xml:space="preserve">Aldebaran</ml:str> </result> </ml:eval> </math> <rendering item-idref="60"/> </region> <region region-id="1135" left="12" top="1376.25" width="294" height="12" align-x="12" align-y="1386" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <f family="Arial" charset="0"> <inlineAttr line-through="false">sitions, observed zenith angles for first pair of stars from Table1</inlineAttr> </f> </text> </region> <region region-id="1136" left="18" top="1407" width="24.75" height="12.75" align-x="30.75" align-y="1416" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">i1</ml:id> <ml:real>0</ml:real> </ml:define> </math> <rendering item-idref="61"/> </region> <region region-id="1137" left="72" top="1407" width="24.75" height="12.75" align-x="84.75" align-y="1416" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">i2</ml:id> <ml:real>2</ml:real> </ml:define> </math> <rendering item-idref="62"/> </region> <region region-id="1138" left="120" top="1407" width="73.5" height="18" align-x="147.75" align-y="1416" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">Star</ml:id> <ml:id xml:space="preserve">i1</ml:id> </ml:apply> <result xmlns="http://schemas.mathsoft.com/math20"> <ml:str xml:space="preserve">Sirius</ml:str> </result> </ml:eval> </math> <rendering item-idref="63"/> </region> <region region-id="1139" left="216" top="1407" width="93" height="18" align-x="243.75" align-y="1416" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">Star</ml:id> <ml:id xml:space="preserve">i2</ml:id> </ml:apply> <result xmlns="http://schemas.mathsoft.com/math20"> <ml:str xml:space="preserve">Aldebaran</ml:str> </result> </ml:eval> </math> <rendering item-idref="64"/> </region> <region region-id="1140" left="6" top="1430.25" width="37.5" height="15.75" align-x="22.5" align-y="1440" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">α1</ml:id> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">α</ml:id> <ml:id xml:space="preserve">i1</ml:id> </ml:apply> </ml:define> </math> <rendering item-idref="65"/> </region> <region region-id="1141" left="72" top="1430.25" width="37.5" height="15.75" align-x="88.5" align-y="1440" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">α2</ml:id> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">α</ml:id> 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disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">ζ2</ml:id> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">ζ</ml:id> <ml:id xml:space="preserve">i2</ml:id> </ml:apply> </ml:define> </math> <rendering item-idref="70"/> </region> <region region-id="1146" left="12" top="1460.25" width="78" height="15.75" align-x="42" align-y="1470" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">SHA1</ml:id> <ml:apply> <ml:id xml:space="preserve">SHA</ml:id> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">α</ml:id> <ml:id xml:space="preserve">i1</ml:id> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="71"/> </region> <region region-id="1147" left="114" top="1461" width="81.75" height="12.75" align-x="143.25" align-y="1470" 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xml:space="preserve">GHA</ml:id> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">α</ml:id> <ml:id xml:space="preserve">i1</ml:id> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="73"/> </region> <region region-id="1149" left="324" top="1461" width="82.5" height="12.75" align-x="354" align-y="1470" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">GHA1</ml:id> <ml:unitOverride> <ml:id xml:space="preserve">deg</ml:id> </ml:unitOverride> <result xmlns="http://schemas.mathsoft.com/math20"> <unitedValue> <ml:real>347.78721845024944</ml:real> <unitMonomial xmlns="http://schemas.mathsoft.com/units10"> <unitReference unit="degree"/> </unitMonomial> </unitedValue> </result> </ml:eval> </math> <rendering item-idref="74"/> </region> <region region-id="1150" left="12" top="1490.25" width="48.75" height="15.75" align-x="27" align-y="1500" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">λ1</ml:id> <ml:apply> <ml:id xml:space="preserve">λ</ml:id> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">α</ml:id> <ml:id xml:space="preserve">i1</ml:id> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="75"/> </region> <region region-id="1151" left="78" top="1490.25" width="62.25" height="13.5" align-x="92.25" align-y="1500" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">λ1</ml:id> <ml:unitOverride> <ml:id xml:space="preserve">deg</ml:id> </ml:unitOverride> <result xmlns="http://schemas.mathsoft.com/math20"> <unitedValue> <ml:real>12.212781549750565</ml:real> <unitMonomial xmlns="http://schemas.mathsoft.com/units10"> <unitReference unit="degree"/> </unitMonomial> </unitedValue> </result> </ml:eval> </math> <rendering item-idref="76"/> </region> <region region-id="1152" left="168" top="1490.25" width="48.75" height="15.75" align-x="183" align-y="1500" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">λ2</ml:id> <ml:apply> <ml:id xml:space="preserve">λ</ml:id> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">α</ml:id> <ml:id xml:space="preserve">i2</ml:id> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="77"/> </region> <region region-id="1153" left="240" top="1490.25" width="66.75" height="13.5" align-x="254.25" align-y="1500" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">λ2</ml:id> <ml:unitOverride> <ml:id xml:space="preserve">deg</ml:id> </ml:unitOverride> <result xmlns="http://schemas.mathsoft.com/math20"> <unitedValue> <ml:real>339.91878154975052</ml:real> <unitMonomial xmlns="http://schemas.mathsoft.com/units10"> <unitReference unit="degree"/> </unitMonomial> </unitedValue> </result> </ml:eval> </math> <rendering item-idref="78"/> </region> <region region-id="1154" left="12" top="1520.25" width="149.25" height="12" align-x="12" align-y="1530" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <f family="Arial" charset="0"> <inlineAttr line-through="false">Calculate A-F variables, equations</inlineAttr> </f> </text> </region> <region region-id="1155" left="36" top="1544.25" width="56.25" height="13.5" align-x="51" align-y="1554" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">a1</ml:id> <ml:apply> <ml:id xml:space="preserve">a</ml:id> <ml:sequence> <ml:id xml:space="preserve">λ1</ml:id> <ml:id xml:space="preserve">δ1</ml:id> </ml:sequence> </ml:apply> </ml:define> </math> <rendering item-idref="79"/> </region> <region region-id="1156" left="114" top="1544.25" width="56.25" height="13.5" align-x="129" align-y="1554" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">a2</ml:id> <ml:apply> <ml:id xml:space="preserve">a</ml:id> <ml:sequence> <ml:id xml:space="preserve">λ2</ml:id> <ml:id xml:space="preserve">δ2</ml:id> </ml:sequence> </ml:apply> </ml:define> </math> <rendering item-idref="80"/> </region> <region region-id="1157" left="204" top="1544.25" width="57.75" height="13.5" align-x="219.75" align-y="1554" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">b1</ml:id> <ml:apply> <ml:id xml:space="preserve">b</ml:id> <ml:sequence> <ml:id xml:space="preserve">λ1</ml:id> <ml:id xml:space="preserve">δ1</ml:id> </ml:sequence> </ml:apply> </ml:define> </math> <rendering item-idref="81"/> </region> <region region-id="1158" left="282" top="1544.25" width="57.75" height="13.5" align-x="297.75" align-y="1554" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">b2</ml:id> <ml:apply> <ml:id xml:space="preserve">b</ml:id> <ml:sequence> <ml:id xml:space="preserve">λ2</ml:id> <ml:id xml:space="preserve">δ2</ml:id> </ml:sequence> </ml:apply> </ml:define> </math> <rendering item-idref="82"/> </region> <region region-id="1159" left="36" top="1568.25" width="42.75" height="13.5" align-x="51" align-y="1578" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">c1</ml:id> <ml:apply> <ml:id xml:space="preserve">c</ml:id> <ml:id xml:space="preserve">δ1</ml:id> </ml:apply> </ml:define> </math> <rendering item-idref="83"/> </region> <region region-id="1160" left="108" top="1568.25" width="42.75" height="13.5" align-x="123" align-y="1578" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">c2</ml:id> <ml:apply> <ml:id xml:space="preserve">c</ml:id> <ml:id xml:space="preserve">δ2</ml:id> </ml:apply> </ml:define> </math> <rendering item-idref="84"/> </region> <region region-id="1161" left="186" top="1568.25" width="44.25" height="13.5" align-x="201.75" align-y="1578" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">p1</ml:id> <ml:apply> <ml:id xml:space="preserve">p</ml:id> <ml:id xml:space="preserve">ζ1</ml:id> </ml:apply> </ml:define> </math> <rendering item-idref="85"/> </region> <region region-id="1162" left="258" top="1568.25" width="44.25" height="13.5" align-x="273.75" align-y="1578" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">p2</ml:id> <ml:apply> <ml:id xml:space="preserve">p</ml:id> <ml:id xml:space="preserve">ζ2</ml:id> </ml:apply> </ml:define> </math> <rendering item-idref="86"/> </region> <region region-id="1163" left="12" top="1599" width="75.75" height="12.75" align-x="25.5" align-y="1608" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">A</ml:id> <ml:apply> <ml:minus/> <ml:apply> <ml:mult style="default"/> <ml:id xml:space="preserve">a1</ml:id> <ml:id xml:space="preserve">b2</ml:id> </ml:apply> <ml:apply> <ml:mult style="default"/> <ml:id xml:space="preserve">a2</ml:id> <ml:id xml:space="preserve">b1</ml:id> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="87"/> </region> <region region-id="1164" left="120" top="1599" width="74.25" height="12.75" align-x="132" align-y="1608" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">B</ml:id> <ml:apply> <ml:minus/> <ml:apply> <ml:mult style="default"/> <ml:id xml:space="preserve">b2</ml:id> <ml:id xml:space="preserve">c1</ml:id> </ml:apply> <ml:apply> <ml:mult style="default"/> <ml:id xml:space="preserve">b1</ml:id> <ml:id xml:space="preserve">c2</ml:id> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="88"/> </region> <region region-id="1165" left="228" top="1604.25" width="51.75" height="12" align-x="228" align-y="1614" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> Equation 14 </text> </region> <region region-id="1166" left="12" top="1623" width="75.75" height="12.75" align-x="24" align-y="1632" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">C</ml:id> <ml:apply> <ml:minus/> <ml:apply> <ml:mult style="default"/> <ml:id xml:space="preserve">b2</ml:id> <ml:id xml:space="preserve">p1</ml:id> </ml:apply> <ml:apply> <ml:mult style="default"/> <ml:id xml:space="preserve">b1</ml:id> <ml:id xml:space="preserve">p2</ml:id> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="89"/> </region> <region region-id="1167" left="120" top="1623" width="73.5" height="12.75" 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<ml:minus/> <ml:apply> <ml:mult style="default"/> <ml:id xml:space="preserve">b1</ml:id> <ml:id xml:space="preserve">c2</ml:id> </ml:apply> <ml:apply> <ml:mult style="default"/> <ml:id xml:space="preserve">b2</ml:id> <ml:id xml:space="preserve">c1</ml:id> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="91"/> </region> <region region-id="1169" left="120" top="1647" width="73.5" height="12.75" align-x="131.25" align-y="1656" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">F</ml:id> <ml:apply> <ml:minus/> <ml:apply> <ml:mult style="default"/> <ml:id xml:space="preserve">c2</ml:id> <ml:id xml:space="preserve">p1</ml:id> </ml:apply> <ml:apply> <ml:mult style="default"/> <ml:id xml:space="preserve">c1</ml:id> <ml:id xml:space="preserve">p2</ml:id> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="92"/> </region> <region region-id="1170" left="12" top="1676.25" width="71.25" height="27.75" align-x="39" align-y="1692" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:function> <ml:id xml:space="preserve">Y</ml:id> <ml:boundVars> <ml:id xml:space="preserve">X</ml:id> </ml:boundVars> </ml:function> <ml:apply> <ml:div/> <ml:apply> <ml:minus/> <ml:id xml:space="preserve">F</ml:id> <ml:apply> <ml:mult style="default"/> <ml:id xml:space="preserve">D</ml:id> <ml:id xml:space="preserve">X</ml:id> </ml:apply> </ml:apply> <ml:id xml:space="preserve">E</ml:id> </ml:apply> </ml:define> </math> <rendering item-idref="93"/> </region> <region region-id="1171" left="114" top="1676.25" width="72.75" height="27.75" align-x="141" align-y="1692" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:function> <ml:id xml:space="preserve">Z</ml:id> <ml:boundVars> <ml:id xml:space="preserve">X</ml:id> </ml:boundVars> </ml:function> <ml:apply> <ml:div/> <ml:apply> <ml:minus/> <ml:id xml:space="preserve">C</ml:id> <ml:apply> <ml:mult style="default"/> <ml:id xml:space="preserve">A</ml:id> <ml:id xml:space="preserve">X</ml:id> </ml:apply> </ml:apply> <ml:id xml:space="preserve">B</ml:id> </ml:apply> </ml:define> </math> <rendering item-idref="94"/> </region> <region region-id="1172" left="222" top="1682.25" width="65.25" height="12" align-x="222" align-y="1692" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> Equation 15a,b </text> </region> <region region-id="1173" left="12" top="1706.25" 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Mathcad Professional 13.0 <description/> <author>Robert Mutel</author> <company/> <keywords/> <revisedBy>Robert Mutel</revisedBy> </userData> <identityInfo> <revision>1</revision> <documentID>a5d72f4a-cbd2-4b9c-88ad-65d14e28a393</documentID> <versionID>c12f3dea-e61e-42b6-b3eb-dde3ff8d0692</versionID> <parentVersionID>00000000-0000-0000-0000-000000000000</parentVersionID> <branchID>00000000-0000-0000-0000-000000000000</branchID> </identityInfo> </metadata> <settings> <presentation> <textRendering> <textStyles> <textStyle name="Normal"> <blockAttr margin-left="0" margin-right="0" text-indent="inherit" text-align="left" list-style-type="inherit" tabs="inherit"/> <inlineAttr font-family="Arial" font-charset="0" font-size="10" font-weight="normal" font-style="normal" underline="false" line-through="false" vertical-align="baseline"/> </textStyle> <textStyle name="Heading 1"> <blockAttr margin-left="0" margin-right="0" text-indent="inherit" text-align="left" list-style-type="inherit" 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text-align="center" list-style-type="inherit" tabs="inherit"/> <inlineAttr font-family="Times New Roman" font-charset="0" font-size="24" font-weight="bold" font-style="normal" underline="false" line-through="false" vertical-align="baseline"/> </textStyle> <textStyle name="Subtitle" base-style="Title"> <blockAttr margin-left="0" margin-right="0" text-indent="inherit" text-align="center" list-style-type="inherit" tabs="inherit"/> <inlineAttr font-family="Times New Roman" font-charset="0" font-size="18" font-weight="normal" font-style="normal" underline="false" line-through="false" vertical-align="baseline"/> </textStyle> </textStyles> </textRendering> <mathRendering equation-color="#000"> <operators multiplication="narrow-dot" derivative="derivative" literal-subscript="large" definition="colon-equal" global-definition="triple-equal" local-definition="left-arrow" equality="bold-equal" symbolic-evaluation="right-arrow"/> <mathStyles> <mathStyle name="Variables" font-family="Times New 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is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <c val="#00f">JD given y,m,d,ut (Meeus p. 61-62)</c> </text> </region> <region region-id="758" left="468" top="63" width="202.5" height="110.25" align-x="531" align-y="72" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:function> <ml:id xml:space="preserve">JD</ml:id> <ml:boundVars> <ml:id xml:space="preserve">y</ml:id> <ml:id xml:space="preserve">m</ml:id> <ml:id xml:space="preserve">d</ml:id> <ml:id xml:space="preserve">ut</ml:id> </ml:boundVars> </ml:function> <ml:program> <ml:ifThen> <ml:apply> <ml:lessThan/> <ml:id xml:space="preserve">m</ml:id> <ml:real>3</ml:real> </ml:apply> <ml:localDefine> <ml:id xml:space="preserve">y</ml:id> <ml:apply> <ml:minus/> <ml:id 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</ml:parens> </ml:apply> </ml:apply> </ml:localDefine> <ml:localDefine> <ml:id xml:space="preserve">c</ml:id> <ml:apply> <ml:minus/> <ml:apply> <ml:minus/> <ml:apply> <ml:plus/> <ml:id xml:space="preserve">d</ml:id> <ml:apply> <ml:div/> <ml:id xml:space="preserve">ut</ml:id> <ml:real>24</ml:real> </ml:apply> </ml:apply> <ml:real>13</ml:real> </ml:apply> <ml:real>1524.5</ml:real> </ml:apply> </ml:localDefine> <ml:localDefine> <ml:id xml:space="preserve">jd</ml:id> <ml:apply> <ml:plus/> <ml:apply> <ml:plus/> <ml:id xml:space="preserve">a</ml:id> <ml:id xml:space="preserve">b</ml:id> </ml:apply> <ml:id xml:space="preserve">c</ml:id> </ml:apply> </ml:localDefine> </ml:program> </ml:define> </math> <rendering item-idref="1"/> </region> <region region-id="134" left="12" top="68.25" width="246.75" height="12" align-x="24.75" align-y="78" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <f family="Arial" charset="0"> <inlineAttr line-through="false">Define ancilliary variables, function definitions, constants</inlineAttr> </f> </text> </region> <region region-id="3" left="24" top="92.25" width="96" height="13.5" align-x="56.25" align-y="102" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:function> <ml:id xml:space="preserve">a</ml:id> <ml:boundVars> <ml:id xml:space="preserve">λ</ml:id> <ml:id xml:space="preserve">δ</ml:id> </ml:boundVars> </ml:function> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:id xml:space="preserve">cos</ml:id> <ml:id xml:space="preserve">λ</ml:id> </ml:apply> <ml:apply> <ml:id xml:space="preserve">cos</ml:id> <ml:id xml:space="preserve">δ</ml:id> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="2"/> </region> <region region-id="7" left="138" top="92.25" width="94.5" height="13.5" align-x="171" align-y="102" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:function> <ml:id xml:space="preserve">b</ml:id> <ml:boundVars> <ml:id xml:space="preserve">λ</ml:id> <ml:id xml:space="preserve">δ</ml:id> </ml:boundVars> </ml:function> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:id xml:space="preserve">sin</ml:id> <ml:id xml:space="preserve">λ</ml:id> </ml:apply> <ml:apply> <ml:id xml:space="preserve">cos</ml:id> <ml:id xml:space="preserve">δ</ml:id> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="3"/> </region> <region region-id="11" left="276" top="92.25" width="51.75" height="12" align-x="276" align-y="102" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> Equation 11 </text> </region> <region region-id="135" left="24" top="116.25" width="54" height="13.5" align-x="46.5" align-y="126" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:function> <ml:id xml:space="preserve">c</ml:id> <ml:boundVars> <ml:id xml:space="preserve">δ</ml:id> </ml:boundVars> </ml:function> <ml:apply> <ml:id xml:space="preserve">sin</ml:id> <ml:id xml:space="preserve">δ</ml:id> </ml:apply> </ml:define> </math> <rendering item-idref="4"/> </region> <region region-id="136" left="102" top="116.25" width="57" height="13.5" align-x="125.25" align-y="126" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:function> <ml:id xml:space="preserve">p</ml:id> <ml:boundVars> <ml:id xml:space="preserve">ζ</ml:id> </ml:boundVars> </ml:function> <ml:apply> <ml:id xml:space="preserve">cos</ml:id> <ml:id xml:space="preserve">ζ</ml:id> </ml:apply> </ml:define> </math> <rendering item-idref="5"/> </region> <region region-id="762" left="186" top="116.25" width="53.25" height="13.5" align-x="198" align-y="126" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">κ</ml:id> <ml:real>1.002738</ml:real> </ml:define> </math> <rendering item-idref="6"/> </region> <region region-id="238" left="12" top="158.25" width="154.5" height="12" align-x="12" align-y="168" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <f family="Arial" charset="0"> <inlineAttr line-through="false">Define xyz -> long-lat<sp count="2"/>(not in paper)</inlineAttr> </f> </text> </region> <region region-id="246" left="24" top="182.25" width="127.5" height="39.75" align-x="67.5" align-y="198" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:function> <ml:id xml:space="preserve">Φ</ml:id> <ml:boundVars> <ml:id xml:space="preserve">x</ml:id> <ml:id xml:space="preserve">y</ml:id> <ml:id xml:space="preserve">z</ml:id> </ml:boundVars> </ml:function> <ml:apply> <ml:id xml:space="preserve">atan</ml:id> <ml:apply> <ml:div/> <ml:id xml:space="preserve">z</ml:id> <ml:apply> <ml:pow/> <ml:parens> <ml:apply> <ml:plus/> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">x</ml:id> <ml:real>2</ml:real> </ml:apply> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">y</ml:id> <ml:real>2</ml:real> </ml:apply> </ml:apply> </ml:parens> <ml:real>0.5</ml:real> </ml:apply> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="7"/> </region> <region region-id="360" left="168" top="194.25" width="109.5" height="12" align-x="174" align-y="204" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> xyz to geocentric latitude </text> </region> <region region-id="760" left="444" top="194.25" width="151.5" height="12" align-x="444" align-y="204" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <sp/> <c val="#00f">GMST (radians)<sp count="2"/>at 0h UT (AA B6)</c> </text> </region> <region region-id="759" left="456" top="219" width="239.25" height="204" align-x="517.5" align-y="228" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:function> <ml:id xml:space="preserve">GST0</ml:id> <ml:boundVars> <ml:id xml:space="preserve">y</ml:id> <ml:id xml:space="preserve">m</ml:id> <ml:id xml:space="preserve">d</ml:id> </ml:boundVars> </ml:function> <ml:program> <ml:localDefine> <ml:id xml:space="preserve">j</ml:id> <ml:apply> <ml:id xml:space="preserve">JD</ml:id> <ml:sequence> <ml:id xml:space="preserve">y</ml:id> <ml:id xml:space="preserve">m</ml:id> <ml:id xml:space="preserve">d</ml:id> <ml:real>0</ml:real> </ml:sequence> </ml:apply> </ml:localDefine> <ml:localDefine> <ml:id xml:space="preserve">t</ml:id> <ml:apply> <ml:div/> <ml:apply> <ml:minus/> <ml:id xml:space="preserve">j</ml:id> <ml:real>2451545.0</ml:real> </ml:apply> <ml:real>36525</ml:real> </ml:apply> </ml:localDefine> <ml:localDefine> <ml:id xml:space="preserve">a</ml:id> <ml:apply> <ml:mult style="default"/> <ml:real>24110.54841</ml:real> <ml:id xml:space="preserve">sec</ml:id> </ml:apply> </ml:localDefine> <ml:localDefine> <ml:id xml:space="preserve">b</ml:id> <ml:apply> <ml:mult style="default"/> <ml:real>8640184.812886</ml:real> <ml:id xml:space="preserve">sec</ml:id> </ml:apply> </ml:localDefine> <ml:localDefine> <ml:id xml:space="preserve">c</ml:id> <ml:apply> <ml:mult style="default"/> <ml:real>0.093104</ml:real> <ml:id xml:space="preserve">sec</ml:id> </ml:apply> </ml:localDefine> <ml:localDefine> <ml:id xml:space="preserve">e</ml:id> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:mult style="default"/> <ml:real>6.2</ml:real> <ml:apply> <ml:pow/> <ml:real>10</ml:real> <ml:real>-6</ml:real> </ml:apply> </ml:apply> <ml:id xml:space="preserve">sec</ml:id> </ml:apply> </ml:localDefine> <ml:localDefine> <ml:id xml:space="preserve">gst</ml:id> <ml:apply> <ml:minus/> <ml:apply> <ml:plus/> <ml:apply> <ml:plus/> <ml:id xml:space="preserve">a</ml:id> <ml:apply> <ml:mult style="default"/> <ml:id xml:space="preserve">b</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> </ml:apply> <ml:apply> <ml:mult style="default"/> <ml:id xml:space="preserve">c</ml:id> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">t</ml:id> <ml:real>2</ml:real> </ml:apply> </ml:apply> </ml:apply> <ml:apply> <ml:mult style="default"/> <ml:id xml:space="preserve">e</ml:id> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">t</ml:id> <ml:real>3</ml:real> </ml:apply> </ml:apply> </ml:apply> </ml:localDefine> <ml:localDefine> <ml:id xml:space="preserve">gst</ml:id> <ml:apply> <ml:id xml:space="preserve">mod</ml:id> <ml:sequence> <ml:id xml:space="preserve">gst</ml:id> <ml:apply> <ml:mult style="default"/> <ml:real>86400</ml:real> <ml:id xml:space="preserve">sec</ml:id> </ml:apply> </ml:sequence> </ml:apply> </ml:localDefine> <ml:ifThen> <ml:apply> <ml:lessThan/> <ml:id xml:space="preserve">gst</ml:id> <ml:apply> <ml:mult style="default"/> <ml:real>0</ml:real> <ml:id xml:space="preserve">sec</ml:id> </ml:apply> </ml:apply> <ml:localDefine> <ml:id xml:space="preserve">gst</ml:id> <ml:apply> <ml:plus/> <ml:id xml:space="preserve">gst</ml:id> <ml:apply> <ml:mult style="default"/> <ml:real>86400</ml:real> <ml:id xml:space="preserve">sec</ml:id> </ml:apply> </ml:apply> </ml:localDefine> </ml:ifThen> <ml:localDefine> <ml:id xml:space="preserve">gst</ml:id> <ml:apply> <ml:mult style="default"/> <ml:id xml:space="preserve">gst</ml:id> <ml:apply> <ml:div/> <ml:apply> <ml:mult style="default"/> <ml:real>2</ml:real> <ml:id xml:space="preserve">π</ml:id> </ml:apply> <ml:apply> <ml:mult style="default"/> <ml:real>86400</ml:real> <ml:id xml:space="preserve">sec</ml:id> </ml:apply> </ml:apply> </ml:apply> </ml:localDefine> </ml:program> </ml:define> </math> <rendering item-idref="8"/> </region> <region region-id="358" left="30" top="236.25" width="93.75" height="13.5" align-x="73.5" align-y="246" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:function> <ml:id xml:space="preserve">Λ</ml:id> <ml:boundVars> <ml:id xml:space="preserve">x</ml:id> <ml:id xml:space="preserve">y</ml:id> <ml:id xml:space="preserve">z</ml:id> </ml:boundVars> </ml:function> <ml:apply> <ml:id xml:space="preserve">atan2</ml:id> <ml:sequence> <ml:id xml:space="preserve">x</ml:id> <ml:id xml:space="preserve">y</ml:id> </ml:sequence> </ml:apply> </ml:define> </math> <rendering item-idref="9"/> </region> <region region-id="359" left="174" top="236.25" width="69" height="12" align-x="180" align-y="246" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> xyz to longitude </text> </region> <region region-id="574" left="6" top="272.25" width="211.5" height="12" align-x="18.75" align-y="282" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <f family="Arial" charset="0"> <inlineAttr line-through="false">Define some handy functions at right (GST0, JD)</inlineAttr> </f> </text> </region> <region region-id="764" left="18" top="301.5" width="194.25" height="28.5" align-x="102.75" align-y="318" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:function> <ml:id xml:space="preserve">hmsrad</ml:id> <ml:boundVars> <ml:id xml:space="preserve">hh</ml:id> <ml:id xml:space="preserve">mm</ml:id> <ml:id xml:space="preserve">ss</ml:id> </ml:boundVars> </ml:function> <ml:apply> <ml:mult style="default"/> <ml:parens> <ml:apply> <ml:plus/> <ml:apply> <ml:plus/> <ml:parens> <ml:id xml:space="preserve">hh</ml:id> </ml:parens> <ml:apply> <ml:div/> <ml:id xml:space="preserve">mm</ml:id> <ml:real>60</ml:real> </ml:apply> </ml:apply> <ml:apply> <ml:div/> <ml:id xml:space="preserve">ss</ml:id> <ml:real>3600</ml:real> </ml:apply> </ml:apply> </ml:parens> <ml:apply> <ml:div/> <ml:id xml:space="preserve">π</ml:id> <ml:real>12</ml:real> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="10"/> </region> <region region-id="831" left="18" top="349.5" width="284.25" height="28.5" align-x="102.75" align-y="366" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:function> <ml:id xml:space="preserve">dmsrad</ml:id> <ml:boundVars> <ml:id xml:space="preserve">dd</ml:id> <ml:id xml:space="preserve">mm</ml:id> <ml:id xml:space="preserve">ss</ml:id> </ml:boundVars> </ml:function> <ml:apply> <ml:mult style="default"/> <ml:parens> <ml:apply> <ml:plus/> <ml:apply> <ml:plus/> <ml:parens> <ml:id xml:space="preserve">dd</ml:id> </ml:parens> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:id xml:space="preserve">sign</ml:id> <ml:id xml:space="preserve">dd</ml:id> </ml:apply> <ml:apply> <ml:div/> <ml:apply> <ml:absval/> <ml:id xml:space="preserve">mm</ml:id> </ml:apply> <ml:real>60</ml:real> </ml:apply> </ml:apply> </ml:apply> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:id xml:space="preserve">sign</ml:id> <ml:id xml:space="preserve">dd</ml:id> </ml:apply> <ml:apply> <ml:div/> <ml:apply> <ml:absval/> <ml:id xml:space="preserve">ss</ml:id> </ml:apply> <ml:real>3600</ml:real> </ml:apply> </ml:apply> </ml:apply> </ml:parens> <ml:apply> <ml:div/> <ml:id xml:space="preserve">π</ml:id> <ml:real>180</ml:real> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="11"/> </region> <region region-id="1045" left="12" top="386.25" width="193.5" height="12" align-x="13.5" align-y="396" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <f family="Arial" charset="0"> <inlineAttr line-through="false">Epoch of observation: 19 Feb 2004 at 20 UT</inlineAttr> </f> </text> </region> <region region-id="1046" left="18" top="410.25" width="234" height="13.5" align-x="48" align-y="420" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">GHAγ</ml:id> <ml:apply> <ml:id xml:space="preserve">mod</ml:id> <ml:sequence> <ml:apply> <ml:plus/> <ml:apply> <ml:id xml:space="preserve">GST0</ml:id> <ml:sequence> <ml:real>2004</ml:real> <ml:real>2</ml:real> <ml:real>19</ml:real> </ml:sequence> </ml:apply> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:id xml:space="preserve">hmsrad</ml:id> <ml:sequence> <ml:real>20</ml:real> <ml:real>0</ml:real> <ml:real>0</ml:real> </ml:sequence> </ml:apply> <ml:id xml:space="preserve">κ</ml:id> </ml:apply> </ml:apply> <ml:apply> <ml:mult style="default"/> <ml:real>2</ml:real> <ml:id xml:space="preserve">π</ml:id> </ml:apply> </ml:sequence> </ml:apply> </ml:define> </math> <rendering item-idref="12"/> </region> <region region-id="1052" left="282" top="410.25" width="77.25" height="13.5" align-x="311.25" align-y="420" show-border="false" show-highlight="true" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">GHAγ</ml:id> <ml:unitOverride> <ml:id xml:space="preserve">deg</ml:id> </ml:unitOverride> <result xmlns="http://schemas.mathsoft.com/math20"> <unitedValue> <ml:real>89.116718450249451</ml:real> <unitMonomial xmlns="http://schemas.mathsoft.com/units10"> <unitReference unit="degree"/> </unitMonomial> </unitedValue> </result> </ml:eval> </math> <rendering item-idref="13"/> </region> <region region-id="1047" left="18" top="440.25" width="96.75" height="13.5" align-x="57.75" align-y="450" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:function> <ml:id xml:space="preserve">SHA</ml:id> <ml:boundVars> <ml:id xml:space="preserve">α</ml:id> </ml:boundVars> </ml:function> <ml:apply> <ml:minus/> <ml:apply> <ml:mult style="default"/> <ml:real>360</ml:real> <ml:id xml:space="preserve">deg</ml:id> </ml:apply> <ml:id xml:space="preserve">α</ml:id> </ml:apply> </ml:define> </math> <rendering item-idref="14"/> </region> <region region-id="1048" left="168" top="440.25" width="46.5" height="12" align-x="186" align-y="450" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> Equation 1 </text> </region> <region region-id="1049" left="18" top="464.25" width="159.75" height="13.5" align-x="58.5" align-y="474" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:function> <ml:id xml:space="preserve">GHA</ml:id> <ml:boundVars> <ml:id xml:space="preserve">α</ml:id> </ml:boundVars> </ml:function> <ml:apply> <ml:id xml:space="preserve">mod</ml:id> <ml:sequence> <ml:apply> <ml:plus/> <ml:id xml:space="preserve">GHAγ</ml:id> <ml:apply> <ml:id xml:space="preserve">SHA</ml:id> <ml:id xml:space="preserve">α</ml:id> </ml:apply> </ml:apply> <ml:apply> <ml:mult style="default"/> <ml:real>2</ml:real> <ml:id xml:space="preserve">π</ml:id> </ml:apply> </ml:sequence> </ml:apply> </ml:define> </math> <rendering item-idref="15"/> </region> <region region-id="1079" left="198" top="464.25" width="110.25" height="13.5" align-x="223.5" align-y="474" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:function> <ml:id xml:space="preserve">λ</ml:id> <ml:boundVars> <ml:id xml:space="preserve">α</ml:id> </ml:boundVars> </ml:function> <ml:apply> <ml:minus/> <ml:apply> <ml:mult style="default"/> <ml:real>360</ml:real> <ml:id xml:space="preserve">deg</ml:id> </ml:apply> <ml:apply> <ml:id xml:space="preserve">GHA</ml:id> <ml:id xml:space="preserve">α</ml:id> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="16"/> </region> <region region-id="1054" left="18" top="488.25" width="60" height="12" align-x="25.5" align-y="498" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <f family="Arial" charset="0"> <inlineAttr line-through="false">Star positions</inlineAttr> </f> </text> </region> <region region-id="1070" left="96" top="489" width="32.25" height="12.75" align-x="104.25" align-y="498" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">i</ml:id> <ml:range> <ml:real>0</ml:real> <ml:real>3</ml:real> </ml:range> </ml:define> </math> <rendering item-idref="17"/> </region> <region region-id="1581" left="156" top="488.25" width="177.75" height="24" align-x="156" align-y="498" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <f family="Arial" charset="0"> <inlineAttr line-through="false">Zenith angles derived from test case: </inlineAttr> </f> <f family="Symbol" charset="2" size="10"> <inlineAttr font-style="normal" underline="false" line-through="false">F</inlineAttr> </f> <f family="Arial" charset="0"> <inlineAttr line-through="false"> = 35.000N, </inlineAttr> </f> <inlineAttr font-style="normal" underline="false" line-through="false"> <f family="Symbol" charset="2" size="10"> l </f> </inlineAttr> <f family="Arial" charset="0"> <inlineAttr line-through="false"> = 75.000E</inlineAttr> </f> </text> </region> <region region-id="1066" left="12" top="530.25" width="87.75" height="82.5" align-x="40.5" align-y="546" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">α</ml:id> <ml:id xml:space="preserve">i</ml:id> </ml:apply> <ml:sequence> <ml:apply> <ml:id xml:space="preserve">hmsrad</ml:id> <ml:sequence> <ml:real>6</ml:real> <ml:real>45</ml:real> <ml:real>19.08</ml:real> </ml:sequence> </ml:apply> <ml:apply> <ml:id xml:space="preserve">hmsrad</ml:id> <ml:sequence> <ml:real>7</ml:real> <ml:real>39</ml:real> <ml:real>30.24</ml:real> </ml:sequence> </ml:apply> <ml:apply> <ml:id xml:space="preserve">hmsrad</ml:id> <ml:sequence> <ml:real>4</ml:real> <ml:real>36</ml:real> <ml:real>8.52</ml:real> </ml:sequence> </ml:apply> <ml:apply> <ml:id xml:space="preserve">hmsrad</ml:id> <ml:sequence> <ml:real>7</ml:real> <ml:real>45</ml:real> <ml:real>33.18</ml:real> </ml:sequence> </ml:apply> </ml:sequence> </ml:define> </math> <rendering item-idref="18"/> </region> <region region-id="1076" left="126" top="530.25" width="93" height="82.5" align-x="154.5" align-y="546" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">δ</ml:id> <ml:id xml:space="preserve">i</ml:id> </ml:apply> <ml:sequence> <ml:apply> <ml:id xml:space="preserve">dmsrad</ml:id> <ml:sequence> <ml:real>-16</ml:real> <ml:real>43</ml:real> <ml:real>12.1</ml:real> </ml:sequence> </ml:apply> <ml:apply> <ml:id xml:space="preserve">dmsrad</ml:id> <ml:sequence> <ml:real>5</ml:real> <ml:real>12</ml:real> <ml:real>58.8</ml:real> </ml:sequence> </ml:apply> <ml:apply> <ml:id xml:space="preserve">dmsrad</ml:id> <ml:sequence> <ml:real>16</ml:real> <ml:real>31</ml:real> <ml:real>6</ml:real> </ml:sequence> </ml:apply> <ml:apply> <ml:id xml:space="preserve">dmsrad</ml:id> <ml:sequence> <ml:real>28</ml:real> <ml:real>01</ml:real> <ml:real>5.4</ml:real> </ml:sequence> </ml:apply> </ml:sequence> </ml:define> </math> <rendering item-idref="19"/> </region> <region region-id="1077" left="246" top="530.25" width="46.5" height="82.5" align-x="267" align-y="546" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">ζ</ml:id> <ml:id xml:space="preserve">i</ml:id> </ml:apply> <ml:sequence> <ml:apply> <ml:mult style="default"/> <ml:real>78.83</ml:real> <ml:id xml:space="preserve">deg</ml:id> </ml:apply> <ml:apply> <ml:mult style="default"/> <ml:real>54.22</ml:real> <ml:id xml:space="preserve">deg</ml:id> </ml:apply> <ml:apply> <ml:mult style="default"/> <ml:real>84.64</ml:real> <ml:id xml:space="preserve">deg</ml:id> </ml:apply> <ml:apply> <ml:mult style="default"/> <ml:real>40.90</ml:real> <ml:id xml:space="preserve">deg</ml:id> </ml:apply> </ml:sequence> </ml:define> </math> <rendering item-idref="20"/> </region> <region region-id="1078" left="342" top="528" width="67.5" height="84.75" align-x="350.25" align-y="546" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">Star</ml:id> <ml:id xml:space="preserve">i</ml:id> </ml:apply> <ml:sequence> <ml:str xml:space="preserve">Sirius</ml:str> <ml:str xml:space="preserve">Procyon</ml:str> <ml:str xml:space="preserve">Aldebaran</ml:str> <ml:str xml:space="preserve">Pollux</ml:str> </ml:sequence> </ml:define> </math> <rendering item-idref="21"/> </region> <region region-id="584" left="12" top="650.25" width="301.5" height="12" align-x="12" align-y="660" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <f family="Arial" charset="0"> <inlineAttr line-through="false">1. </inlineAttr> </f> <f family="Arial" charset="0"> <inlineAttr line-through="false">Positions, observed zenith angles for three stars from Megastar</inlineAttr> </f> </text> </region> <region region-id="1080" left="18" top="681" width="24.75" height="12.75" align-x="30.75" align-y="690" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">i1</ml:id> <ml:real>0</ml:real> </ml:define> </math> <rendering item-idref="22"/> </region> <region region-id="1081" left="72" top="681" width="24.75" height="12.75" align-x="84.75" align-y="690" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" 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tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <f family="Arial" charset="0"> <inlineAttr line-through="false">Calculate A-F variables, equations</inlineAttr> </f> </text> </region> <region region-id="1155" left="36" top="1544.25" width="56.25" height="13.5" align-x="51" align-y="1554" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">a1</ml:id> <ml:apply> <ml:id xml:space="preserve">a</ml:id> <ml:sequence> <ml:id xml:space="preserve">λ1</ml:id> <ml:id xml:space="preserve">δ1</ml:id> </ml:sequence> </ml:apply> </ml:define> </math> <rendering item-idref="79"/> </region> <region region-id="1156" left="114" top="1544.25" width="56.25" height="13.5" align-x="129" align-y="1554" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">a2</ml:id> <ml:apply> <ml:id xml:space="preserve">a</ml:id> <ml:sequence> <ml:id xml:space="preserve">λ2</ml:id> <ml:id xml:space="preserve">δ2</ml:id> </ml:sequence> </ml:apply> </ml:define> </math> <rendering item-idref="80"/> </region> <region region-id="1157" left="204" top="1544.25" width="57.75" height="13.5" align-x="219.75" align-y="1554" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">b1</ml:id> <ml:apply> <ml:id xml:space="preserve">b</ml:id> <ml:sequence> <ml:id xml:space="preserve">λ1</ml:id> <ml:id xml:space="preserve">δ1</ml:id> </ml:sequence> </ml:apply> </ml:define> </math> <rendering item-idref="81"/> </region> <region region-id="1158" left="282" top="1544.25" width="57.75" height="13.5" align-x="297.75" align-y="1554" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">b2</ml:id> <ml:apply> <ml:id xml:space="preserve">b</ml:id> <ml:sequence> <ml:id xml:space="preserve">λ2</ml:id> <ml:id xml:space="preserve">δ2</ml:id> </ml:sequence> </ml:apply> </ml:define> </math> <rendering item-idref="82"/> </region> <region region-id="1159" left="36" top="1568.25" width="42.75" height="13.5" align-x="51" align-y="1578" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">c1</ml:id> <ml:apply> <ml:id xml:space="preserve">c</ml:id> <ml:id xml:space="preserve">δ1</ml:id> </ml:apply> </ml:define> </math> <rendering item-idref="83"/> </region> <region region-id="1160" left="108" top="1568.25" width="42.75" height="13.5" align-x="123" align-y="1578" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">c2</ml:id> <ml:apply> <ml:id xml:space="preserve">c</ml:id> <ml:id xml:space="preserve">δ2</ml:id> </ml:apply> </ml:define> </math> <rendering item-idref="84"/> </region> <region region-id="1161" left="186" top="1568.25" width="44.25" height="13.5" align-x="201.75" align-y="1578" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">p1</ml:id> <ml:apply> <ml:id xml:space="preserve">p</ml:id> <ml:id xml:space="preserve">ζ1</ml:id> </ml:apply> </ml:define> </math> <rendering item-idref="85"/> </region> <region region-id="1162" left="258" top="1568.25" width="44.25" height="13.5" align-x="273.75" align-y="1578" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">p2</ml:id> <ml:apply> <ml:id xml:space="preserve">p</ml:id> <ml:id xml:space="preserve">ζ2</ml:id> </ml:apply> </ml:define> </math> <rendering item-idref="86"/> </region> <region region-id="1163" left="12" top="1599" width="75.75" height="12.75" align-x="25.5" align-y="1608" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">A</ml:id> <ml:apply> <ml:minus/> <ml:apply> <ml:mult style="default"/> <ml:id xml:space="preserve">a1</ml:id> <ml:id xml:space="preserve">b2</ml:id> </ml:apply> <ml:apply> <ml:mult style="default"/> <ml:id xml:space="preserve">a2</ml:id> <ml:id xml:space="preserve">b1</ml:id> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="87"/> </region> <region region-id="1164" left="120" top="1599" width="74.25" height="12.75" align-x="132" align-y="1608" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">B</ml:id> <ml:apply> <ml:minus/> <ml:apply> <ml:mult style="default"/> <ml:id xml:space="preserve">b2</ml:id> <ml:id xml:space="preserve">c1</ml:id> </ml:apply> <ml:apply> <ml:mult style="default"/> <ml:id xml:space="preserve">b1</ml:id> <ml:id xml:space="preserve">c2</ml:id> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="88"/> </region> <region region-id="1165" left="228" top="1604.25" width="51.75" height="12" align-x="228" align-y="1614" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> Equation 14 </text> </region> <region region-id="1166" left="12" top="1623" width="75.75" height="12.75" align-x="24" align-y="1632" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">C</ml:id> <ml:apply> <ml:minus/> <ml:apply> <ml:mult style="default"/> <ml:id xml:space="preserve">b2</ml:id> <ml:id xml:space="preserve">p1</ml:id> </ml:apply> <ml:apply> <ml:mult style="default"/> <ml:id xml:space="preserve">b1</ml:id> <ml:id xml:space="preserve">p2</ml:id> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="89"/> </region> <region region-id="1167" left="120" top="1623" width="73.5" height="12.75" align-x="132.75" align-y="1632" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">D</ml:id> <ml:apply> <ml:minus/> <ml:apply> <ml:mult style="default"/> <ml:id xml:space="preserve">a1</ml:id> <ml:id xml:space="preserve">c2</ml:id> </ml:apply> <ml:apply> <ml:mult style="default"/> <ml:id xml:space="preserve">a2</ml:id> <ml:id xml:space="preserve">c1</ml:id> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="90"/> </region> <region region-id="1168" left="12" top="1647" width="73.5" height="12.75" align-x="23.25" align-y="1656" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">E</ml:id> <ml:apply> <ml:minus/> <ml:apply> <ml:mult style="default"/> <ml:id xml:space="preserve">b1</ml:id> <ml:id xml:space="preserve">c2</ml:id> </ml:apply> <ml:apply> <ml:mult style="default"/> <ml:id xml:space="preserve">b2</ml:id> <ml:id xml:space="preserve">c1</ml:id> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="91"/> </region> <region region-id="1169" left="120" top="1647" width="73.5" height="12.75" align-x="131.25" align-y="1656" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">F</ml:id> <ml:apply> <ml:minus/> <ml:apply> <ml:mult style="default"/> <ml:id xml:space="preserve">c2</ml:id> <ml:id xml:space="preserve">p1</ml:id> </ml:apply> <ml:apply> <ml:mult style="default"/> <ml:id xml:space="preserve">c1</ml:id> <ml:id xml:space="preserve">p2</ml:id> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="92"/> </region> <region region-id="1170" left="12" top="1676.25" width="71.25" height="27.75" align-x="39" align-y="1692" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:function> <ml:id xml:space="preserve">Y</ml:id> <ml:boundVars> <ml:id xml:space="preserve">X</ml:id> </ml:boundVars> </ml:function> <ml:apply> <ml:div/> <ml:apply> <ml:minus/> <ml:id xml:space="preserve">F</ml:id> <ml:apply> <ml:mult style="default"/> <ml:id xml:space="preserve">D</ml:id> <ml:id xml:space="preserve">X</ml:id> </ml:apply> </ml:apply> <ml:id xml:space="preserve">E</ml:id> </ml:apply> </ml:define> </math> <rendering item-idref="93"/> </region> <region region-id="1171" left="114" top="1676.25" width="72.75" height="27.75" align-x="141" align-y="1692" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:function> <ml:id xml:space="preserve">Z</ml:id> <ml:boundVars> <ml:id xml:space="preserve">X</ml:id> </ml:boundVars> </ml:function> <ml:apply> <ml:div/> <ml:apply> <ml:minus/> <ml:id xml:space="preserve">C</ml:id> <ml:apply> <ml:mult style="default"/> <ml:id xml:space="preserve">A</ml:id> <ml:id xml:space="preserve">X</ml:id> </ml:apply> </ml:apply> <ml:id xml:space="preserve">B</ml:id> </ml:apply> </ml:define> </math> <rendering item-idref="94"/> </region> <region region-id="1172" left="222" top="1682.25" width="65.25" height="12" align-x="222" align-y="1692" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> Equation 15a,b </text> </region> <region region-id="1173" left="12" top="1706.25" width="60.75" height="12" align-x="12" align-y="1716" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <f family="Arial" charset="0"> <inlineAttr line-through="false">First solution</inlineAttr> </f> </text> </region> <region region-id="1174" left="18" top="1731" width="25.5" height="12.75" align-x="31.5" align-y="1740" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">X</ml:id> <ml:real>1</ml:real> </ml:define> </math> <rendering item-idref="95"/> </region> <region region-id="1175" left="66" top="1730.25" width="40.5" height="12" align-x="66" align-y="1740" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> trial value </text> </region> <region region-id="1176" left="138" top="1731" width="24" height="12.75" align-x="149.25" align-y="1740" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:id xml:space="preserve" xmlns:ml="http://schemas.mathsoft.com/math20">Given</ml:id> </math> <rendering item-idref="96"/> </region> <region region-id="1177" left="186" top="1725" width="103.5" height="18.75" align-x="278.25" align-y="1740" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:apply xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:equal/> <ml:apply> <ml:plus/> <ml:apply> <ml:plus/> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">X</ml:id> <ml:real>2</ml:real> </ml:apply> <ml:apply> <ml:pow/> <ml:apply> <ml:id xml:space="preserve">Y</ml:id> <ml:id xml:space="preserve">X</ml:id> </ml:apply> <ml:real>2</ml:real> </ml:apply> </ml:apply> <ml:apply> <ml:pow/> <ml:apply> <ml:id xml:space="preserve">Z</ml:id> <ml:id xml:space="preserve">X</ml:id> </ml:apply> <ml:real>2</ml:real> </ml:apply> </ml:apply> <ml:real>1</ml:real> </ml:apply> </math> <rendering item-idref="97"/> </region> <region region-id="1178" left="6" top="1761" width="54.75" height="12.75" align-x="20.25" align-y="1770" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">x1</ml:id> <ml:apply> <ml:Find auto-method="true" method="conjugate" derivative-estimation="central" variable-estimation="tangent" linear-check="false" multistart="false" evolutionary="false"/> <ml:id xml:space="preserve">X</ml:id> </ml:apply> </ml:define> </math> <rendering item-idref="98"/> </region> <region region-id="1179" left="78" top="1761" width="45" height="12.75" align-x="93.75" align-y="1770" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">y1</ml:id> <ml:apply> <ml:id xml:space="preserve">Y</ml:id> <ml:id xml:space="preserve">x1</ml:id> </ml:apply> </ml:define> </math> <rendering item-idref="99"/> </region> <region region-id="1180" left="144" top="1761" width="43.5" height="12.75" align-x="158.25" align-y="1770" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">z1</ml:id> <ml:apply> <ml:id xml:space="preserve">Z</ml:id> <ml:id xml:space="preserve">x1</ml:id> </ml:apply> </ml:define> </math> <rendering item-idref="100"/> </region> <region region-id="1181" left="18" top="1784.25" width="75.75" height="12" align-x="33" align-y="1794" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <f family="Arial" charset="0"> <inlineAttr line-through="false">Second solution</inlineAttr> </f> </text> </region> <region region-id="1182" left="6" top="1809" width="25.5" height="12.75" align-x="19.5" align-y="1818" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">X</ml:id> <ml:real>0</ml:real> </ml:define> </math> <rendering item-idref="101"/> </region> <region region-id="1183" left="54" top="1808.25" width="40.5" height="12" align-x="54" align-y="1818" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> trial value </text> </region> <region region-id="1184" left="126" top="1809" width="24" height="12.75" align-x="137.25" align-y="1818" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:id xml:space="preserve" xmlns:ml="http://schemas.mathsoft.com/math20">Given</ml:id> </math> <rendering item-idref="102"/> </region> <region region-id="1185" left="174" top="1803" width="103.5" height="18.75" align-x="266.25" align-y="1818" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:apply xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:equal/> <ml:apply> <ml:plus/> <ml:apply> <ml:plus/> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">X</ml:id> <ml:real>2</ml:real> </ml:apply> <ml:apply> <ml:pow/> <ml:apply> <ml:id xml:space="preserve">Y</ml:id> <ml:id xml:space="preserve">X</ml:id> </ml:apply> <ml:real>2</ml:real> </ml:apply> </ml:apply> <ml:apply> <ml:pow/> <ml:apply> <ml:id xml:space="preserve">Z</ml:id> <ml:id xml:space="preserve">X</ml:id> </ml:apply> <ml:real>2</ml:real> </ml:apply> </ml:apply> <ml:real>1</ml:real> </ml:apply> </math> <rendering item-idref="103"/> </region> <region region-id="1186" left="6" top="1833" width="54.75" height="12.75" align-x="20.25" align-y="1842" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">x2</ml:id> <ml:apply> <ml:Find auto-method="true" method="conjugate" derivative-estimation="central" variable-estimation="tangent" linear-check="false" multistart="false" evolutionary="false"/> <ml:id xml:space="preserve">X</ml:id> </ml:apply> </ml:define> </math> <rendering item-idref="104"/> </region> <region region-id="1187" left="78" top="1833" width="45" height="12.75" align-x="93.75" align-y="1842" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">y2</ml:id> <ml:apply> <ml:id xml:space="preserve">Y</ml:id> <ml:id xml:space="preserve">x2</ml:id> </ml:apply> </ml:define> </math> <rendering item-idref="105"/> </region> <region region-id="1188" left="144" top="1833" width="43.5" height="12.75" align-x="158.25" align-y="1842" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">z2</ml:id> <ml:apply> <ml:id xml:space="preserve">Z</ml:id> <ml:id xml:space="preserve">x2</ml:id> </ml:apply> </ml:define> </math> <rendering item-idref="106"/> </region> <region region-id="1189" left="6" top="1868.25" width="104.25" height="13.5" align-x="62.25" align-y="1878" show-border="false" show-highlight="true" is-protected="true" z-order="0" background-color="#ffffce" tag=""> <math optimize="false" disable-calc="false"> <ml:eval xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:apply> <ml:id xml:space="preserve">Λ</ml:id> <ml:sequence> <ml:id xml:space="preserve">x1</ml:id> <ml:id xml:space="preserve">y1</ml:id> <ml:id xml:space="preserve">z1</ml:id> </ml:sequence> </ml:apply> 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