<html><head></head><body style="word-wrap: break-word; -webkit-nbsp-mode: space; -webkit-line-break: after-white-space; "><div>Dear All,</div><div><br></div><div>Please find below an opportunity for measuring the distance to Mars. Please contact John directly in case you are interested. Thanks!</div><div><br></div><div>Kind regards,</div><div><br></div><div>Christian</div><div><br></div><div><blockquote type="cite"><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px;"><span style="font-family:'Helvetica'; font-size:medium; color:rgba(0, 0, 0, 1);"><b>Von: </b></span><span style="font-family:'Helvetica'; font-size:medium;">"John Clark" <<a href="mailto:john.clark@johnclarkastronomy.co.uk">john.clark@johnclarkastronomy.co.uk</a>><br></span></div><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px;"><span style="font-family:'Helvetica'; font-size:medium; color:rgba(0, 0, 0, 1);"><b>Datum: </b></span><span style="font-family:'Helvetica'; font-size:medium;">3. Oktober 2009 14:53:32 GMT+02:00<br></span></div><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px;"><span style="font-family:'Helvetica'; font-size:medium; color:rgba(0, 0, 0, 1);"><b>An: </b></span><span style="font-family:'Helvetica'; font-size:medium;"><<a href="mailto:assa@saao.ac.za">assa@saao.ac.za</a>><br></span></div><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px;"><span style="font-family:'Helvetica'; font-size:medium; color:rgba(0, 0, 0, 1);"><b>Betreff: </b></span><span style="font-family:'Helvetica'; font-size:medium;"><b>Measuring the Astronomical unit by parallax measurement on Mars</b><br></span></div><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px;"><span style="font-family:'Helvetica'; font-size:medium; color:rgba(0, 0, 0, 1);"><b>Antwort an: </b></span><span style="font-family:'Helvetica'; font-size:medium;"><<a href="mailto:john.clark@johnclarkastronomy.co.uk">john.clark@johnclarkastronomy.co.uk</a>><br></span></div><br><o:smarttagtype namespaceuri="urn:schemas-microsoft-com:office:smarttags" name="country-region">
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<div class="Section1"><p class="MsoNormal"><font size="2" face="Arial"><span style="font-size:10.0pt;
font-family:Arial">Dear Sir,<o:p></o:p></span></font></p><p class="MsoNormal"><font size="2" face="Arial"><span style="font-size:10.0pt;
font-family:Arial"><o:p> </o:p></span></font></p><p class="MsoNormal"><font size="2" face="Arial"><span style="font-size:10.0pt;
font-family:Arial">I am a UK-based amateur astronomer with an interest in solar
system measurements. I have spent some time over the last few months
estimating the length of the astronomical unit by timing eclipses of Jupiter’s
moon Io, essentially reversing an observation by Roemer who discovered the
finite speed of light by timing such eclipses. I measured the speed of
light in a university laboratory, and back-calculated the AU from my own
observations of Io over a couple of years.<o:p></o:p></span></font></p><p class="MsoNormal"><font size="2" face="Arial"><span style="font-size:10.0pt;
font-family:Arial"><o:p> </o:p></span></font></p><p class="MsoNormal"><font size="2" face="Arial"><span style="font-size:10.0pt;
font-family:Arial">This method worked, but it is difficult to get an accurate
value. My value was 20% low compared to the accepted value.<o:p></o:p></span></font></p><p class="MsoNormal"><font size="2" face="Arial"><span style="font-size:10.0pt;
font-family:Arial"><o:p> </o:p></span></font></p><p class="MsoNormal"><font size="2" face="Arial"><span style="font-size:10.0pt;
font-family:Arial">My impression is that the method of Cassini and Richer
(1672) is likely to be more accurate, but it requires simultaneously measuring and
comparing the position of Mars from two faraway locations on Earth. This measurement
would have to be done to within at least one second of arc. This is not
as hard as it sounds, but it obviously isn’t trivial.<o:p></o:p></span></font></p><p class="MsoNormal"><font size="2" face="Arial"><span style="font-size:10.0pt;
font-family:Arial"><o:p> </o:p></span></font></p><p class="MsoNormal"><font size="2" face="Arial"><span style="font-size:10.0pt;
font-family:Arial">I wondered if there is anyone in <st1:country-region w:st="on"><st1:place w:st="on">South Africa</st1:place></st1:country-region> who is
interested/crazy enough to collaborate with me to try this measurement during
the forthcoming opposition of Mars? It would then be at its closest to Earth,
so that the parallax would maximise.<o:p></o:p></span></font></p><p class="MsoNormal"><font size="2" face="Arial"><span style="font-size:10.0pt;
font-family:Arial"><o:p> </o:p></span></font></p><p class="MsoNormal"><font size="2" face="Arial"><span style="font-size:10.0pt;
font-family:Arial">Based on a rough estimate, it is about 10,000 km from the <st1:country-region w:st="on"><st1:place w:st="on">UK</st1:place></st1:country-region> to SA over
the Earth’s surface, so the chord length (straight line distance) is
about 9,000 km. Mars will be at about 100,000,000 km away at its closest
approach, so we are looking for a parallax of 9,000 parts in 100,000,000 or
about 18.6 arc seconds. A measurement good to 1 arc second would therefore have
an error of 1 in 18.6 or 5.4%. Obviously a measurement good to 0.5 arc
sec would have half that error. With good amateur equipment that should
be feasible. <o:p></o:p></span></font></p><p class="MsoNormal"><font size="2" face="Arial"><span style="font-size:10.0pt;
font-family:Arial"><o:p> </o:p></span></font></p><p class="MsoNormal"><font size="2" face="Arial"><span style="font-size:10.0pt;
font-family:Arial">I can help with the maths needed to post-process the photos.<o:p></o:p></span></font></p><p class="MsoNormal"><font size="2" face="Arial"><span style="font-size:10.0pt;
font-family:Arial"><o:p> </o:p></span></font></p><p class="MsoNormal"><font size="2" face="Arial"><span style="font-size:10.0pt;
font-family:Arial">Yours sincerely,<o:p></o:p></span></font></p><p class="MsoNormal"><font size="2" face="Arial"><span style="font-size:10.0pt;
font-family:Arial"><o:p> </o:p></span></font></p><p class="MsoNormal"><font size="2" face="Arial"><span style="font-size:10.0pt;
font-family:Arial">John.<o:p></o:p></span></font></p><p class="MsoNormal"><font size="2" face="Arial"><span style="font-size:10.0pt;
font-family:Arial"><o:p> </o:p></span></font></p>
<div><p class="MsoNormal"><font size="2" color="blue" face="Tahoma"><span style="font-size:
10.0pt;font-family:Tahoma;color:blue">Dr John D. Clark<o:p></o:p></span></font></p><p class="MsoNormal"><font size="2" color="blue" face="Tahoma"><span style="font-size:
10.0pt;font-family:Tahoma;color:blue"><o:p> </o:p></span></font></p><p class="MsoNormal"><st1:street w:st="on"><st1:address w:st="on"><font size="2" color="blue" face="Tahoma"><span style="font-size:10.0pt;font-family:Tahoma;
color:blue">323 Wootton Road</span></font></st1:address></st1:street><font size="2" color="blue" face="Tahoma"><span style="font-size:10.0pt;font-family:Tahoma;
color:blue"><o:p></o:p></span></font></p><p class="MsoNormal"><st1:place w:st="on"><font size="2" color="blue" face="Tahoma"><span style="font-size:10.0pt;font-family:Tahoma;color:blue">King's Lynn</span></font></st1:place><font size="2" color="blue" face="Tahoma"><span style="font-size:10.0pt;font-family:Tahoma;
color:blue"><o:p></o:p></span></font></p><p class="MsoNormal"><st1:place w:st="on"><st1:city w:st="on"><font size="2" color="blue" face="Tahoma"><span style="font-size:10.0pt;font-family:Tahoma;
color:blue">Norfolk</span></font></st1:city></st1:place><font size="2" color="blue" face="Tahoma"><span style="font-size:10.0pt;font-family:Tahoma;
color:blue"> <o:p></o:p></span></font></p><p class="MsoNormal"><st1:country-region w:st="on"><st1:place w:st="on"><font size="2" color="blue" face="Tahoma"><span style="font-size:10.0pt;font-family:Tahoma;
color:blue">England</span></font></st1:place></st1:country-region><font size="2" color="blue" face="Tahoma"><span style="font-size:10.0pt;font-family:Tahoma;
color:blue"><o:p></o:p></span></font></p><p class="MsoNormal"><font size="2" color="blue" face="Tahoma"><span style="font-size:
10.0pt;font-family:Tahoma;color:blue">PE30 3AX<o:p></o:p></span></font></p><p class="MsoNormal"><font size="2" color="blue" face="Tahoma"><span style="font-size:
10.0pt;font-family:Tahoma;color:blue"><o:p> </o:p></span></font></p><p class="MsoNormal"><font size="2" color="blue" face="Tahoma"><span style="font-size:
10.0pt;font-family:Tahoma;color:blue">+44 1553 679378<o:p></o:p></span></font></p><p class="MsoNormal"><font size="2" color="blue" face="Tahoma"><span style="font-size:
10.0pt;font-family:Tahoma;color:blue"><o:p> </o:p></span></font></p><p class="MsoNormal"><font size="2" color="blue" face="Tahoma"><span style="font-size:
10.0pt;font-family:Tahoma;color:blue"><a href="x-msg://15/john.clark@johnclarkastronomy.co.uk">john.clark@johnclarkastronomy.co.uk</a>
<a href="http://www.johnclarkastronomy.co.uk/">http://www.johnclarkastronomy.co.uk</a>
<o:p></o:p></span></font></p><p class="MsoNormal"><font size="2" color="blue" face="Tahoma"><span style="font-size:
10.0pt;font-family:Tahoma;color:blue"><o:p> </o:p></span></font></p><p class="MsoNormal"><font size="2" color="blue" face="Tahoma"><span style="font-size:
10.0pt;font-family:Tahoma;color:blue"><a href="http://www.springer.com/astronomy/book/978-0-387-89560-4">Measure Solar
System Objects and their Movements for Yourself! by John D. Clark</a><o:p></o:p></span></font></p>
</div><div style="margin-top: 0cm; margin-right: 0cm; margin-left: 0cm; margin-bottom: 0.0001pt; "><font size="2" color="blue" face="Tahoma"><span style="font-size:10.0pt;font-family:Tahoma;
color:blue"><o:p> </o:p></span></font></div><p class="MsoNormal"><font size="3" face="Times New Roman"><span style="font-size:
12.0pt"><o:p> </o:p></span></font></p>
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