<?xml version="1.0" encoding="ISO-8859-1"?><article xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance">
<front>
<journal-meta>
<journal-id>0185-1101</journal-id>
<journal-title><![CDATA[Revista mexicana de astronomía y astrofísica]]></journal-title>
<abbrev-journal-title><![CDATA[Rev. mex. astron. astrofis]]></abbrev-journal-title>
<issn>0185-1101</issn>
<publisher>
<publisher-name><![CDATA[Universidad Nacional Autónoma de México, Instituto de Astronomía]]></publisher-name>
</publisher>
</journal-meta>
<article-meta>
<article-id>S0185-11012017000200004</article-id>
<title-group>
<article-title xml:lang="en"><![CDATA[Analysis of Hansen&#8217;s Inferior and Superior Partial Anomalies and the Division of the Elliptic Orbit Into Two Segments]]></article-title>
</title-group>
<contrib-group>
<contrib contrib-type="author">
<name>
<surname><![CDATA[Sharaf]]></surname>
<given-names><![CDATA[M. A.]]></given-names>
</name>
<xref ref-type="aff" rid="Aff"/>
</contrib>
<contrib contrib-type="author">
<name>
<surname><![CDATA[Saad]]></surname>
<given-names><![CDATA[A. S.]]></given-names>
</name>
<xref ref-type="aff" rid="Aff"/>
<xref ref-type="aff" rid="Aaf"/>
</contrib>
</contrib-group>
<aff id="Af1">
<institution><![CDATA[,Cairo University Faculty of Science Astronomy, Space Science and Meteorology Department]]></institution>
<addr-line><![CDATA[ ]]></addr-line>
<country>Egypt</country>
</aff>
<aff id="Af2">
<institution><![CDATA[,National Research Institute of Astronomy and Geophysics Department of Astronomy ]]></institution>
<addr-line><![CDATA[Cairo ]]></addr-line>
<country>Egypt</country>
</aff>
<aff id="Af3">
<institution><![CDATA[,Qassim University  ]]></institution>
<addr-line><![CDATA[Buraidah ]]></addr-line>
<country>KSA</country>
</aff>
<pub-date pub-type="pub">
<day>00</day>
<month>00</month>
<year>2017</year>
</pub-date>
<pub-date pub-type="epub">
<day>00</day>
<month>00</month>
<year>2017</year>
</pub-date>
<volume>53</volume>
<numero>2</numero>
<copyright-statement/>
<copyright-year/>
<self-uri xlink:href="http://www.scielo.org.mx/scielo.php?script=sci_arttext&amp;pid=S0185-11012017000200004&amp;lng=en&amp;nrm=iso"></self-uri><self-uri xlink:href="http://www.scielo.org.mx/scielo.php?script=sci_abstract&amp;pid=S0185-11012017000200004&amp;lng=en&amp;nrm=iso"></self-uri><self-uri xlink:href="http://www.scielo.org.mx/scielo.php?script=sci_pdf&amp;pid=S0185-11012017000200004&amp;lng=en&amp;nrm=iso"></self-uri><abstract abstract-type="short" xml:lang="en"><p><![CDATA[ABSTRACT In this paper, a novel analysis was established to prove how Hansen&#8217;s inferior and superior partial anomalies k and k 1 can divide the elliptic orbit into two segments. The analysis depends on the departures of r (for k) and 1/r (for k 1) from their minima. By these departures, we can find: (i) Transformations relating the eccentric anomaly to k and the true anomaly to k 1. (ii) Expressions for k and k 1 in terms of the orbital elements. (iii) The interpretation and the intervals of definition of two moduli (X, S) related to k and k 1. (iv) The extreme values of r and the elliptic equations in terms of k and k 1. (v) For r ' and r '', the modulus X as a measure of the asymmetry of r ' (or r '') from r '' (or r '), and the modulus S 12 as a measure of the asymmetry of r ' and r '' from the minimum value of r. (vi) A description of the segments represented by k and k 1. (vii) The relative position of the radius vector at k = 0o and k 1 = 180o.]]></p></abstract>
<abstract abstract-type="short" xml:lang="es"><p><![CDATA[RESUMEN Presentamos un nuevo análisis para demostrar que las anomalías parciales superior e inferior de Hansen, k y k 1, pueden dividir a la órbita elíptica en dos segmentos. El análisis depende de qué tanto se alejan r (para k) y 1/r (para k 1) de sus mínimos. Con estas diferencias podemos encontrar lo siguiente. (i) Transformaciones que relacionan a la anomalía excéntrica con k y a la anomalía verdadera con k 1. (ii) Expresiones para k y k 1 en términos de los elementos orbitales. (iii) La interpretación y los intervalos de definición para los módulos X y S relacionados con k y k 1. (iv) Los valores extremos de r y las ecuaciones elípticas en términos de k y k 1. (v) Para r ' y r '' el módulo X como una medida de la asimetría de r ' (o bien r '') respecto de r '' (o bien r '), mientras que el módulo S 12 como una medida de la asimetría de r ' y r '' respecto al valor minimo de r. (vi) Una descripción de los segmentos representados por k y k 1. (vii) La posición relativa del radio vector en k = 0o y k 1 = 180o.]]></p></abstract>
<kwd-group>
<kwd lng="en"><![CDATA[celestial mechanics]]></kwd>
<kwd lng="en"><![CDATA[comets]]></kwd>
<kwd lng="en"><![CDATA[general]]></kwd>
<kwd lng="en"><![CDATA[methods]]></kwd>
<kwd lng="en"><![CDATA[analytical]]></kwd>
</kwd-group>
</article-meta>
</front><back>
<ref-list>
<ref id="B1">
<nlm-citation citation-type="">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Hansen]]></surname>
<given-names><![CDATA[P. A.]]></given-names>
</name>
</person-group>
<source><![CDATA[Suppl. Compt. Rend. Acad. Sci.]]></source>
<year>1856</year>
<volume>1</volume>
<page-range>121</page-range><publisher-loc><![CDATA[Paris ]]></publisher-loc>
</nlm-citation>
</ref>
<ref id="B2">
<nlm-citation citation-type="">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Nacozy]]></surname>
<given-names><![CDATA[P. E.]]></given-names>
</name>
</person-group>
<source><![CDATA[AJ]]></source>
<year>1969</year>
<volume>74</volume>
<page-range>544</page-range></nlm-citation>
</ref>
<ref id="B3">
<nlm-citation citation-type="">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Sharaf]]></surname>
<given-names><![CDATA[M. A.]]></given-names>
</name>
</person-group>
<source><![CDATA[Ap &amp; SS]]></source>
<year>1982</year>
<volume>84</volume>
<page-range>73</page-range></nlm-citation>
</ref>
<ref id="B4">
<nlm-citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Skripnichenko]]></surname>
<given-names><![CDATA[V. I.]]></given-names>
</name>
<name>
<surname><![CDATA[Chebatorev]]></surname>
<given-names><![CDATA[G. A.]]></given-names>
</name>
<name>
<surname><![CDATA[Kazimirchak-Polanskaia]]></surname>
<given-names><![CDATA[E. I.]]></given-names>
</name>
<name>
<surname><![CDATA[Marsden]]></surname>
<given-names><![CDATA[B. G.]]></given-names>
</name>
</person-group>
<source><![CDATA[IAU 45, The Motion, Evolution of Orbits and Origin of Comets]]></source>
<year>1972</year>
<page-range>52</page-range><publisher-loc><![CDATA[Holland ]]></publisher-loc>
<publisher-name><![CDATA[Dordrecht, Reidel]]></publisher-name>
</nlm-citation>
</ref>
</ref-list>
</back>
</article>
