http://the-moon.us/index.php?title=Librations&feed=atom&action=historyLibrations - Revision history2024-03-28T08:27:05ZRevision history for this page on the wikiMediaWiki 1.31.1http://the-moon.us/index.php?title=Librations&diff=16262&oldid=prevApi at 10:01, 16 April 20182018-04-16T10:01:30Z<p></p>
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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>* The Moon's librations tend to make the observed center point wander around the "official" center in a quasi-circular or elliptical pattern. It would be rare, indeed, for the point of zero longitude and latitude (the "[[Oppolzer%20A|mean center]]") to actually be observed in the center, and even then, it would be seen so only for a single observer.</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 Moon's librations tend to make the observed center point wander around the "official" center in a quasi-circular or elliptical pattern. It would be rare, indeed, for the point of zero longitude and latitude (the "[[Oppolzer%20A|mean center]]") to actually be observed in the center, and even then, it would be seen so only for a single observer.</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 librations in longitude and latitude are frequently abbreviated by the letters "l" and "b" although this convention is by no means universal. "L" and "B" were probably originally abbreviations for the German words "''länge''" (longitude) and "''breite''" (latitude). On diagrams, and in mathematical discussions they are sometimes replaced by the Greek letters ''lambda'' and ''beta'', although again, this is not a universal conention.</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 librations in longitude and latitude are frequently abbreviated by the letters "l" and "b" although this convention is by no means universal. "L" and "B" were probably originally abbreviations for the German words "''länge''" (longitude) and "''breite''" (latitude). On diagrams, and in mathematical discussions they are sometimes replaced by the Greek letters ''lambda'' and ''beta'', although again, this is not a universal conention.</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 magnitudes of the librations are traditionally stated as +/- numbers (rather than N-S/E-W). As indicated in the definition, these are the selenographic coordinates of the Moon's apparent center. In longitude ("l"), positive values are in the [[Mare%20Crisium|Mare Crisium]] direction. In latitude ("b"), they are in the [[Mare%20Frigoris|Mare Frigoris]] direction. Hence a "+" value for "l" means the [[Mare%20Crisium|Mare Crisium]] limb is tipped into view. A "+" value for "b" means the [[Mare%20Frigoris|Mare Frigoris]] limb is tipped into view. The convention that longitudes towards [[Mare%20Crisium|Mare Crisium]] are positive is a very old one, so no change in the way librations are stated or understood was required when the IAU [[IAU%<del class="diffchange diffchange-inline">20Directions</del>|reversed]] the meaning of "east" and "west" on the Moon.</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 magnitudes of the librations are traditionally stated as +/- numbers (rather than N-S/E-W). As indicated in the definition, these are the selenographic coordinates of the Moon's apparent center. In longitude ("l"), positive values are in the [[Mare%20Crisium|Mare Crisium]] direction. In latitude ("b"), they are in the [[Mare%20Frigoris|Mare Frigoris]] direction. Hence a "+" value for "l" means the [[Mare%20Crisium|Mare Crisium]] limb is tipped into view. A "+" value for "b" means the [[Mare%20Frigoris|Mare Frigoris]] limb is tipped into view. The convention that longitudes towards [[Mare%20Crisium|Mare Crisium]] are positive is a very old one, so no change in the way librations are stated or understood was required when the IAU [[IAU%<ins class="diffchange diffchange-inline">20directions</ins>|reversed]] the meaning of "east" and "west" on the Moon.</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 /> <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 /> <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=Librations&diff=11732&oldid=prevApi at 00:35, 16 April 20182018-04-16T00:35:05Z<p></p>
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<td colspan="2" style="background-color: #fff; color: #222; text-align: center;">Revision as of 00:35, 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>=Librations=</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>=Librations=</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">[#Librations Librations]</div><div style="margin-left: 2em">[#Librations-Description Description]</div><div style="margin-left: 2em">[#Librations-Additional Information Additional Information]</div><div style="margin-left: 2em">[#Librations-LPOD Articles LPOD Articles]</div><div style="margin-left: 2em">[#toc4  ]</div><div style="margin-left: 2em">[#Librations-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>  Changes in the orientation of the Moon as seen from Earth, expressed in terms of the [[selenographic%20coordinates|selenographic]] longitude and latitude of the observed center (also known as the [[Sub-Earth%20point|Sub-Earth point]]).<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>  Changes in the orientation of the Moon as seen from Earth, expressed in terms of the [[selenographic%20coordinates|selenographic]] longitude and latitude of the observed center (also known as the [[Sub-Earth%20point|Sub-Earth point]]).<br /> <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>----</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=Librations&diff=8915&oldid=prevApi at 23:01, 15 April 20182018-04-15T23:01:12Z<p></p>
<table class="diff diff-contentalign-left" data-mw="interface">
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<td colspan="2" style="background-color: #fff; color: #222; text-align: center;">Revision as of 23:01, 15 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><div style="margin-left: 1em">[#Librations Librations]</div><div style="margin-left: 2em">[#Librations-Description Description]</div><div style="margin-left: 2em">[#Librations-Additional Information Additional Information]</div><div style="margin-left: 2em">[#Librations-LPOD Articles LPOD Articles]</div><div style="margin-left: 2em">[#toc4  ]</div><div style="margin-left: 2em">[#Librations-Bibliography Bibliography]</div></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><div style="margin-left: 1em">[#Librations Librations]</div><div style="margin-left: 2em">[#Librations-Description Description]</div><div style="margin-left: 2em">[#Librations-Additional Information Additional Information]</div><div style="margin-left: 2em">[#Librations-LPOD Articles LPOD Articles]</div><div style="margin-left: 2em">[#toc4  ]</div><div style="margin-left: 2em">[#Librations-Bibliography Bibliography]</div></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>==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="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>  Changes in the orientation of the Moon as seen from Earth, expressed in terms of the [<del class="diffchange diffchange-inline">/</del>selenographic%20coordinates selenographic] longitude and latitude of the observed center (also known as the [<del class="diffchange diffchange-inline">/</del>Sub-Earth%20point Sub-Earth point]).<br /> <br />  </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>  Changes in the orientation of the Moon as seen from Earth, expressed in terms of the [<ins class="diffchange diffchange-inline">[</ins>selenographic%20coordinates<ins class="diffchange diffchange-inline">|</ins>selenographic<ins class="diffchange diffchange-inline">]</ins>] longitude and latitude of the observed center (also known as the [<ins class="diffchange diffchange-inline">[</ins>Sub-Earth%20point<ins class="diffchange diffchange-inline">|</ins>Sub-Earth point<ins class="diffchange diffchange-inline">]</ins>]).<br /> <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>==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>* The Moon basically keeps the same face (the "nearside") pointed towards the Earth. However, its exact orientation is constantly changing at the level of a few degrees.</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 Moon basically keeps the same face (the "nearside") pointed towards the Earth. However, its exact orientation is constantly changing at the level of a few degrees.</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>* By convention, the surface feature at the [<del class="diffchange diffchange-inline">/</del>Oppolzer%20A average center point] of this apparent disk is taken as the point of zero longitude and latitude. At any moment, features up to about 12° from this point can occupy the apparent center. The '''librations''' refer to the longitude and latitude of the feature currently seen at the Moon's apparent center.</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>* By convention, the surface feature at the [<ins class="diffchange diffchange-inline">[</ins>Oppolzer%20A<ins class="diffchange diffchange-inline">|</ins>average center point<ins class="diffchange diffchange-inline">]</ins>] of this apparent disk is taken as the point of zero longitude and latitude. At any moment, features up to about 12° from this point can occupy the apparent center. The '''librations''' refer to the longitude and latitude of the feature currently seen at the Moon's apparent center.</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 major part of the Moon's '''libration in latitude''' is due to the inclination of the Moon's spin axis relative to the plane of of its orbit. This amounts to a variation of about ±6½° in the latitude of the observed center point (Roncoli, 2005, puts the maximum at 6.87°).</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 major part of the Moon's '''libration in latitude''' is due to the inclination of the Moon's spin axis relative to the plane of of its orbit. This amounts to a variation of about ±6½° in the latitude of the observed center point (Roncoli, 2005, puts the maximum at 6.87°).</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 major part of the Moon's '''libration in longitude''' is due to its spinning like a top at constant velocity (relative to the stars), yet travelling in an elliptical orbit (which causes our angle of viewing it to change at a varying speed). The result is that the apparent center point varies by around ±8° in longitude (Roncoli, 2005, puts the maximum at 8.16°).</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 major part of the Moon's '''libration in longitude''' is due to its spinning like a top at constant velocity (relative to the stars), yet travelling in an elliptical orbit (which causes our angle of viewing it to change at a varying speed). The result is that the apparent center point varies by around ±8° in longitude (Roncoli, 2005, puts the maximum at 8.16°).</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>* In addition to these basic rocking motions, an observer's exact location on Earth will can change his perspective. An observer in the Earth's far north sees more of the Moon's northern parts; while one observing the Moon at moonrise sees more of the leading limb. This affect alters the coordinates of the apparent center by up to about ±1°. These true '''librations''', as actually seen by the observer, are called the '''topocentric librations''' (as opposed to the '''geocentric librations''' -- which are computed for an imaginary observer at the Earth's center, and, although frequently tabulated in Almanacs, seldom apply to any real observer).</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>* In addition to these basic rocking motions, an observer's exact location on Earth will can change his perspective. An observer in the Earth's far north sees more of the Moon's northern parts; while one observing the Moon at moonrise sees more of the leading limb. This affect alters the coordinates of the apparent center by up to about ±1°. These true '''librations''', as actually seen by the observer, are called the '''topocentric librations''' (as opposed to the '''geocentric librations''' -- which are computed for an imaginary observer at the Earth's center, and, although frequently tabulated in Almanacs, seldom apply to any real observer).</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>* Any variation beyond that which can be attributed to an idealized spinning top (such as would be observed if the Moon's spin rate about its axis were not perfectly constant) is categorized as a '''physical libration'''.</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>* Any variation beyond that which can be attributed to an idealized spinning top (such as would be observed if the Moon's spin rate about its axis were not perfectly constant) is categorized as a '''physical libration'''.</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 Moon's librations tend to make the observed center point wander around the "official" center in a quasi-circular or elliptical pattern. It would be rare, indeed, for the point of zero longitude and latitude (the "[<del class="diffchange diffchange-inline">/</del>Oppolzer%20A mean center]") to actually be observed in the center, and even then, it would be seen so only for a single observer.</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 Moon's librations tend to make the observed center point wander around the "official" center in a quasi-circular or elliptical pattern. It would be rare, indeed, for the point of zero longitude and latitude (the "[<ins class="diffchange diffchange-inline">[</ins>Oppolzer%20A<ins class="diffchange diffchange-inline">|</ins>mean center<ins class="diffchange diffchange-inline">]</ins>]") to actually be observed in the center, and even then, it would be seen so only for a single observer.</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 librations in longitude and latitude are frequently abbreviated by the letters "l" and "b" although this convention is by no means universal. "L" and "B" were probably originally abbreviations for the German words "''länge''" (longitude) and "''breite''" (latitude). On diagrams, and in mathematical discussions they are sometimes replaced by the Greek letters ''lambda'' and ''beta'', although again, this is not a universal conention.</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 librations in longitude and latitude are frequently abbreviated by the letters "l" and "b" although this convention is by no means universal. "L" and "B" were probably originally abbreviations for the German words "''länge''" (longitude) and "''breite''" (latitude). On diagrams, and in mathematical discussions they are sometimes replaced by the Greek letters ''lambda'' and ''beta'', although again, this is not a universal conention.</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 magnitudes of the librations are traditionally stated as +/- numbers (rather than N-S/E-W). As indicated in the definition, these are the selenographic coordinates of the Moon's apparent center. In longitude ("l"), positive values are in the [<del class="diffchange diffchange-inline">/</del>Mare%20Crisium Mare Crisium] direction. In latitude ("b"), they are in the [<del class="diffchange diffchange-inline">/</del>Mare%20Frigoris Mare Frigoris] direction. Hence a "+" value for "l" means the [<del class="diffchange diffchange-inline">/</del>Mare%20Crisium Mare Crisium] limb is tipped into view. A "+" value for "b" means the [<del class="diffchange diffchange-inline">/</del>Mare%20Frigoris Mare Frigoris] limb is tipped into view. The convention that longitudes towards [<del class="diffchange diffchange-inline">/</del>Mare%20Crisium Mare Crisium] are positive is a very old one, so no change in the way librations are stated or understood was required when the IAU [<del class="diffchange diffchange-inline">/</del>IAU%20Directions reversed] the meaning of "east" and "west" on the Moon.</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 magnitudes of the librations are traditionally stated as +/- numbers (rather than N-S/E-W). As indicated in the definition, these are the selenographic coordinates of the Moon's apparent center. In longitude ("l"), positive values are in the [<ins class="diffchange diffchange-inline">[</ins>Mare%20Crisium<ins class="diffchange diffchange-inline">|</ins>Mare Crisium<ins class="diffchange diffchange-inline">]</ins>] direction. In latitude ("b"), they are in the [<ins class="diffchange diffchange-inline">[</ins>Mare%20Frigoris<ins class="diffchange diffchange-inline">|</ins>Mare Frigoris<ins class="diffchange diffchange-inline">]</ins>] direction. Hence a "+" value for "l" means the [<ins class="diffchange diffchange-inline">[</ins>Mare%20Crisium<ins class="diffchange diffchange-inline">|</ins>Mare Crisium<ins class="diffchange diffchange-inline">]</ins>] limb is tipped into view. A "+" value for "b" means the [<ins class="diffchange diffchange-inline">[</ins>Mare%20Frigoris<ins class="diffchange diffchange-inline">|</ins>Mare Frigoris<ins class="diffchange diffchange-inline">]</ins>] limb is tipped into view. The convention that longitudes towards [<ins class="diffchange diffchange-inline">[</ins>Mare%20Crisium<ins class="diffchange diffchange-inline">|</ins>Mare Crisium<ins class="diffchange diffchange-inline">]</ins>] are positive is a very old one, so no change in the way librations are stated or understood was required when the IAU [<ins class="diffchange diffchange-inline">[</ins>IAU%20Directions<ins class="diffchange diffchange-inline">|</ins>reversed<ins class="diffchange diffchange-inline">]</ins>] the meaning of "east" and "west" on the Moon.</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 /> <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 /> <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=Librations&diff=6787&oldid=prevApi at 03:22, 12 April 20182018-04-12T03:22:54Z<p></p>
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<td colspan="2" style="background-color: #fff; color: #222; text-align: center;">Revision as of 03:22, 12 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>==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>
<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>  See LPOD list in page [http://the-moon.<del class="diffchange diffchange-inline">wikispaces.com</del>/Limb Limb]<br />  </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>  See LPOD list in page [http://the-moon.<ins class="diffchange diffchange-inline">us/wiki</ins>/Limb Limb]<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>== ==</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="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>==Bibliography==</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>==Bibliography==</div></td></tr>
</table>Apihttp://the-moon.us/index.php?title=Librations&diff=1653&oldid=prevApi: Created page with "<div id="content_view" class="wiki" style="display: block"> =Librations= (glossary entry)<br /> <div id="toc"> =Table of Contents= <div style="margin-left: 1em">[#Librati..."2018-04-11T04:16:28Z<p>Created page with "<div id="content_view" class="wiki" style="display: block"> =Librations= (glossary entry)<br /> <div id="toc"> =Table of Contents= <div style="margin-left: 1em">[#Librati..."</p>
<p><b>New page</b></p><div><div id="content_view" class="wiki" style="display: block"><br />
=Librations=<br />
(glossary entry)<br /> <div id="toc"><br />
=Table of Contents=<br />
<div style="margin-left: 1em">[#Librations Librations]</div><div style="margin-left: 2em">[#Librations-Description Description]</div><div style="margin-left: 2em">[#Librations-Additional Information Additional Information]</div><div style="margin-left: 2em">[#Librations-LPOD Articles LPOD Articles]</div><div style="margin-left: 2em">[#toc4 ]</div><div style="margin-left: 2em">[#Librations-Bibliography Bibliography]</div></div><br /> <br />
==Description==<br />
Changes in the orientation of the Moon as seen from Earth, expressed in terms of the [/selenographic%20coordinates selenographic] longitude and latitude of the observed center (also known as the [/Sub-Earth%20point Sub-Earth point]).<br /> <br /> <br />
==Additional Information==<br />
* The Moon basically keeps the same face (the "nearside") pointed towards the Earth. However, its exact orientation is constantly changing at the level of a few degrees.<br />
* By convention, the surface feature at the [/Oppolzer%20A average center point] of this apparent disk is taken as the point of zero longitude and latitude. At any moment, features up to about 12° from this point can occupy the apparent center. The '''librations''' refer to the longitude and latitude of the feature currently seen at the Moon's apparent center.<br />
* The major part of the Moon's '''libration in latitude''' is due to the inclination of the Moon's spin axis relative to the plane of of its orbit. This amounts to a variation of about ±6½° in the latitude of the observed center point (Roncoli, 2005, puts the maximum at 6.87°).<br />
* The major part of the Moon's '''libration in longitude''' is due to its spinning like a top at constant velocity (relative to the stars), yet travelling in an elliptical orbit (which causes our angle of viewing it to change at a varying speed). The result is that the apparent center point varies by around ±8° in longitude (Roncoli, 2005, puts the maximum at 8.16°).<br />
* In addition to these basic rocking motions, an observer's exact location on Earth will can change his perspective. An observer in the Earth's far north sees more of the Moon's northern parts; while one observing the Moon at moonrise sees more of the leading limb. This affect alters the coordinates of the apparent center by up to about ±1°. These true '''librations''', as actually seen by the observer, are called the '''topocentric librations''' (as opposed to the '''geocentric librations''' -- which are computed for an imaginary observer at the Earth's center, and, although frequently tabulated in Almanacs, seldom apply to any real observer).<br />
* Any variation beyond that which can be attributed to an idealized spinning top (such as would be observed if the Moon's spin rate about its axis were not perfectly constant) is categorized as a '''physical libration'''.<br />
* The Moon's librations tend to make the observed center point wander around the "official" center in a quasi-circular or elliptical pattern. It would be rare, indeed, for the point of zero longitude and latitude (the "[/Oppolzer%20A mean center]") to actually be observed in the center, and even then, it would be seen so only for a single observer.<br />
* The librations in longitude and latitude are frequently abbreviated by the letters "l" and "b" although this convention is by no means universal. "L" and "B" were probably originally abbreviations for the German words "''länge''" (longitude) and "''breite''" (latitude). On diagrams, and in mathematical discussions they are sometimes replaced by the Greek letters ''lambda'' and ''beta'', although again, this is not a universal conention.<br />
* The magnitudes of the librations are traditionally stated as +/- numbers (rather than N-S/E-W). As indicated in the definition, these are the selenographic coordinates of the Moon's apparent center. In longitude ("l"), positive values are in the [/Mare%20Crisium Mare Crisium] direction. In latitude ("b"), they are in the [/Mare%20Frigoris Mare Frigoris] direction. Hence a "+" value for "l" means the [/Mare%20Crisium Mare Crisium] limb is tipped into view. A "+" value for "b" means the [/Mare%20Frigoris Mare Frigoris] limb is tipped into view. The convention that longitudes towards [/Mare%20Crisium Mare Crisium] are positive is a very old one, so no change in the way librations are stated or understood was required when the IAU [/IAU%20Directions reversed] the meaning of "east" and "west" on the Moon.<br />
<br /> <br /> <br />
==LPOD Articles==<br />
See LPOD list in page [http://the-moon.wikispaces.com/Limb Limb]<br /> <br />
== ==<br />
==Bibliography==<br />
<br />
* [http://en.wikipedia.org/wiki/Libration Libration] (Wikipedia)<br />
* Ralph B. Roncoli. 2005. [http://ssd.jpl.nasa.gov/?lunar_doc Lunar Constants and Models Document]. JPL Technical Document D-32296.<br />
* Weimer, Th. 1979. [http://adsabs.harvard.edu/abs/1979M&P....20..157W Cartography of the marginal zones of the moon]. ''Moon and the Planets'', vol. 20, Apr. 1979, p. 157-162. In French.<br />
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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