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<front>
<journal-meta>
<journal-id journal-id-type="pmc">706</journal-id>
<journal-title-group>
<journal-title specific-use="original" xml:lang="es">Ingeniería y Universidad</journal-title>
</journal-title-group>
<issn pub-type="ppub">0123-2126</issn>
<issn pub-type="epub">2011-2769</issn>
<publisher>
<publisher-name>Pontificia Universidad Javeriana</publisher-name>
<publisher-loc>
<country>Colombia</country>
<email>reving@javeriana.edu.co</email>
</publisher-loc>
</publisher>
</journal-meta>
<article-meta>
<article-id pub-id-type="art-access-id" specific-use="pmc">7062790006</article-id>
<article-id pub-id-type="doi">https://doi.org/10.11144/Javeriana.iued29.saco</article-id>
<article-categories>
<subj-group subj-group-type="heading">
<subject>Artículos</subject>
</subj-group>
</article-categories>
<title-group>
<article-title xml:lang="en">Simulation of Access, Coverage, and Orbital Decay for an Optical Micro-Satellite for Colombia<xref ref-type="fn" rid="fn1">*</xref>
</article-title>
<trans-title-group>
<trans-title xml:lang="es">Simulación del acceso, la cobertura y la decadencia
orbital de un microsatélite óptico para Colombia</trans-title>
</trans-title-group>
</title-group>
<contrib-group>
<contrib contrib-type="author" corresp="no">
<contrib-id contrib-id-type="orcid">https://orcid.org/0000-0001-7298-7519</contrib-id>
<name name-style="western">
<surname>Cortés García</surname>
<given-names>Ernesto David</given-names>
</name>
<xref ref-type="aff" rid="aff1"/>
</contrib>
<contrib contrib-type="author" corresp="no">
<contrib-id contrib-id-type="orcid">https://orcid.org/0000-0002-2054-3251</contrib-id>
<name name-style="western">
<surname>Saenz Hernández</surname>
<given-names>Germán Darío</given-names>
</name>
<xref ref-type="aff" rid="aff2"/>
</contrib>
<contrib contrib-type="author" corresp="no">
<contrib-id contrib-id-type="orcid">https://orcid.org/0000-0003-2473-0932</contrib-id>
<name name-style="western">
<surname>Cárdenas Espinosa</surname>
<given-names>Lorena Paola</given-names>
</name>
<xref ref-type="aff" rid="aff3"/>
</contrib>
<contrib contrib-type="author" corresp="yes">
<contrib-id contrib-id-type="orcid">https://orcid.org/0000-0001-6017-1934</contrib-id>
<name name-style="western">
<surname>Muñoz Giraldo</surname>
<given-names>Santiago</given-names>
</name>
<xref ref-type="corresp" rid="corresp1"><sup>a</sup></xref>
<xref ref-type="aff" rid="aff4"/>
<email>santiago.munoz@fac.mil.co</email>
</contrib>
<contrib contrib-type="author" corresp="no">
<contrib-id contrib-id-type="orcid">https://orcid.org/0000-0002-1903-1910</contrib-id>
<name name-style="western">
<surname>Salek Chaves</surname>
<given-names>Dib Ziyari</given-names>
</name>
<xref ref-type="aff" rid="aff5"/>
</contrib>
<contrib contrib-type="author" corresp="no">
<contrib-id contrib-id-type="orcid">https://orcid.org/0009-0004-2457-7354</contrib-id>
<name name-style="western">
<surname>Guerrero Sánchez</surname>
<given-names>Rubén Darío</given-names>
</name>
<xref ref-type="aff" rid="aff6"/>
</contrib>
</contrib-group>
<aff id="aff1">
<institution content-type="original">Colombian Air Force</institution>
<institution content-type="orgname">Colombian Air Force</institution>
<country country="CO">Colombia</country>
</aff>
<aff id="aff2">
<institution content-type="original">Colombian Air Force</institution>
<institution content-type="orgname">Colombian Air Force</institution>
<country country="CO">Colombia</country>
</aff>
<aff id="aff3">
<institution content-type="original">Colombian Air Force</institution>
<institution content-type="orgname">Colombian Air Force</institution>
<country country="CO">Colombia</country>
</aff>
<aff id="aff4">
<institution content-type="original">Colombian Air Force</institution>
<institution content-type="orgname">Colombian Air Force</institution>
<country country="CO">Colombia</country>
</aff>
<aff id="aff5">
<institution content-type="original">Colombian Air Force</institution>
<institution content-type="orgname">Colombian Air Force</institution>
<country country="CO">Colombia</country>
</aff>
<aff id="aff6">
<institution content-type="original">Colombian Air Force</institution>
<institution content-type="orgname">Colombian Air Force</institution>
<country country="CO">Colombia</country>
</aff>
<author-notes>
<corresp id="corresp1">
<email>
<sup>a</sup>Corresponding
author. E-mail: santiago.munoz@fac.mil.co</email>
</corresp>
</author-notes>
<pub-date pub-type="epub-ppub">
<season>January-December</season>
<year>2025</year>
</pub-date>
<volume>29</volume>
<history>
<date date-type="received" publication-format="dd mes yyyy">
<day>28</day>
<month>10</month>
<year>2024</year>
</date>
<date date-type="accepted" publication-format="dd mes yyyy">
<day>29</day>
<month>08</month>
<year>2025</year>
</date>
<date date-type="pub" publication-format="dd mes yyyy">
<day>09</day>
<month>10</month>
<year>2025</year>
</date>
</history>
<permissions>
<ali:free_to_read/>
<license xlink:href="https://creativecommons.org/licenses/by-nc/4.0/">
<ali:license_ref>https://creativecommons.org/licenses/by-nc/4.0/</ali:license_ref>
<license-p>Esta obra está bajo una Licencia Creative Commons Atribución-NoComercial 4.0 Internacional.</license-p>
</license>
</permissions>
<abstract xml:lang="en">
<title>Abstract</title>
<p>The selection of the operational orbit is a critical component for the success of satellite missions, as it must meet specific user requirements, payload constraints, and communication needs. This paper comprehensively analyzes the criteria and parameters used to determine the best orbit for satellite missions, focusing on design variables derived from mission requirements and technical constraints. Several fundamental aspects are evaluated, including coverage of areas of interest, access times to ground stations, revisit times, and satellite lifespan in orbit, through simulations of orbital scenarios. The results show that orbits with inclinations of 16° provide an optimal balance between coverage and revisit times, maximizing operational efficiency over Colombian territory. Satellite constellations are also analyzed, highlighting specific combinations that improve coverage and access times. Furthermore, the analysis of orbital decay and lifespan in orbit confirms that the selected orbits comply with international standards for mitigating collision risk. This article offers a guide for orbit selection in satellite missions, emphasizing a Low-Earth Orbit (LEO) mission, ensuring operational benefits and minimizing risks.</p>
</abstract>
<trans-abstract xml:lang="es">
<title>Resumen</title>
<p>La selección de una órbita operacional es un factor crítico para el éxito de las misiones satelitales, ya que debe cumplir con requisitos específicos del usuario, restricciones de carga útil y necesidades de comunicación. Este artículo presenta un análisis exhaustivo de los criterios y parámetros utilizados para determinar la órbita óptima para misiones satelitales, enfocándose en variables de diseño derivadas de los requisitos de la misión y restricciones técnicas. Se evalúan aspectos clave, como la cobertura de áreas de interés, los tiempos de acceso a estaciones terrestres, los tiempos de revisita y la vida útil del satélite en órbita, a través de simulaciones de escenarios orbitales. Los resultados indican que las órbitas con inclinaciones de 16° proporcionan un equilibrio óptimo entre cobertura y tiempos de revisita, maximizando la eficiencia operacional sobre el territorio colombiano. El estudio también examina constelaciones de satélites, destacando configuraciones específicas que mejoran la cobertura y los tiempos de acceso. Además, el análisis de la desintegración orbital y la vida útil en órbita confirma que las órbitas seleccionadas cumplen con los estándares internacionales de mitigación de riesgos de colisión. Este artículo sirve como guía para la selección de órbitas en misiones satelitales, con énfasis en misiones en órbitas bajas, asegurando beneficios operacionales y minimizando riesgos.</p>
</trans-abstract>
<kwd-group xml:lang="en">
<title>Keywords</title>
<kwd>Satellite Orbits</kwd>
<kwd>Coverage</kwd>
<kwd>Revisit Time</kwd>
<kwd>Orbit Lifespan</kwd>
<kwd>Simulation</kwd>
<kwd>Decay</kwd>
<kwd>Microsatellite</kwd>
</kwd-group>
<kwd-group xml:lang="es">
<title>Palabras clave</title>
<kwd>órbitas satelitales</kwd>
<kwd>cobertura</kwd>
<kwd>tiempos de revisita</kwd>
<kwd>vida útil en órbita</kwd>
<kwd>simulación</kwd>
<kwd>decaimiento</kwd>
<kwd>microsatélite</kwd>
</kwd-group>
<counts>
<fig-count count="11"/>
<table-count count="5"/>
<equation-count count="0"/>
<ref-count count="21"/>
</counts>
<custom-meta-group>
<custom-meta>
<meta-name>How to
cite this article</meta-name>
<meta-value>E D Cortés García, G D Saenz Hernández, L P
Cárdenas Espinosa, S Muñoz Giraldo, D Z Salek Chaves, R D Guerrero Sánchez, “Simulation of Access,
Coverage, and Orbital Decay for an Optical Micro-Satellite for Colombia” Ing. Univ. vol. 29, 2025. <ext-link ext-link-type="uri" xlink:href="https://doi.org/10.11144/Javeriana.iued29.saco">https://doi.org/10.11144/Javeriana.iued29.saco</ext-link>
</meta-value>
</custom-meta>
</custom-meta-group>
</article-meta>
</front>
<body>
<sec sec-type="intro">
<title><bold>Introduction</bold></title>
<p>The space industry has experienced significant growth in recent decades, driven by the development of advanced technologies and the increasing demand for satellite services. This has encouraged emerging countries to develop their capabilities in the space sector, starting from mission design to in-depth analysis [<xref ref-type="bibr" rid="ref1">1</xref>]. In this context, orbit selection for satellite missions has become a critical factor in maximizing operational efficiency and ensuring mission success. The proper selection of orbit must consider various factors, including coverage of areas of interest, access times to ground stations, revisit times, and the satellite’s orbital lifespan [<xref ref-type="bibr" rid="ref2">2</xref>].</p>
<p>In the case of Colombia, the Colombian Airspace Force (FAC) has led significant advances in the space domain with the launch of the FACSAT-1 satellite and the co-development of the FACSAT-2 “Chiribiquete” satellite mission. These assets have contributed to the development of capabilities, including data collection from Earth Observation sensors, autonomous satellite operation, as well as capability enhancement in mission design, software development, payload operation, and data analysis applications. These foundations have set the stage for future mission developments in the country.</p>
<p>FACSAT-1, launched in 2018, was the country’s first Earth observation satellite, which enabled the autonomous operation of an optical data acquisition system. FACSAT-2, its successor, has improved payload and communication capabilities. The primary payload acquires multispectral images, while a secondary payload collects spectral signatures. These data are used for developments such as deforestation analyses and Greenhouse Gas (GHG) emission monitoring [<xref ref-type="bibr" rid="ref3">3</xref>] [<xref ref-type="bibr" rid="ref4">4</xref>].</p>
<p>Currently, a new satellite mission is under analysis, building on the achievements of its predecessors and incorporating technological advancements and lessons learned to optimize performance. This article focuses on the orbit selection for a future satellite mission by analyzing parameters and criteria that ensure a balance between coverage, access times, revisit times, and orbital lifespan, to maximize return on investment. Through simulations and evaluations of different orbital scenarios, this research seeks to identify the best configuration to meet the objectives of a new Earth observation mission with enhanced capabilities to address the country’s needs.</p>
<p>To achieve this, a detailed analysis of orbital variables is presented, evaluating inclined orbits and sun-synchronous orbits (SSO) to determine which offers the best balance between coverage and operational efficiency. The results of this research provide a guide for orbit selection in future satellite missions, contributing to the ongoing development of Colombia’s space capabilities.</p>
</sec>
<sec>
<title>Materials and Methods: Mission and Requirements</title>
<p>
<xref ref-type="fig" rid="gf1">Figure 1</xref> presents the methodology developed to select the most suitable orbit by transforming mission requirements, payload constraints, and communication requirements into design variables, thereby establishing the orbital parameters for selection [<xref ref-type="bibr" rid="ref5">5</xref>].</p>
<p>
<fig id="gf1">
<label><bold>Figure 1</bold></label>
<caption>
<title>Methodology for Orbital Selection</title>
</caption>
<alt-text>Figure 1 Methodology for Orbital Selection</alt-text>
<graphic xlink:href="7062790006_gf2.png" position="anchor" orientation="portrait"/>
<attrib>Source: Authors.</attrib>
</fig>
</p>
<p>The choice of the operational orbit for an Earth observation satellite mission is determined by user requirements, as these guide the design and development of systems that must operate reliably under extreme conditions [<xref ref-type="bibr" rid="ref6">6</xref>]. <xref ref-type="table" rid="gt1">Table 1</xref> presents the main mission requirements, including the constraints provided by the payload and communications systems. [<xref ref-type="bibr" rid="ref5">5</xref>].</p>
<p>Among the mission requirements, some of the most relevant aspects include: the type of orbit and altitude, which determine the range of latitudes available for the satellite to cover; the area of interest; the number of accesses; and the revisit times, which determine what regions on Earth can be studied and how they can be accessed. Lastly, the orbital lifespan refers to how long the satellite can remain in orbit while operating nominally.</p>
<p>Within the payload constraints, the Off-Nadir angle is particularly noteworthy, as it defines the maximum inclination a satellite can achieve from the nadir side while maintaining effective imaging capabilities [<xref ref-type="bibr" rid="ref7">7</xref>]. The operational time refers to the optimal period during which a sensor can effectively capture data, considering environmental conditions and the orbital trajectory [<xref ref-type="bibr" rid="ref8">8</xref>].</p>
<p>Finally, among the communication constraints, the elevation angle stands out as a limitation caused by Colombia’s mountainous terrain. The minimum access time determines the efficiency of the link between satellites and ground stations, which affects the quality of communication services. [<xref ref-type="bibr" rid="ref9">9</xref>] [<xref ref-type="bibr" rid="ref10">10</xref>].</p>
<p>
<table-wrap id="gt1">
<label>Table 1</label>
<caption>
<title><bold> Mission Requirements and Constraints</bold></title>
</caption>
<alt-text>Table 1  Mission Requirements and Constraints</alt-text>
<graphic xlink:href="7062790006_gt12.png" position="anchor" orientation="portrait"/>
<attrib>Source:
Authors.</attrib>
</table-wrap>
</p>
<p>The criteria outlined in <xref ref-type="table" rid="gt1">Table 1</xref> are the primary focus for simulating scenarios, allowing the identification of the best orbital aspects that benefit the satellite mission. The aim is to find a way to address and satisfy these requirements [<xref ref-type="bibr" rid="ref11">11</xref>].</p>
<p>
<xref ref-type="table" rid="gt2">Table 2</xref> lists the design variables and orbital parameters determined from the mission requirements and constraints. These primarily correspond to the type of orbit, the altitude, the inclination, the eccentricity-perigee argument, the RAAN (Right Ascension of Ascending Node), the sensor, the Off-Nadir angle, the revisit time, and the elevation angle.</p>
<p>
<table-wrap id="gt2">
<label>Table 2</label>
<caption>
<title>Effects of Design
Variables and Orbital Parameters on Selection Criteria</title>
</caption>
<alt-text>Table 2  Effects of Design
Variables and Orbital Parameters on Selection Criteria</alt-text>
<graphic xlink:href="7062790006_gt10.png" position="anchor" orientation="portrait"/>
<attrib>Source:
Authors.</attrib>
</table-wrap>
</p>
<p>The variables and parameters have been selected based on their impact on factors of interest for the mission [<xref ref-type="bibr" rid="ref10">10</xref>], including coverage, orbital lifespan, image resolution, eclipse times, and communication times, among others. The selection criteria arising from the analysis of these factors provide the necessary parameters for simulating various orbital scenarios. Consequently, there will be a specific number of possibilities for the scenarios, and the results will subsequently be analyzed and compared against the selection criteria to identify an orbit with the most favorable aspects for the satellite mission [<xref ref-type="bibr" rid="ref12">12</xref>].</p>
</sec>
<sec sec-type="results">
<title><bold>Results</bold></title>
<sec>
<title>
<italic><bold>Design and Simulation (Scenarios)</bold></italic>
</title>
<p>Based on the selection criteria, three main variables are identified for running the simulations and defining the criteria.</p>
<p>
<list list-type="order">
<list-item>
<p> Coverage
of the Region: to analyze the coverage of the area of interest.</p>
</list-item>
<list-item>
<p> Access
Times to Ground Stations: to analyze the link times between ground stations and
the satellite</p>
</list-item>
<list-item>
<p> Orbital
Decay: to analyze the satellite’s orbital lifespan [<xref ref-type="bibr" rid="ref13">13</xref>]</p>
</list-item>
</list>
</p>
<p>The next simulations are focused on each criterion described. To complement each scenario, some simulation parameters must be defined. <xref ref-type="table" rid="gt3">Table 3</xref> summarizes these elements:</p>
<p>
<table-wrap id="gt3">
<label>Table 3</label>
<caption>
<title>General Aspects of the Simulation
Scenarios</title>
</caption>
<alt-text>Table 3 General Aspects of the Simulation
Scenarios</alt-text>
<graphic xlink:href="7062790006_gt11.jpg" position="anchor" orientation="portrait"/>
<attrib>Source:
Authors.</attrib>
</table-wrap>
</p>
<p>In the following paragraphs, the results obtained from each simulation will be briefly presented:</p>
<sec>
<title><bold><italic>Coverage</italic></bold></title>
<p>This simulation utilizes a defined “rectangular” region to include territories that are not part of the continental section of Colombia, such as the islands, allowing for a comprehensive analysis of its territory.</p>
<p><bold>Orbital Plane 10°</bold></p>
<p><bold>Nadir: </bold>In general, <xref ref-type="fig" rid="gf2">Figure 2</xref> shows the coverage of a LEO satellite with an inclination of 10° over one year of simulation. The figure illustrates the number of passes over Colombian territory in the Nadir operation.</p>
<p>
<fig id="gf2">
<label><bold>Figure 2</bold></label>
<caption>
<title><bold>Number of Passes
for 10° Orbit in Nadir</bold></title>
</caption>
<alt-text>Figure 2 Number of Passes
for 10° Orbit in Nadir</alt-text>
<graphic xlink:href="7062790006_gf3.png" position="anchor" orientation="portrait"/>
<attrib>Source:
Authors.</attrib>
</fig>
</p>
<p>The defined region would receive about 12 passes annually, corresponding to an average frequency of one pass per month. The figure depicts a purple area that represents a region of zero coverage, encompassing Barranquilla, La Jagua, and San Andrés. This limitation would prevent meeting the requirement for complete coverage over Colombia. The area with the highest revisit rate would be at the border of the zero-coverage region, as it represents the perigee/apogee of the orbit.</p>
<p><bold>Oblique:</bold>
<xref ref-type="fig" rid="gf3">Figure 3</xref> illustrates the coverage simulation, showing the number of passes during the Offset operation</p>
<p>
<fig id="gf3">
<label><bold>Figure 3</bold></label>
<caption>
<title><bold>Number of Passes for 10° Orbit in Oblique
(Offset)</bold></title>
</caption>
<alt-text>Figure 3 Number of Passes for 10° Orbit in Oblique
(Offset)</alt-text>
<graphic xlink:href="7062790006_gf4.png" position="anchor" orientation="portrait"/>
<attrib>Source:
Authors.</attrib>
</fig>
</p>
<p>By <xref ref-type="fig" rid="gf3">Figure 3</xref>, an expansion in the coverage area is observed. However, Barranquilla, La Jagua, and San Andrés remain part of the zero-coverage region. Similarly, the number of passes over the Colombian territory increases, with an average of 135 passes per year (11.25 passes per month).</p>
<p><bold>Orbital plane 16°</bold></p>
<p><bold>Nadir</bold>. <xref ref-type="fig" rid="gf4">Figure 4</xref> illustrates the coverage simulation, showing the number of passes during Nadir operation.</p>
<p>
<fig id="gf4">
<label><bold>Figure 4</bold></label>
<caption>
<title><bold>Number of Passes for 16° Orbit in Nadir</bold></title>
</caption>
<alt-text>Figure 4 Number of Passes for 16° Orbit in Nadir</alt-text>
<graphic xlink:href="7062790006_gf5.png" position="anchor" orientation="portrait"/>
<attrib>Source:
Authors.</attrib>
</fig>
</p>
<p>The defined region would have an average of 10 total passes (2 passes per month). There is a region of zero coverage within the defined area, but it is not part of Colombia. The area with the highest number of passes is outside Colombia. Additionally, it is observed that with this inclination and sensor operation, a complete coverage of the Colombian territory is achieved, ranging from 2 to 14 passes.</p>
<p><bold>Oblique</bold>. <xref ref-type="fig" rid="gf5">Figure 5</xref> illustrates the coverage simulation, showing the number of passes during the Offset operation.</p>
<p>
<fig id="gf5">
<label><bold>Figure 5</bold></label>
<caption>
<title><bold>Number of Passes for 16° Orbit in Oblique (Offset)</bold></title>
</caption>
<alt-text>Figure 5 Number of Passes for 16° Orbit in Oblique (Offset)</alt-text>
<graphic xlink:href="7062790006_gf6.png" position="anchor" orientation="portrait"/>
<attrib>Source:
Authors.</attrib>
</fig>
</p>
<p>In oblique orientation, as illustrated in <xref ref-type="fig" rid="gf5">Figure 5</xref>, a greater degree of uniformity is observed in the annual number of passes over the territory, with values ranging from 77 to 117 passes per year. This includes regions such as Barranquilla, La Jagua, and San Andrés. The results indicate that a portion of the territory is expected to have at least 6.42 passes per month, which is similar to the overall average of 11 passes per month. In this case, the region with the highest number of passes does not belong to Colombia.</p>
<p><bold>Orbital Plane 97°</bold></p>
<p><bold>Nadir</bold>: <xref ref-type="fig" rid="gf6">Figure 6</xref> presents the coverage simulation results, detailing the number of passes achieved during Nadir operations.</p>
<p>
<fig id="gf6">
<label><bold>Figure 6 </bold></label>
<caption>
<title><bold>Number of Passes for 97° Orbit in Nadir</bold></title>
</caption>
<alt-text>Figure 6  Number of Passes for 97° Orbit in Nadir</alt-text>
<graphic xlink:href="7062790006_gf7.png" position="anchor" orientation="portrait"/>
<attrib>Source:
Authors.</attrib>
</fig>
</p>
<p>The defined region would have an average of 2 total passes. Observing <xref ref-type="fig" rid="gf6">Figure 6</xref>, a high degree of uniformity is noted, with at least 1 annual pass at each point within the defined region, implying a complete coverage of the area. Certain small regions receive only three passes annually, resulting in an average interval of 121 days between passes.</p>
<p><bold>Oblique:</bold>
<xref ref-type="fig" rid="gf7">Figure 7</xref> illustrates the coverage simulation, the number of passes during the Offset operation.</p>
<p>
<fig id="gf7">
<label><bold>Figure 7</bold></label>
<caption>
<title><bold>Number of Passes for 97° Orbit in Oblique (Offset)</bold></title>
</caption>
<alt-text>Figure 7 Number of Passes for 97° Orbit in Oblique (Offset)</alt-text>
<graphic xlink:href="7062790006_gf8.png" position="anchor" orientation="portrait"/>
<attrib>Source:
Authors.</attrib>
</fig>
</p>
<p>As shown in <xref ref-type="fig" rid="gf7">Figure 7</xref>, the coverage area expands into a vertical-diagonal band, receiving 18–23 annual passes. The region averages 20 passes per year, or 1.67 per month.</p>
</sec>
<sec>
<title><bold><italic>Communication Access</italic></bold></title>
<p>This simulation uses a 50 km grid, with each node representing a ground station in Colombia. For COLAF, key target points include Cali, Bogotá, Barranquilla, La Jagua, and San Andrés, as they are major cities or strategic sites for building a ground segment facility.</p>
<p><bold>Orbital Plane 16°</bold></p>
<p><bold>Average Access Time (s): </bold>
<xref ref-type="fig" rid="gf8">Figure 8</xref> illustrates the average access times for a 16° inclined orbit.</p>
<p>
<fig id="gf8">
<label><bold>Figure 8</bold></label>
<caption>
<title><bold>Average Access Time for 16° Orbit</bold></title>
</caption>
<alt-text>Figure 8 Average Access Time for 16° Orbit</alt-text>
<graphic xlink:href="7062790006_gf9.png" position="anchor" orientation="portrait"/>
<attrib>Source:
Authors.</attrib>
</fig>
</p>
<p>The average access times in this orbit range from 5.6 to 7.18 minutes, as illustrated in <xref ref-type="fig" rid="gf8">Figure 8</xref>. The area with the highest access times is in the north, including BAQ, GUJ, and SPP, while the area with the lowest access times is in the south. The average communication time for the region is approximately 6.58 minutes, while the ground stations in Cali and Bogotá have an average access time of 6.38 minutes.</p>
<p><bold>Maximum Revisit Times (s): </bold>
<xref ref-type="fig" rid="gf9">Figure 9</xref> illustrates the total revisit times for a 16° inclined orbit.</p>
<p>
<fig id="gf9">
<label><bold>Figure 9</bold></label>
<caption>
<title><bold>Total Revisit Times for
16° Orbit</bold></title>
</caption>
<alt-text>Figure 9 Total Revisit Times for
16° Orbit</alt-text>
<graphic xlink:href="7062790006_gf10.png" position="anchor" orientation="portrait"/>
<attrib>Source:
Authors.</attrib>
</fig>
</p>
<p>The longest revisit times are found in the northern area of the defined region, with a minimum of 13 hours. The southern zone achieves the shortest revisit times, with a maximum of 6.69 hours, making it the most favorable area for this orbit. The stations in Cali and Bogotá have a revisit time of 8.36 hours, while Barranquilla and La Jagua have a revisit time of 11.69 hours. On average, the territory has a revisit time of 9.2 hours.</p>
<p><bold>Orbital Plane 97°</bold></p>
<p><bold>Average Access Time (s): </bold>
<xref ref-type="fig" rid="gf10">Figure 10</xref> illustrates the average access times for a 97° orbit.</p>
<p>
<fig id="gf10">
<label><bold>Figure
10 </bold></label>
<caption>
<title><bold>Average Access Time for
97° Orbit</bold></title>
</caption>
<alt-text>Figure
10  Average Access Time for
97° Orbit</alt-text>
<graphic xlink:href="7062790006_gf11.png" position="anchor" orientation="portrait"/>
<attrib>Source:
Authors.</attrib>
</fig>
</p>
<p>In this orbit, the average access times are between 5.97 and 6.07 minutes, resulting in a reduced and nearly uniform spectrum across the entire defined region. The Colombian territory has an average access time of approximately 6 minutes, with the ground stations in Cali and Bogotá falling within this average range. The western zone comprises areas with maximum coverage, in which San Andrés is located.</p>
<p><bold>Maximum Revisit Times (s):</bold>
<xref ref-type="fig" rid="gf11">Figure 11</xref> illustrates the total revisit times for a 97° inclined orbit.</p>
<p>
<fig id="gf11">
<label><bold>Figure
11</bold></label>
<caption>
<title><bold>Total Revisit Times for 97° Orbit</bold></title>
</caption>
<alt-text>Figure
11 Total Revisit Times for 97° Orbit</alt-text>
<graphic xlink:href="7062790006_gf12.png" position="anchor" orientation="portrait"/>
<attrib>Source:
Authors.</attrib>
</fig>
</p>
<p>
<xref ref-type="fig" rid="gf11">Figure 11</xref> shows the maximum revisit times obtained for this 97° orbit. Where uniformity in revisit times is achieved across the entire Colombian territory, with a duration of 11.83 hours.</p>
</sec>
<sec>
<title><bold><italic>Orbital Decay</italic></bold></title>
<p>In this scenario, dimensions sourced from multiple suppliers are used, and the satellites are modeled as rectangular prisms for simulation purposes. Additionally, standard values for the drag coefficient and reflectivity are used, being 2.2 and 1.3, respectively [<xref ref-type="bibr" rid="ref14">14</xref>] [<xref ref-type="bibr" rid="ref15">15</xref>] [<xref ref-type="bibr" rid="ref16">16</xref>]<italic>. </italic>
<xref ref-type="table" rid="gt4">Table 4</xref> summarizes the results obtained from two simulation software packages: DRAMA and STK.</p>
<p>
<table-wrap id="gt4">
<label>Table 4</label>
<caption>
<title><bold>Orbital Decay Results in
Years</bold></title>
</caption>
<alt-text>Table 4 Orbital Decay Results in
Years</alt-text>
<graphic xlink:href="7062790006_gt8.png" position="anchor" orientation="portrait"/>
<attrib>Source:
Authors.</attrib>
</table-wrap>
</p>
</sec>
</sec>
<p>In
general, it is observed that SSO orbits provide greater longevity compared to
orbits near the equator.</p>
</sec>
<sec>
<title><bold>Results
Analysis</bold></title>
<sec>
<title>
<italic>Simulation Results</italic>
</title>
<sec>
<title>
<italic>Coverage Analysis:</italic>
</title>
<p>
<list list-type="bullet">
<list-item>
<p><bold><italic> Relationship between proximity to the
equator and number of passes:</italic></bold> Orbits closer to the equator exhibit a
greater number of passes over the territory, as observed for orbits with a 10°
inclination. However, due to the geometry of their trajectory, these orbits do
not cover the northernmost regions of the country. This makes them inadequate
for achieving complete coverage of the Colombian territory and, therefore,
unsuitable for the mission.</p>
</list-item>
<list-item>
<p><bold><italic>Efficiency of the 16° orbit:</italic></bold>
The 16° orbit is projected to be the most effective, with part of the area
estimated to receive at least 6.42 passes per month, thereby increasing the
frequency of territorial imaging.  </p>
</list-item>
<list-item>
<p><bold><italic> Coverage distribution in the
northern region of the country:</italic></bold> There is a general trend toward
greater coverage in northern Colombia for a 16° orbit, with the La Guajira
region recording the highest number of passes in the entire country.</p>
</list-item>
</list>
</p>
<sec>
<title><bold><italic>Communication
Access Analysis:</italic></bold></title>
<p>
<list list-type="bullet">
<list-item>
<p><bold><italic>Impact of Latitude and Orbital
Inclination on Ground Stations:</italic></bold> As the latitude of the ground station
increases, fewer passes per day and longer revisit times are observed.
Similarly, an increase in orbital inclination results in a reduction in daily
passes and an increase in revisit times.</p>
</list-item>
<list-item>
<p><bold><italic>Comparison of Orbits in
Different Cities:</italic></bold> The orbit with an inclination of 16° is the
second-best option for Cali and Bogotá, and the best option for La Jagua and
San Andrés. In Barranquilla, the 10° and 16° orbits yield similar results.</p>
</list-item>
<list-item>
<p><bold><italic>Overall
Performance of the 16° Orbit:</italic></bold> The 16° orbit provides the most frequent
daily passes, shorter access times, and reduced revisit intervals compared to
other orbits. These parameters support consistent communication between
satellites and ground stations in Colombia.</p>
</list-item>
<list-item>
<p><bold><italic>Performance of the 97° Orbits:</italic></bold>
The 97° orbit presents the shortest communication times, the lowest number of
passes per day, and the highest revisit times across all ground stations in
Colombia.</p>
</list-item>
</list>
</p>
</sec>
<sec>
<title><bold><italic>Orbital Decay:</italic></bold></title>
<p>
<list list-type="bullet">
<list-item>
<p>
<italic>Debris Mitigation Requirements
According to ECSS-U-AS-10C Standard</italic> [<xref ref-type="bibr" rid="ref17">17</xref>]: The
ECSS-U-AS-10C standard—Adoption Notice of ISO 24113: Space Systems—addresses
the requirements for debris mitigation and establishes that satellites in low
orbit should not operate for more than 25 years. They must also remain inactive
for a maximum of 5 years to minimize collision risks. The FACSAT-3 mission
meets the specifications outlined in international standards.</p>
</list-item>
<list-item>
<p><bold><italic>Orbital
Eccentricity and Satellite Lifespan:</italic></bold> Satellites with lower orbital
eccentricity, meaning a more circular orbit, tend to have a longer operational
lifespan.</p>
</list-item>
<list-item>
<p><bold><italic>Comparison of Orbital Lifespan
in 16° and 97° Orbits:</italic></bold> Orbits with an inclination of 16° show a
shorter orbital lifespan for satellites compared to 97° orbits, with factors
such as gravitational field and atmospheric density variation directly
influencing these results.</p>
</list-item>
<list-item>
<p><bold><italic>Orbital Lifespan Range for the FACSAT-3
Satellite:</italic></bold> In general, the orbital lifespan of the satellite
for the FACSAT-3 mission would range from 8.87 to 14.66 years, representing the
worst and best cases, respectively.</p>
</list-item>
</list>
</p>
</sec>
</sec>
</sec>
<sec>
<title>
<italic><bold>Results - Selection
Criteria</bold></italic>
</title>
<p>The
main criteria selected for the orbit design are the payload constraints, which include
resolution, speeds (orbital and satellite) for image capture, offset angle,
coverage of the area of interest, and revisit time. </p>
<p>
<list list-type="bullet">
<list-item>
<p><bold>Coverage:</bold>
It is a key consideration that the designed satellite must cover the entire
Colombian territory, including its associated islands. This aspect is achieved
with orbits of inclination ≥ 16° and an oblique pointing of ± 7.5° for image
capture.</p>
</list-item>
<list-item>
<p><bold>Revisit
Time: </bold>For operational and communication interests, the shortest revisit
times are required. These values are found in orbits with planes close to the
equator. These orbits also provide the greatest number of accesses and possible
passes for the mission. Therefore, the 16° orbit would have two important, favorable aspects for mission
development.</p>
</list-item>
<list-item>
<p><bold>Resolution
and Speeds for Capture</bold>: The camera resolution depends on the operational
altitude range for execution, and each altitude corresponds to a specific
orbital speed. Lower orbital speeds are preferable, as they facilitate target
capture. Considering these factors, the optimal altitude range for satellite
operation is between 430 and 530 km.</p>
</list-item>
<list-item>
<p><bold> Orbital Lifespan:</bold> An orbital lifespan greater than 5 years is
required for operations. Additionally, the guidelines for space debris
mitigation indicate that a maximum lifespan of 25 years should be planned to
reduce the risk of collisions in the orbital environment [<xref ref-type="bibr" rid="ref18">18</xref>] [<xref ref-type="bibr" rid="ref19">19</xref>] (Compliance for LEO
satellites. ISO 27852: 2011). Polar orbits have the longest times in orbit, but
this is not as significant compared to quasi-equatorial orbits. Orbital
eccentricity influences the duration of an orbital lifespan; orbits that are
more circular (with eccentricity approaching zero) typically result in longer
lifespans and more consistent orbital velocities.</p>
</list-item>
<list-item>
<p><bold>Elevation
Angle:</bold> Based on the geographical features of Colombia, certain ground
stations require a minimum elevation angle of 10° to maintain communication
with the satellite. Additionally, the communication system specifies a minimum
access duration of 300 seconds for data transfer, which is supported by the
defined orbital characteristics.</p>
</list-item>
</list>
</p>
</sec>
</sec>
<sec>
<title><bold>Conclusions: Orbital Selection</bold></title>
<p>After analyzing the previously obtained results, an updated table detailing the orbital requirements for the FACSAT-3 mission is presented below (<xref ref-type="table" rid="gt5">Table 05</xref>):</p>
<p>
<list list-type="bullet">
<list-item>
<p>Based on the analysis of
the simulations conducted, an orbit with a 16° inclination offers the best
balance between territorial coverage, revisit time, and access to ground
stations for the FACSAT-3 mission. This configuration ensures complete coverage
of Colombian territory, including its islands, with an average of 11 monthly
passes in oblique mode, and a range between 2 and 14 passes in the Nadir mode.</p>
</list-item>
<list-item>
<p> The simulations also show
that this orbit meets the technical communication requirements (access times
between 5.6 and 7.2 minutes per station, elevation angle ≥ 10°, and a minimum
contact time of 300 seconds), as well as international regulations on space
debris mitigation (ECSS-U-AS-10C). Although SSO orbits at 97° offer longer
orbital lifespans, their less favorable revisit and access times make them less
suitable for the mission’s objectives.</p>
</list-item>
<list-item>
<p> In terms of payload
operation, an altitude between 430 and 530 km is confirmed to optimize image
quality and enable suitable orbital velocities for data acquisition. This
configuration supports an orbital lifespan between 8.9 and 12.2 years at this
inclination, remaining within the range established by international standards.</p>
</list-item>
</list>
</p>
<p>This
table summarizes all the simulations, results, and analyses conducted for the
orbital design. This orbit incorporates the requirements for the FACSAT-3
mission and the best aspects for its execution.</p>
<p>
<table-wrap id="gt5">
<label>Table 0 5</label>
<caption>
<title> Selected Aspects for the FACSAT-3 Mission Orbit.</title>
</caption>
<alt-text>Table 0 5  Selected Aspects for the FACSAT-3 Mission Orbit.</alt-text>
<graphic xlink:href="7062790006_gt7.png" position="anchor" orientation="portrait"/>
<attrib>Source:
Authors.</attrib>
</table-wrap>
</p>
<p>In
conclusion, based on the coverage criteria, link times, orbital lifespan, and
compliance with international standards, a 16° inclined orbit with both nadir
and oblique (±7.5°) operation represents the best option for Colombia’s optical
microsatellite Earth observation mission.</p>
</sec>
</body>
<back>
<ack>
<title>Acknowledgments</title>
<p>To the Colombian Aerospace Force and the Center for
Research and Development in Aerospace Technologies (CITAE).</p>
</ack>
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<fn-group>
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<label>*</label>
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</fn>
</fn-group>
</back>
</article>
