http://the-moon.us/index.php?title=Xi-Eta&feed=atom&action=historyXi-Eta - Revision history2024-03-28T11:03:40ZRevision history for this page on the wikiMediaWiki 1.31.1http://the-moon.us/index.php?title=Xi-Eta&diff=13182&oldid=prevApi at 00:59, 16 April 20182018-04-16T00:59:02Z<p></p>
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<td colspan="2" style="background-color: #fff; color: #222; text-align: center;">Revision as of 00:59, 16 April 2018</td>
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<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>=Xi-Eta Coordinates=</div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>=Xi-Eta Coordinates=</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>  (glossary entry)<br /> <div id="toc"></div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>  (glossary entry)<br /> <div id="toc"></div></td></tr>
<tr><td class='diff-marker'>−</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div><del class="diffchange diffchange-inline">=Table of Contents=</del></div></td><td class='diff-marker'>+</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><br />  </div></td></tr>
<tr><td class='diff-marker'>−</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div><del class="diffchange diffchange-inline"><div style="margin-left: 1em">[#Xi-Eta Coordinates Xi-Eta Coordinates]</div><div style="margin-left: 2em">[#Xi-Eta Coordinates-Description Description]</div><div style="margin-left: 2em">[#Xi-Eta Coordinates-Additional Information Additional Information]</div><div style="margin-left: 2em">[#Xi-Eta Coordinates-LPOD Articles LPOD Articles]</div><div style="margin-left: 2em">[#Xi-Eta Coordinates-Bibliography Bibliography]</div></div></del><br />  </div></td><td colspan="2"> </td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>==Description==</div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>==Description==</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>  A system for expressing the position of a nearside lunar feature in terms of its X-Y coordinates in a standard zero-libration lunar atlas view. The radius of the Moon is 1 in this system. '''Xi''' (a Greek letter) is the horizontal (X) coordinate measured from -1 on the equatorial west limb to +1 on the equatorial east limb. '''Eta''' (another Greek letter) is the vertical (Y) coordinate, ranging from +1 at the north pole to -1 at the south pole.<br /> <br />  </div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>  A system for expressing the position of a nearside lunar feature in terms of its X-Y coordinates in a standard zero-libration lunar atlas view. The radius of the Moon is 1 in this system. '''Xi''' (a Greek letter) is the horizontal (X) coordinate measured from -1 on the equatorial west limb to +1 on the equatorial east limb. '''Eta''' (another Greek letter) is the vertical (Y) coordinate, ranging from +1 at the north pole to -1 at the south pole.<br /> <br />  </div></td></tr>
<tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l16" >Line 16:</td>
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<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>** Longitude = ArcSin[Xi/Cos(Lat)] ''<-- use computed latitude here''</div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>** Longitude = ArcSin[Xi/Cos(Lat)] ''<-- use computed latitude here''</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>* The projected positions of a lunar feature as seen on an actual plate (displaced from that feature's standard position by [[librations|librations]]) are conventionally referred to as "x" and "y".</div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>* The projected positions of a lunar feature as seen on an actual plate (displaced from that feature's standard position by [[librations|librations]]) are conventionally referred to as "x" and "y".</div></td></tr>
<tr><td class='diff-marker'>−</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>* In their classic book [[Wilkins%20and%20Moore|The Moon]], Wilkins and Moore use some kind of extended Xi-Eta system to express the positions of features beyond the mean limb, but the rules they use for this are not explained. <span class="membersnap">- <del class="diffchange diffchange-inline">[http://www.wikispaces.com/user/view/JimMosher [[Image:JimMosher-lg.jpg|16px|JimMosher]]] [http://www.wikispaces.com/user/view/JimMosher JimMosher]</del></span></div></td><td class='diff-marker'>+</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>* In their classic book [[Wilkins%20and%20Moore|The Moon]], Wilkins and Moore use some kind of extended Xi-Eta system to express the positions of features beyond the mean limb, but the rules they use for this are not explained. <span class="membersnap">- <ins class="diffchange diffchange-inline">Jim Mosher</ins></span></div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>* Since the Moon is spherical, rather than flat, a better representation of the three-dimensional position of a lunar surface feature can be obtained by introducing a third parameter '''Zeta''' representing the distance "in and out of the paper". Again, this will run from +1 (point closest to Earth) to -1 (point farthest from the Earth). All features that are on the nearside and mean libration will have Zeta>0, while all those on the farside will have Zeta<0. For a spherical Moon of radius 1, the Pythagorean theorem dictates that the sum of the squares of the three parameters will equal one. Hence given Xi and Eta, the magnitude of Zeta must be:</div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>* Since the Moon is spherical, rather than flat, a better representation of the three-dimensional position of a lunar surface feature can be obtained by introducing a third parameter '''Zeta''' representing the distance "in and out of the paper". Again, this will run from +1 (point closest to Earth) to -1 (point farthest from the Earth). All features that are on the nearside and mean libration will have Zeta>0, while all those on the farside will have Zeta<0. For a spherical Moon of radius 1, the Pythagorean theorem dictates that the sum of the squares of the three parameters will equal one. Hence given Xi and Eta, the magnitude of Zeta must be:</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div><br />  </div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div><br />  </div></td></tr>
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<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div><br />  </div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div><br />  </div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td></tr>
<tr><td class='diff-marker'>−</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>* differing slightly from 1 (indicating small deviations relative to the mean radius). But his does not seem to be the practice among selenographers. See, for example, pages 223-228 of Ralph Baldwin's [http://www.worldcat.org/oclc/530705 The Measure of the Moon] (1963), where the sum of squares of Xi, Eta and Zeta is always forced to 1, and the deviations from sphericity are represented by a separate parameter, h. <span class="membersnap">- <del class="diffchange diffchange-inline">[http://www.wikispaces.com/user/view/JimMosher [[Image:JimMosher-lg.jpg|16px|JimMosher]]] [http://www.wikispaces.com/user/view/JimMosher JimMosher]</del></span></div></td><td class='diff-marker'>+</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>* differing slightly from 1 (indicating small deviations relative to the mean radius). But his does not seem to be the practice among selenographers. See, for example, pages 223-228 of Ralph Baldwin's [http://www.worldcat.org/oclc/530705 The Measure of the Moon] (1963), where the sum of squares of Xi, Eta and Zeta is always forced to 1, and the deviations from sphericity are represented by a separate parameter, h. <span class="membersnap">- <ins class="diffchange diffchange-inline">Jim Mosher</ins></span></div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td></tr>
<tr><td class='diff-marker'>−</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>* It might be noted that "east-west" (the '''Xi''' coordinate) and "north-south" (the '''Eta''' coordinate) in the Xi-Eta system are not always the same as "east-west" (a difference in longitude) and "north-south" (a difference in latitude) in the longitude-latitude system. Indeed, just to the "left" and "right" of the Moon's poles, the relative senses of the two systems can be rotated by as much as 90°. This, and the tendency to think almost always in terms of a projected nearside view, leads to a little-noticed (and perhaps trivial) ambiguity in lunar terminology. The statement that ''"[[Nansen|Nansen]] is to the east of [[Peary|Peary]]"'' is implicitly referring to the projected positions of those two craters in the Xi-Eta system. The equally valid statement that ''"[[Nansen|Nansen]] is south of [[Peary|Peary]]"'' is implicitly referring to the longitude-latitude system. But when the features are unfamiliar, as when one reads that "''feature X is located 10 km SE of crater Y''" it can be very hard to tell if the writer is thinking in terms of projected Xi-Eta directions, or (what is more properly called a "bearing") a direction relative to the N-S meridian (the line of constant longitude) through crater Y. <span class="membersnap">- <del class="diffchange diffchange-inline">[http://www.wikispaces.com/user/view/JimMosher [[Image:JimMosher-lg.jpg|16px|JimMosher]]] [http://www.wikispaces.com/user/view/JimMosher JimMosher]</del></span></div></td><td class='diff-marker'>+</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>* It might be noted that "east-west" (the '''Xi''' coordinate) and "north-south" (the '''Eta''' coordinate) in the Xi-Eta system are not always the same as "east-west" (a difference in longitude) and "north-south" (a difference in latitude) in the longitude-latitude system. Indeed, just to the "left" and "right" of the Moon's poles, the relative senses of the two systems can be rotated by as much as 90°. This, and the tendency to think almost always in terms of a projected nearside view, leads to a little-noticed (and perhaps trivial) ambiguity in lunar terminology. The statement that ''"[[Nansen|Nansen]] is to the east of [[Peary|Peary]]"'' is implicitly referring to the projected positions of those two craters in the Xi-Eta system. The equally valid statement that ''"[[Nansen|Nansen]] is south of [[Peary|Peary]]"'' is implicitly referring to the longitude-latitude system. But when the features are unfamiliar, as when one reads that "''feature X is located 10 km SE of crater Y''" it can be very hard to tell if the writer is thinking in terms of projected Xi-Eta directions, or (what is more properly called a "bearing") a direction relative to the N-S meridian (the line of constant longitude) through crater Y. <span class="membersnap">- <ins class="diffchange diffchange-inline">Jim Mosher</ins></span></div></td></tr>
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<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>==LPOD Articles==</div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>==LPOD Articles==</div></td></tr>
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<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>----</div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>----</div></td></tr>
<tr><td class='diff-marker'>−</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>  <del class="diffchange diffchange-inline">This page has been edited 1 times. The last modification was made by <span class="membersnap">- [http://www.wikispaces.com/user/view/tychocrater [[Image:tychocrater-lg.jpg|16px|tychocrater]]] [http://www.wikispaces.com/user/view/tychocrater tychocrater]</span> on Jun 13, 2009 3:24 pm - ''mgx2''</del></div></div></td><td class='diff-marker'>+</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>  </div></div></td></tr>
</table>Apihttp://the-moon.us/index.php?title=Xi-Eta&diff=10242&oldid=prevApi at 23:23, 15 April 20182018-04-15T23:23:21Z<p></p>
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<td colspan="2" style="background-color: #fff; color: #222; text-align: center;">← Older revision</td>
<td colspan="2" style="background-color: #fff; color: #222; text-align: center;">Revision as of 23:23, 15 April 2018</td>
</tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l8" >Line 8:</td>
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<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>==Additional Information==</div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>==Additional Information==</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>* Although the IAU convention for east and west on the Moon was reversed in the early 1960's, the convention for '''Xi''' is unaffected.</div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>* Although the IAU convention for east and west on the Moon was reversed in the early 1960's, the convention for '''Xi''' is unaffected.</div></td></tr>
<tr><td class='diff-marker'>−</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>* Many of the older lunar maps, such as the ''[<del class="diffchange diffchange-inline">/</del>System%20of%20Lunar%20Craters System of Lunar Craters]'' maps and many others, are plotted on rectangular grids labeled with the Xi-Eta positions.</div></td><td class='diff-marker'>+</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>* Many of the older lunar maps, such as the ''[<ins class="diffchange diffchange-inline">[</ins>System%20of%20Lunar%20Craters<ins class="diffchange diffchange-inline">|</ins>System of Lunar Craters<ins class="diffchange diffchange-inline">]</ins>]'' maps and many others, are plotted on rectangular grids labeled with the Xi-Eta positions.</div></td></tr>
<tr><td class='diff-marker'>−</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>* According to the rules of trigonometry, the position of a feature of known [<del class="diffchange diffchange-inline">/</del>selenographic%20coordinates selenographic] longitude and latitude can be reduced to the Xi-Eta system using the following formulas:</div></td><td class='diff-marker'>+</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>* According to the rules of trigonometry, the position of a feature of known [<ins class="diffchange diffchange-inline">[</ins>selenographic%20coordinates<ins class="diffchange diffchange-inline">|</ins>selenographic<ins class="diffchange diffchange-inline">]</ins>] longitude and latitude can be reduced to the Xi-Eta system using the following formulas:</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>** Xi = Cos(Lat)*Sin(Lon)</div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>** Xi = Cos(Lat)*Sin(Lon)</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>** Eta = Sin(Lat)</div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>** Eta = Sin(Lat)</div></td></tr>
<tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l15" >Line 15:</td>
<td colspan="2" class="diff-lineno">Line 15:</td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>** Latitude = ArcSin(Eta) ''<-- compute this first''</div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>** Latitude = ArcSin(Eta) ''<-- compute this first''</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>** Longitude = ArcSin[Xi/Cos(Lat)] ''<-- use computed latitude here''</div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>** Longitude = ArcSin[Xi/Cos(Lat)] ''<-- use computed latitude here''</div></td></tr>
<tr><td class='diff-marker'>−</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>* The projected positions of a lunar feature as seen on an actual plate (displaced from that feature's standard position by [<del class="diffchange diffchange-inline">/</del>librations librations]) are conventionally referred to as "x" and "y".</div></td><td class='diff-marker'>+</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>* The projected positions of a lunar feature as seen on an actual plate (displaced from that feature's standard position by [<ins class="diffchange diffchange-inline">[</ins>librations<ins class="diffchange diffchange-inline">|</ins>librations<ins class="diffchange diffchange-inline">]</ins>]) are conventionally referred to as "x" and "y".</div></td></tr>
<tr><td class='diff-marker'>−</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>* In their classic book [<del class="diffchange diffchange-inline">/</del>Wilkins%20and%20Moore The Moon], Wilkins and Moore use some kind of extended Xi-Eta system to express the positions of features beyond the mean limb, but the rules they use for this are not explained. <span class="membersnap">- [http://www.wikispaces.com/user/view/JimMosher [[Image:JimMosher-lg.jpg|16px|JimMosher]]] [http://www.wikispaces.com/user/view/JimMosher JimMosher]</span></div></td><td class='diff-marker'>+</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>* In their classic book [<ins class="diffchange diffchange-inline">[</ins>Wilkins%20and%20Moore<ins class="diffchange diffchange-inline">|</ins>The Moon<ins class="diffchange diffchange-inline">]</ins>], Wilkins and Moore use some kind of extended Xi-Eta system to express the positions of features beyond the mean limb, but the rules they use for this are not explained. <span class="membersnap">- [http://www.wikispaces.com/user/view/JimMosher [[Image:JimMosher-lg.jpg|16px|JimMosher]]] [http://www.wikispaces.com/user/view/JimMosher JimMosher]</span></div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>* Since the Moon is spherical, rather than flat, a better representation of the three-dimensional position of a lunar surface feature can be obtained by introducing a third parameter '''Zeta''' representing the distance "in and out of the paper". Again, this will run from +1 (point closest to Earth) to -1 (point farthest from the Earth). All features that are on the nearside and mean libration will have Zeta>0, while all those on the farside will have Zeta<0. For a spherical Moon of radius 1, the Pythagorean theorem dictates that the sum of the squares of the three parameters will equal one. Hence given Xi and Eta, the magnitude of Zeta must be:</div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>* Since the Moon is spherical, rather than flat, a better representation of the three-dimensional position of a lunar surface feature can be obtained by introducing a third parameter '''Zeta''' representing the distance "in and out of the paper". Again, this will run from +1 (point closest to Earth) to -1 (point farthest from the Earth). All features that are on the nearside and mean libration will have Zeta>0, while all those on the farside will have Zeta<0. For a spherical Moon of radius 1, the Pythagorean theorem dictates that the sum of the squares of the three parameters will equal one. Hence given Xi and Eta, the magnitude of Zeta must be:</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div><br />  </div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div><br />  </div></td></tr>
<tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l31" >Line 31:</td>
<td colspan="2" class="diff-lineno">Line 31:</td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>* differing slightly from 1 (indicating small deviations relative to the mean radius). But his does not seem to be the practice among selenographers. See, for example, pages 223-228 of Ralph Baldwin's [http://www.worldcat.org/oclc/530705 The Measure of the Moon] (1963), where the sum of squares of Xi, Eta and Zeta is always forced to 1, and the deviations from sphericity are represented by a separate parameter, h. <span class="membersnap">- [http://www.wikispaces.com/user/view/JimMosher [[Image:JimMosher-lg.jpg|16px|JimMosher]]] [http://www.wikispaces.com/user/view/JimMosher JimMosher]</span></div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>* differing slightly from 1 (indicating small deviations relative to the mean radius). But his does not seem to be the practice among selenographers. See, for example, pages 223-228 of Ralph Baldwin's [http://www.worldcat.org/oclc/530705 The Measure of the Moon] (1963), where the sum of squares of Xi, Eta and Zeta is always forced to 1, and the deviations from sphericity are represented by a separate parameter, h. <span class="membersnap">- [http://www.wikispaces.com/user/view/JimMosher [[Image:JimMosher-lg.jpg|16px|JimMosher]]] [http://www.wikispaces.com/user/view/JimMosher JimMosher]</span></div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td></tr>
<tr><td class='diff-marker'>−</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>* It might be noted that "east-west" (the '''Xi''' coordinate) and "north-south" (the '''Eta''' coordinate) in the Xi-Eta system are not always the same as "east-west" (a difference in longitude) and "north-south" (a difference in latitude) in the longitude-latitude system. Indeed, just to the "left" and "right" of the Moon's poles, the relative senses of the two systems can be rotated by as much as 90°. This, and the tendency to think almost always in terms of a projected nearside view, leads to a little-noticed (and perhaps trivial) ambiguity in lunar terminology. The statement that ''"[<del class="diffchange diffchange-inline">/</del>Nansen Nansen] is to the east of [<del class="diffchange diffchange-inline">/</del>Peary Peary]"'' is implicitly referring to the projected positions of those two craters in the Xi-Eta system. The equally valid statement that ''"[<del class="diffchange diffchange-inline">/</del>Nansen Nansen] is south of [<del class="diffchange diffchange-inline">/</del>Peary Peary]"'' is implicitly referring to the longitude-latitude system. But when the features are unfamiliar, as when one reads that "''feature X is located 10 km SE of crater Y''" it can be very hard to tell if the writer is thinking in terms of projected Xi-Eta directions, or (what is more properly called a "bearing") a direction relative to the N-S meridian (the line of constant longitude) through crater Y. <span class="membersnap">- [http://www.wikispaces.com/user/view/JimMosher [[Image:JimMosher-lg.jpg|16px|JimMosher]]] [http://www.wikispaces.com/user/view/JimMosher JimMosher]</span></div></td><td class='diff-marker'>+</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>* It might be noted that "east-west" (the '''Xi''' coordinate) and "north-south" (the '''Eta''' coordinate) in the Xi-Eta system are not always the same as "east-west" (a difference in longitude) and "north-south" (a difference in latitude) in the longitude-latitude system. Indeed, just to the "left" and "right" of the Moon's poles, the relative senses of the two systems can be rotated by as much as 90°. This, and the tendency to think almost always in terms of a projected nearside view, leads to a little-noticed (and perhaps trivial) ambiguity in lunar terminology. The statement that ''"[<ins class="diffchange diffchange-inline">[</ins>Nansen<ins class="diffchange diffchange-inline">|</ins>Nansen<ins class="diffchange diffchange-inline">]</ins>] is to the east of [<ins class="diffchange diffchange-inline">[</ins>Peary<ins class="diffchange diffchange-inline">|</ins>Peary<ins class="diffchange diffchange-inline">]</ins>]"'' is implicitly referring to the projected positions of those two craters in the Xi-Eta system. The equally valid statement that ''"[<ins class="diffchange diffchange-inline">[</ins>Nansen<ins class="diffchange diffchange-inline">|</ins>Nansen<ins class="diffchange diffchange-inline">]</ins>] is south of [<ins class="diffchange diffchange-inline">[</ins>Peary<ins class="diffchange diffchange-inline">|</ins>Peary<ins class="diffchange diffchange-inline">]</ins>]"'' is implicitly referring to the longitude-latitude system. But when the features are unfamiliar, as when one reads that "''feature X is located 10 km SE of crater Y''" it can be very hard to tell if the writer is thinking in terms of projected Xi-Eta directions, or (what is more properly called a "bearing") a direction relative to the N-S meridian (the line of constant longitude) through crater Y. <span class="membersnap">- [http://www.wikispaces.com/user/view/JimMosher [[Image:JimMosher-lg.jpg|16px|JimMosher]]] [http://www.wikispaces.com/user/view/JimMosher JimMosher]</span></div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div><br />  </div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div><br />  </div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>==LPOD Articles==</div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>==LPOD Articles==</div></td></tr>
</table>Apihttp://the-moon.us/index.php?title=Xi-Eta&diff=3339&oldid=prevApi: Created page with "<div id="content_view" class="wiki" style="display: block"> =Xi-Eta Coordinates= (glossary entry)<br /> <div id="toc"> =Table of Contents= <div style="margin-left: 1em">[..."2018-04-11T05:08:29Z<p>Created page with "<div id="content_view" class="wiki" style="display: block"> =Xi-Eta Coordinates= (glossary entry)<br /> <div id="toc"> =Table of Contents= <div style="margin-left: 1em">[..."</p>
<p><b>New page</b></p><div><div id="content_view" class="wiki" style="display: block"><br />
=Xi-Eta Coordinates=<br />
(glossary entry)<br /> <div id="toc"><br />
=Table of Contents=<br />
<div style="margin-left: 1em">[#Xi-Eta Coordinates Xi-Eta Coordinates]</div><div style="margin-left: 2em">[#Xi-Eta Coordinates-Description Description]</div><div style="margin-left: 2em">[#Xi-Eta Coordinates-Additional Information Additional Information]</div><div style="margin-left: 2em">[#Xi-Eta Coordinates-LPOD Articles LPOD Articles]</div><div style="margin-left: 2em">[#Xi-Eta Coordinates-Bibliography Bibliography]</div></div><br /> <br />
==Description==<br />
A system for expressing the position of a nearside lunar feature in terms of its X-Y coordinates in a standard zero-libration lunar atlas view. The radius of the Moon is 1 in this system. '''Xi''' (a Greek letter) is the horizontal (X) coordinate measured from -1 on the equatorial west limb to +1 on the equatorial east limb. '''Eta''' (another Greek letter) is the vertical (Y) coordinate, ranging from +1 at the north pole to -1 at the south pole.<br /> <br /> <br />
==Additional Information==<br />
* Although the IAU convention for east and west on the Moon was reversed in the early 1960's, the convention for '''Xi''' is unaffected.<br />
* Many of the older lunar maps, such as the ''[/System%20of%20Lunar%20Craters System of Lunar Craters]'' maps and many others, are plotted on rectangular grids labeled with the Xi-Eta positions.<br />
* According to the rules of trigonometry, the position of a feature of known [/selenographic%20coordinates selenographic] longitude and latitude can be reduced to the Xi-Eta system using the following formulas:<br />
** Xi = Cos(Lat)*Sin(Lon)<br />
** Eta = Sin(Lat)<br />
* A position given in terms of Xi and Eta can be similarly converted to the now more conventional longitude-latitude system:<br />
** Latitude = ArcSin(Eta) ''<-- compute this first''<br />
** Longitude = ArcSin[Xi/Cos(Lat)] ''<-- use computed latitude here''<br />
* The projected positions of a lunar feature as seen on an actual plate (displaced from that feature's standard position by [/librations librations]) are conventionally referred to as "x" and "y".<br />
* In their classic book [/Wilkins%20and%20Moore The Moon], Wilkins and Moore use some kind of extended Xi-Eta system to express the positions of features beyond the mean limb, but the rules they use for this are not explained. <span class="membersnap">- [http://www.wikispaces.com/user/view/JimMosher [[Image:JimMosher-lg.jpg|16px|JimMosher]]] [http://www.wikispaces.com/user/view/JimMosher JimMosher]</span><br />
* Since the Moon is spherical, rather than flat, a better representation of the three-dimensional position of a lunar surface feature can be obtained by introducing a third parameter '''Zeta''' representing the distance "in and out of the paper". Again, this will run from +1 (point closest to Earth) to -1 (point farthest from the Earth). All features that are on the nearside and mean libration will have Zeta>0, while all those on the farside will have Zeta<0. For a spherical Moon of radius 1, the Pythagorean theorem dictates that the sum of the squares of the three parameters will equal one. Hence given Xi and Eta, the magnitude of Zeta must be:<br />
<br /> <br />
<br />
** Zeta = Sqrt(1 - Sqr(Xi) - Sqr(Eta))<br />
<br /> <br />
<br />
* with the sign being decided by the features location on the nearside (+) or farside (-). Since the Moon is not perfectly spherical, one might think that the constraint on the sum of squares would be relaxed to permit representing actual points in space with values of the radial distance:<br />
<br /> <br />
<br />
** R = Sqrt(Sqr(Xi) + Sqr(Eta) + Sqr(Zeta))<br />
<br /> <br />
<br />
* differing slightly from 1 (indicating small deviations relative to the mean radius). But his does not seem to be the practice among selenographers. See, for example, pages 223-228 of Ralph Baldwin's [http://www.worldcat.org/oclc/530705 The Measure of the Moon] (1963), where the sum of squares of Xi, Eta and Zeta is always forced to 1, and the deviations from sphericity are represented by a separate parameter, h. <span class="membersnap">- [http://www.wikispaces.com/user/view/JimMosher [[Image:JimMosher-lg.jpg|16px|JimMosher]]] [http://www.wikispaces.com/user/view/JimMosher JimMosher]</span><br />
<br />
* It might be noted that "east-west" (the '''Xi''' coordinate) and "north-south" (the '''Eta''' coordinate) in the Xi-Eta system are not always the same as "east-west" (a difference in longitude) and "north-south" (a difference in latitude) in the longitude-latitude system. Indeed, just to the "left" and "right" of the Moon's poles, the relative senses of the two systems can be rotated by as much as 90°. This, and the tendency to think almost always in terms of a projected nearside view, leads to a little-noticed (and perhaps trivial) ambiguity in lunar terminology. The statement that ''"[/Nansen Nansen] is to the east of [/Peary Peary]"'' is implicitly referring to the projected positions of those two craters in the Xi-Eta system. The equally valid statement that ''"[/Nansen Nansen] is south of [/Peary Peary]"'' is implicitly referring to the longitude-latitude system. But when the features are unfamiliar, as when one reads that "''feature X is located 10 km SE of crater Y''" it can be very hard to tell if the writer is thinking in terms of projected Xi-Eta directions, or (what is more properly called a "bearing") a direction relative to the N-S meridian (the line of constant longitude) through crater Y. <span class="membersnap">- [http://www.wikispaces.com/user/view/JimMosher [[Image:JimMosher-lg.jpg|16px|JimMosher]]] [http://www.wikispaces.com/user/view/JimMosher JimMosher]</span><br />
<br /> <br />
==LPOD Articles==<br />
<br /> <br />
==Bibliography==<br />
<br /> <br /><br />
----<br />
This page has been edited 1 times. The last modification was made by <span class="membersnap">- [http://www.wikispaces.com/user/view/tychocrater [[Image:tychocrater-lg.jpg|16px|tychocrater]]] [http://www.wikispaces.com/user/view/tychocrater tychocrater]</span> on Jun 13, 2009 3:24 pm - ''mgx2''</div></div>Api