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 bullet;position:absolute;left:-3.87%'>&#8226;</span>The earth is at the ce=
ntre
 of the Universe </span><span style=3D'position:absolute;top:38.0%;left:9.7=
3%;
 width:100.18%;height:6.75%'>with all the astral stuff rotating around it o=
n </span><span
 style=3D'position:absolute;top:44.5%;left:9.73%;width:84.45%;height:6.75%'=
>the
 inside of a sphere (the celestial </span><span style=3D'position:absolute;
 top:50.74%;left:9.73%;width:84.45%;height:6.75%'>sphere)&#13;</span></div>
 <div class=3DB style=3D'mso-line-spacing:"90 20 0"'><span style=3D'positio=
n:absolute;
 top:58.5%;left:9.73%;width:99.43%;height:6.75%'><span style=3D'mso-special=
-format:
 bullet;position:absolute;left:-3.76%'>&#8226;</span>All the astral stuff s=
tays
 fixed on the inside </span><span style=3D'position:absolute;top:65.0%;
 left:9.73%;width:84.45%;height:6.75%'>of the celestial sphere&#13;</span><=
/div>
 <div class=3DB style=3D'mso-line-spacing:"90 20 0";position:absolute;top:7=
2.75%;
 left:5.99%;width:88.2%;height:6.75%'><span style=3D'position:absolute;
 top:0%;left:4.24%;width:95.75%;height:100.0%'><span style=3D'visibility:hi=
dden'><span
 style=3D'mso-special-format:bullet;position:absolute;left:-4.43%'>&#8226;<=
/span></span>&#13;</span></div>
 <div class=3DB2 style=3D'mso-line-spacing:"90 20 0";position:absolute;top:=
80.25%;
 left:15.91%;width:78.08%;height:5.25%'><span style=3D'mso-special-format:n=
obullet;
 display:none'>&#8226;</span><i>And that inverted Bowl they call the Sky </=
i>&#13;</div>
 <div class=3DB2 style=3D'mso-line-spacing:"90 20 0";position:absolute;top:=
86.0%;
 left:15.91%;width:78.08%;height:5.25%'><span style=3D'mso-special-format:n=
obullet;
 display:none'>&#8226;</span>-- <i>Rubiayat of Omar Khayyam</i></div>
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 at the North </span></span><span style=3D'position:absolute;top:25.64%;
 left:6.66%;width:91.0%;height:26.92%'><span style=3D'font-size:75%'>Pole, =
you
 measure the angle </span></span><span style=3D'position:absolute;top:50.0%;
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35%;
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 <div v:shape=3D"_x0000_s13314" class=3DT style=3D'position:absolute;top:8.=
0%;
 left:5.99%;width:88.2%;height:9.25%'>Corrections to the Angle</div>
 <div v:shape=3D"_x0000_s13315" class=3DB>
 <div style=3D'mso-line-spacing:"80 20 0"'><span style=3D'position:absolute;
 top:23.5%;left:9.73%;width:95.88%;height:4.5%'><span style=3D'font-size:63=
%'><span
 style=3D'mso-special-format:bullet;position:absolute;left:-3.9%'>&#8226;</=
span></span><span
 style=3D'font-size:63%'>Adjustment will correct most errors of measurement=
 but
 usually a </span></span><span style=3D'position:absolute;top:27.0%;left:9.=
73%;
 width:99.06%;height:4.5%'><span style=3D'font-size:63%'>small error remain=
s this
 is the </span><span style=3D'font-size:63%;color:red'>INDEX ERROR</span><s=
pan
 style=3D'font-size:63%'> and is said to be &#8216;on&#8217; </span></span>=
<span
 style=3D'position:absolute;top:30.75%;left:9.73%;width:84.45%;height:4.5%'=
><span
 style=3D'font-size:63%'>or &#8216;off the arc&#8217;&#13;</span></span></d=
iv>
 <div style=3D'mso-line-spacing:"80 20 0"'><span style=3D'position:absolute;
 top:35.0%;left:9.73%;width:97.94%;height:4.5%'><span style=3D'font-size:63=
%'><span
 style=3D'mso-special-format:bullet;position:absolute;left:-3.82%'>&#8226;<=
/span></span><span
 style=3D'font-size:63%'>You are normally not exactly on the surface of the=
 earth
 (sea!) and </span></span><span style=3D'position:absolute;top:38.75%;left:=
9.73%;
 width:84.45%;height:4.5%'><span style=3D'font-size:63%'>so there is a corr=
ection
 for your height of eye called </span><span style=3D'font-size:63%;color:re=
d'>DIP&#13;</span></span></div>
 <div style=3D'mso-line-spacing:"80 20 0"'><span style=3D'position:absolute;
 top:43.25%;left:9.73%;width:93.07%;height:4.5%'><span style=3D'font-size:6=
3%'><span
 style=3D'mso-special-format:bullet;position:absolute;left:-4.02%'>&#8226;<=
/span></span><span
 style=3D'font-size:63%'>The amount of atmosphere the light passes through =
varies
 with </span></span><span style=3D'position:absolute;top:46.75%;left:9.73%;
 width:100.93%;height:4.5%'><span style=3D'font-size:63%'>angle and the
 atmosphere bends the light so there is a correction for </span></span><span
 style=3D'position:absolute;top:50.24%;left:9.73%;width:84.45%;height:4.5%'=
><span
 style=3D'font-size:63%;color:red'>REFRACTION&#13;</span></span></div>
 <div style=3D'mso-line-spacing:"80 20 0"'><span style=3D'position:absolute;
 top:54.75%;left:9.73%;width:95.5%;height:4.5%'><span style=3D'font-size:63=
%'><span
 style=3D'mso-special-format:bullet;position:absolute;left:-3.92%'>&#8226;<=
/span></span><span
 style=3D'font-size:63%'>Remember we said all bodies were on the celestial
 sphere? Well </span></span><span style=3D'position:absolute;top:58.25%;
 left:9.73%;width:94.19%;height:4.5%'><span style=3D'font-size:63%'>some bo=
dies
 are much closer (mainly the moon) and have to be </span></span><span
 style=3D'position:absolute;top:61.75%;left:9.73%;width:88.01%;height:4.5%'=
><span
 style=3D'font-size:63%'>corrected for not being &#8216;points&#8217; this
 correction is </span><span style=3D'font-size:63%;color:red'>PARALLAX&#13;=
</span></span></div>
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0%;
 left:5.99%;width:88.2%;height:9.25%'>Intercept Method</div>
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 top:24.5%;left:9.73%;width:95.5%;height:6.75%'><span class=3DBB
 style=3D'position:absolute;left:-3.92%'>&#8226;</span>Now let the two obse=
rvers
 compare their </span><span style=3D'position:absolute;top:31.5%;left:9.73%;
 width:84.45%;height:6.75%'>&#8216;altitude&#8217; readings.&#13;</span>
 <div style=3D'position:absolute;top:40.0%;left:5.99%;width:101.49%;height:=
6.75%'><span
 style=3D'position:absolute;top:0%;left:3.69%;width:96.3%;height:100.0%'><s=
pan
 class=3DBB style=3D'position:absolute;left:-3.83%'>&#8226;</span>Lets say =
they
 were 38<span style=3D'font-size:66%;position:relative;top:-.45em;mso-text-=
raise:
 30%'>o </span>32.6&#8217; and 38<span style=3D'font-size:66%;position:rela=
tive;
 top:-.45em;mso-text-raise:30%'>o</span>42.8&#8217; &#13;</span></div>
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.75%'><span
 class=3DBB style=3D'position:absolute;left:-3.8%'>&#8226;</span>So one is =
10.2 nm
 closer to the body than </span><span style=3D'position:absolute;top:55.75%;
 left:9.73%;width:87.64%;height:6.75%'>the other <span style=3D'color:red'>A
 MINUTE IS A NAUTICAL </span></span><span style=3D'position:absolute;top:62=
.74%;
 left:9.73%;width:84.45%;height:6.75%'><span style=3D'color:red'>MILE</span=
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<div id=3DSlideObj class=3Dsld style=3D'position:absolute;top:0px;left:0px;
width:534px;height:400px;font-size:16px;background-color:white;clip:rect(0%=
, 101%, 101%, 0%);
visibility:hidden'><p:slide coordsize=3D"720,540"
 colors=3D"#ffffff,#000000,#808080,#000000,#bbe0e3,#333399,#009999,#99cc00"
 masterhref=3D"master03.xml">
 <p:shaperange href=3D"master03.xml#_x0000_s1025"/><![if !ppt]><p:shaperange
  href=3D"master03.xml#_x0000_s1028"/><p:shaperange
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  href=3D"master03.xml#_x0000_m1027"/><v:shape id=3D"_x0000_s16387" type=3D=
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 <div v:shape=3D"_x0000_s16386" class=3DT style=3D'position:absolute;top:8.=
0%;
 left:5.99%;width:88.2%;height:9.25%'>Intercept Method</div>
 <div v:shape=3D"_x0000_s16387" class=3DB>
 <div style=3D'mso-line-spacing:"90 20 0"'><span style=3D'position:absolute;
 top:23.75%;left:9.73%;width:94.38%;height:6.75%'><span style=3D'mso-specia=
l-format:
 bullet;position:absolute;left:-3.96%'>&#8226;</span>The method is a simple
 extension of the </span><span style=3D'position:absolute;top:30.25%;left:9=
.73%;
 width:84.45%;height:6.75%'>&#8216;lighthouse&#8217; situation&#13;</span><=
/div>
 <div style=3D'mso-line-spacing:"90 20 0"'><span style=3D'position:absolute;
 top:38.0%;left:9.73%;width:84.45%;height:6.75%'><span style=3D'mso-special=
-format:
 bullet;position:absolute;left:-4.43%'>&#8226;</span>We take an <span
 style=3D'color:red'>ASSUMED POSITION</span>, </span><span style=3D'positio=
n:absolute;
 top:44.5%;left:9.73%;width:93.63%;height:6.75%'>sometimes deliberately cho=
sen
 to make </span><span style=3D'position:absolute;top:50.74%;left:9.73%;
 width:93.44%;height:6.75%'>the maths or tables easier and work out </span>=
<span
 style=3D'position:absolute;top:57.25%;left:9.73%;width:99.43%;height:6.75%=
'>the <span
 style=3D'color:red'>CALCULATED ALTITUDE</span> of the body </span><span
 style=3D'position:absolute;top:63.5%;left:9.73%;width:84.45%;height:6.75%'=
>if we
 had been there&#13;</span></div>
 <div style=3D'mso-line-spacing:"90 20 0"'><span style=3D'position:absolute;
 top:71.25%;left:9.73%;width:84.45%;height:6.75%'><span style=3D'mso-specia=
l-format:
 bullet;position:absolute;left:-4.43%'>&#8226;</span>Then we compare our <s=
pan
 style=3D'color:red'>OBSERVED </span></span><span style=3D'position:absolut=
e;
 top:77.75%;left:9.73%;width:84.45%;height:6.75%'><span style=3D'color:red'=
>ALTITUDE</span></span></div>
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width:534px;height:400px;font-size:16px;background-color:white;clip:rect(0%=
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visibility:hidden'><p:slide coordsize=3D"720,540"
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 masterhref=3D"master03.xml">
 <p:shaperange href=3D"master03.xml#_x0000_s1025"/><![if !ppt]><p:shaperange
  href=3D"master03.xml#_x0000_s1028"/><p:shaperange
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 <div v:shape=3D"_x0000_s17410" class=3DT style=3D'position:absolute;top:8.=
0%;
 left:5.99%;width:88.2%;height:9.25%'>Intercept</div>
 <div v:shape=3D"_x0000_s17411" class=3DB><span style=3D'position:absolute;
 top:24.5%;left:9.73%;width:95.5%;height:6.75%'><span class=3DBB
 style=3D'position:absolute;left:-3.92%'>&#8226;</span>Either they will be =
the
 same (so we were </span><span style=3D'position:absolute;top:31.5%;left:9.=
73%;
 width:84.45%;height:6.75%'>where we assumed we were)&#13;</span><span
 style=3D'position:absolute;top:40.0%;left:9.73%;width:98.31%;height:6.75%'=
><span
 class=3DBB style=3D'position:absolute;left:-3.8%'>&#8226;</span>Or the <sp=
an
 style=3D'color:red'>OBSERVED ALTITUDE</span> is less, so </span><span
 style=3D'position:absolute;top:47.25%;left:9.73%;width:84.45%;height:6.75%=
'>we
 are further away&#13;</span><span style=3D'position:absolute;top:55.75%;
 left:9.73%;width:98.5%;height:6.75%'><span class=3DBB style=3D'position:ab=
solute;
 left:-3.8%'>&#8226;</span>Or the OBSERVED ALTITUDE is greater, </span><span
 style=3D'position:absolute;top:62.74%;left:9.73%;width:84.45%;height:6.75%=
'>so
 we are closer</span></div>
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<div id=3DSlideObj class=3Dsld style=3D'position:absolute;top:0px;left:0px;
width:534px;height:400px;font-size:16px;background-color:white;clip:rect(0%=
, 101%, 101%, 0%);
visibility:hidden'><p:slide coordsize=3D"720,540"
 colors=3D"#ffffff,#000000,#808080,#000000,#bbe0e3,#333399,#009999,#99cc00"
 masterhref=3D"master03.xml">
 <p:shaperange href=3D"master03.xml#_x0000_s1025"/><![if !ppt]><p:shaperange
  href=3D"master03.xml#_x0000_s1028"/><p:shaperange
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 <div v:shape=3D"_x0000_s18434" class=3DT style=3D'position:absolute;top:8.=
0%;
 left:5.99%;width:88.2%;height:9.25%'>Intercept</div>
 <div v:shape=3D"_x0000_s18435" class=3DB>
 <div style=3D'position:absolute;top:24.5%;left:5.99%;width:88.2%;height:6.=
75%'><span
 style=3D'position:absolute;top:0%;left:4.24%;width:95.75%;height:100.0%'><=
span
 class=3DBB style=3D'position:absolute;left:-4.43%'>&#8226;</span>We plot o=
ur <span
 style=3D'color:red'>ASSUMED POSITION&#13;</span></span></div>
 <span style=3D'position:absolute;top:33.0%;left:9.73%;width:100.56%;height=
:6.75%'><span
 class=3DBB style=3D'position:absolute;left:-3.72%'>&#8226;</span>We pass a=
 line
 through this in the direction </span><span style=3D'position:absolute;
 top:40.0%;left:9.73%;width:99.62%;height:6.75%'>of the body. The direction=
 is
 the <span style=3D'color:red'>AZIMUTH&#13;</span></span><span style=3D'pos=
ition:
 absolute;top:48.5%;left:9.73%;width:91.57%;height:6.75%'><span class=3DBB
 style=3D'position:absolute;left:-4.08%'>&#8226;</span>If observed altitude=
 is
 greater we move </span><span style=3D'position:absolute;top:55.75%;left:9.=
73%;
 width:95.13%;height:6.75%'>towards the body, if less than away from </span=
><span
 style=3D'position:absolute;top:62.74%;left:9.73%;width:100.56%;height:6.75=
%'>this
 point we draw a perpendicular this is a </span><span style=3D'position:abs=
olute;
 top:69.75%;left:9.73%;width:101.12%;height:6.75%'>section of the circle of
 equal amplitude that </span><span style=3D'position:absolute;top:77.0%;
 left:9.73%;width:92.88%;height:6.75%'>we are on, it is our <span
 style=3D'color:red'>LINE OF POSITION&#13;</span></span>
 <div style=3D'position:absolute;top:85.5%;left:5.99%;width:88.2%;height:6.=
75%'><span
 style=3D'mso-special-format:nobullet;display:none'>&#8226;</span><span
 style=3D'mso-special-format:lastCR;display:none'>&#13;</span></div>
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