{"id":39,"date":"2024-09-23T04:34:48","date_gmt":"2024-09-23T03:34:48","guid":{"rendered":"https:\/\/blogs.imperial.ac.uk\/parikshit\/?p=39"},"modified":"2024-09-23T05:04:49","modified_gmt":"2024-09-23T04:04:49","slug":"solar-radiation-pressure-satellites","status":"publish","type":"post","link":"https:\/\/blogs.imperial.ac.uk\/parikshit\/2024\/09\/23\/solar-radiation-pressure-satellites\/","title":{"rendered":"How Solar Radiation Pressure Affects Satellites: Calculating Instantaneous Force and Acceleration"},"content":{"rendered":"<figure id=\"attachment_75\" aria-describedby=\"caption-attachment-75\" style=\"width: 1920px\" class=\"wp-caption aligncenter\"><img loading=\"lazy\" decoding=\"async\" width=\"1920\" height=\"1080\" class=\"wp-image-75 size-full\" src=\"http:\/\/blogs.imperial.ac.uk\/parikshit\/files\/2024\/09\/Untitled-design.png\" alt=\"\" \/><figcaption id=\"caption-attachment-75\" class=\"wp-caption-text\">CREDIT: ESA<\/figcaption><\/figure>\n<p>First of all, hello again! Apologies for the long break\u2014final year kept me busy, along with my part-time work, so I didn\u2019t have much time to post. But now that things have settled down, I\u2019m excited to start sharing the blogs I\u2019ve been planning. I\u2019ll be posting regularly, starting with today\u2019s topic.<br \/>\nIn this blog, we\u2019ll dive into Solar Radiation Pressure and explore how it affects satellites.<br \/>\nLet\u2019s begin!<br \/>\nIn space, even the smallest forces can have significant effects on satellites over time. One of the key forces acting on a satellite is solar radiation pressure.<\/p>\n<p><strong>What is Solar Radiation Pressure?<\/strong><br \/>\nSolar radiation pressure is the force exerted by photons from the Sun as they strike and reflect off the surface of a satellite. While seemingly insignificant, the pressure can considerably impact a satellite&#8217;s orbit, particularly its perigee height especially over long durations.<\/p>\n<p>This force depends on:<\/p>\n<ol>\n<li style=\"text-align: left\">The satellite&#8217;s <em>distance from the Sun<\/em>.<\/li>\n<li style=\"text-align: left\">The satellite\u2019s <em>cross-sectional area<\/em> facing the Sun.<\/li>\n<li style=\"text-align: left\">The <em>reflective properties<\/em> of the satellite\u2019s surface<\/li>\n<\/ol>\n<p>In the May 1960 paper, &#8220;The Influence of the Solar Radiation Pressure on the Motion of an Artificial Satellite,&#8221; researchers focused on the Vanguard I satellite, launched into Earth orbit on 17 March 1958. This satellite, intended for geodetic measurements, was designed with a diameter of 16.5 cm and a mass of 1.47 kg. Early orbit analyses of Vanguard I revealed unexpected discrepancies between the observed and predicted perigee heights.<\/p>\n<p>The researchers explored solar radiation pressure as a potential cause for these deviations. Their investigation, using analytical methods to model the effects of solar radiation pressure on satellite orbits, indicated that this pressure significantly contributed to the observed perturbations in Vanguard I&#8217;s perigee height. This finding highlighted that even though solar radiation pressure is a relatively small force, it could cause substantial orbital deviations, particularly for satellites with a high area-to-mass ratio like Vanguard I.<\/p>\n<p>So, how do we calculate solar radiation pressure and its effect on a satellite\u2019s motion? Below, we\u2019ll walk through the key steps and formulas that help determine the instantaneous force and acceleration on a satellite caused by this pressure.<\/p>\n<p>Let\u2019s break it down:<\/p>\n<p><strong>Step 1: Calculating Solar Radiation Pressure<\/strong><\/p>\n<p>Solar radiation pressure at Earth&#8217;s distance from the Sun is given by the following formula:<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" width=\"171\" height=\"90\" class=\"aligncenter wp-image-56 \" src=\"http:\/\/blogs.imperial.ac.uk\/parikshit\/files\/2024\/09\/Screenshot-2024-09-23-032531.png\" alt=\"Solar radiation pressure at Earth's distance from the Sun\" \/>Where<\/p>\n<p><em>P<\/em> is the solar radiation pressure.<\/p>\n<p><em>L<\/em> is the Sun\u2019s luminosity (3.828 \u00d710^26 W) .<\/p>\n<p><em>r<\/em> is the distance from the Sun (Earth&#8217;s distance is 1.496 \u00d7 10^11 m<em>\u00a0<\/em>)<\/p>\n<p><em>c<\/em> is the speed of light (3\u00d710^8 m\/s)<\/p>\n<p>&nbsp;<\/p>\n<p>Substituting Earth\u2019s distance into this equation gives us a solar radiation pressure at Earth:<br \/>\nP \u22484.56 \u00d7 10^(-6) N\/m^2<\/p>\n<p>This value will be used to calculate the force acting on a satellite.<\/p>\n<p>&nbsp;<\/p>\n<p><strong>Step 2: Calculating the Force on the Satellite<\/strong><\/p>\n<p>Once we know the solar radiation pressure, we can calculate the force on the satellite. The force depends on the satellite\u2019s cross-sectional area (<em>A<\/em>) and its reflectivity(<em>\u03c1<\/em>). The formula for the force is:<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" width=\"164\" height=\"44\" class=\"aligncenter wp-image-60 \" src=\"http:\/\/blogs.imperial.ac.uk\/parikshit\/files\/2024\/09\/Screenshot-2024-09-23-033522.png\" alt=\"Calculating the Force on the Satellite\" \/>Where:<\/p>\n<p><em>F<\/em> is the force exerted on the satellite.<\/p>\n<p><em>A<\/em> is the satellite&#8217;s cross-sectional area in square meters.<\/p>\n<p><em>\u03c1<\/em> is the reflectivity coefficient (ranging from 0 for a perfectly absorbing surface to 1 for a perfectly reflective surface).<\/p>\n<p>&nbsp;<\/p>\n<p><strong>Example Calculation:<\/strong><\/p>\n<p>Let\u2019s say a satellite has a <em>cross-sectional<\/em> area of 10 m\u00b2 and reflects 30% of the radiation<\/p>\n<p>(i.e <em>\u03c1=0.3<\/em> ). The force acting on this satellite would be:<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" width=\"300\" height=\"115\" class=\"size-medium wp-image-65 aligncenter\" src=\"http:\/\/blogs.imperial.ac.uk\/parikshit\/files\/2024\/09\/Screenshot-2024-09-23-034207-300x115.png\" alt=\"Example 1\" \/>So, the instantaneous force acting on the satellite due to solar radiation pressure is<em>\u00a0F=5.928 \u00d710^(-4) N<\/em><\/p>\n<p>&nbsp;<\/p>\n<p><strong>Step 3: Calculating the Acceleration on the Satellite<\/strong><\/p>\n<p>Next, we calculate the <strong>acceleration<\/strong> on the satellite due to the solar radiation pressure. Acceleration is simply the force divided by the satellite\u2019s mass ( ):<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" width=\"99\" height=\"74\" class=\"size-full wp-image-68 aligncenter\" src=\"http:\/\/blogs.imperial.ac.uk\/parikshit\/files\/2024\/09\/Screenshot-2024-09-23-034641.png\" alt=\"Calculating the Acceleration on the Satellite\" \/>Where:<\/p>\n<p><em>a<\/em> is the acceleration<\/p>\n<p><em>F<\/em> is the force due to solar radiation pressure.<\/p>\n<p><em>m<\/em> is the mass of the satellite in kilograms.<\/p>\n<p><strong>Example Calculation:<\/strong><\/p>\n<p>For a satellite with a mass of 500 kg, the acceleration would be:<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" width=\"246\" height=\"140\" class=\"size-full wp-image-69 aligncenter\" src=\"http:\/\/blogs.imperial.ac.uk\/parikshit\/files\/2024\/09\/Screenshot-2024-09-23-034749.png\" alt=\"Example 2\" \/>Although the force and acceleration caused by solar radiation pressure are small, they are persistent. Over time, they can lead to measurable changes in the satellite\u2019s trajectory, especially for satellites with large area-to-mass ratios. For lightweight satellites, like CubeSats, solar radiation pressure can become a dominant factor affecting their orbits.<\/p>\n<p>In terms of application this force can be utilised for example in solar sails the force from solar radiation pressure can be used\u00a0 for propulsion, enabling satellites to move without fuel.<\/p>\n<p><strong>Conclusion<\/strong><\/p>\n<p>Solar radiation pressure, while small, exerts a continuous force on satellites. By calculating the instantaneous force and acceleration due to this pressure, we can understand how sunlight can gradually change a satellite\u2019s orbit.<\/p>\n<p>In future blogs, we will explore how this force can affect a satellite\u2019s orbit over time, including resonant orbits and eccentricity changes<\/p>\n<p>&nbsp;<\/p>\n<p><strong>Disclaimer:<\/strong> I am not a mathematician or physicist; the information presented here is sourced from various online references, which I have linked below. If you have any suggestions or feedback, feel free to reach out to me at <a rel=\"noopener\">ppadole@imperial.ac.uk<\/a>\u00a0?<\/p>\n<p><strong>Source List\u00a0<\/strong><\/p>\n<p><a href=\"http:\/\/burro.astr.cwru.edu\/Academics\/Astr221\/SolarSys\/Comets\/tails.html\">Comet Tails and Solar Radiation Pressure<\/a><\/p>\n<p><a href=\"https:\/\/www.grc.nasa.gov\/www\/k-12\/Numbers\/Math\/Mathematical_Thinking\/sunlight_exerts_pressure.htm\">NASA\u2019s Explanation of Sunlight Exerting Pressure<\/a><\/p>\n<p><a href=\"https:\/\/www.britannica.com\/science\/luminosity\">Luminosity from Britannica<\/a><\/p>\n<p><a href=\"https:\/\/www.desy.de\/user\/projects\/Physics\/ParticleAndNuclear\/photon_mass.html\">Photon Mass and Physics<\/a><\/p>\n<p><a href=\"https:\/\/www.science.org\/doi\/epdf\/10.1126\/science.131.3404.920\">Scientific Article on Solar Radiation Pressure<\/a><\/p>\n<p><a href=\"https:\/\/ntrs.nasa.gov\/citations\/20150019717\">NASA Technical Report on Solar Radiation<\/a><\/p>\n<p><a href=\"https:\/\/www.sciencedirect.com\/topics\/engineering\/solar-radiation-pressure\">Solar Radiation Pressure in Engineering<\/a><\/p>\n<p><a href=\"https:\/\/nssdc.gsfc.nasa.gov\/nmc\/spacecraft\/display.action?id=1958-002B\">NSSDC Spacecraft Data on Vanguard I<\/a><\/p>\n<p><a href=\"https:\/\/www.esa.int\/ESA_Multimedia\/Images\/2008\/03\/Solar_radiation_pressure\">SRP Image ESA<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"<p>First of all, hello again! Apologies for the long break\u2014final year kept me busy, along with my part-time work, so I didn\u2019t have much time to post. But now that things have settled down, I\u2019m excited to start sharing the blogs I\u2019ve been planning. I\u2019ll be posting regularly, starting with today\u2019s topic. In this blog, [&hellip;]<\/p>\n","protected":false},"author":1743,"featured_media":0,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[3],"tags":[],"class_list":["post-39","post","type-post","status-publish","format-standard","hentry","category-maths-and-physics"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v27.2 - https:\/\/yoast.com\/product\/yoast-seo-wordpress\/ -->\n<title>How Solar Radiation Pressure Affects Satellites: Calculating Instantaneous Force and Acceleration Parikshit Padole<\/title>\n<meta name=\"description\" content=\"Discover how solar radiation pressure influences satellite motion and orbit deviations over time. Learn how sunlight impacts space technology.\" \/>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/blogs.imperial.ac.uk\/parikshit\/2024\/09\/23\/solar-radiation-pressure-satellites\/\" \/>\n<meta property=\"og:locale\" content=\"en_GB\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"How Solar Radiation Pressure Affects Satellites: Calculating Instantaneous Force and Acceleration Parikshit Padole\" \/>\n<meta property=\"og:description\" content=\"Discover how solar radiation pressure influences satellite motion and orbit deviations over time. Learn how sunlight impacts space technology.\" \/>\n<meta property=\"og:url\" content=\"https:\/\/blogs.imperial.ac.uk\/parikshit\/2024\/09\/23\/solar-radiation-pressure-satellites\/\" \/>\n<meta property=\"og:site_name\" content=\"Parikshit Padole\" \/>\n<meta property=\"article:published_time\" content=\"2024-09-23T03:34:48+00:00\" \/>\n<meta property=\"article:modified_time\" content=\"2024-09-23T04:04:49+00:00\" \/>\n<meta property=\"og:image\" content=\"http:\/\/blogs.imperial.ac.uk\/parikshit\/files\/2024\/09\/Untitled-design.png\" \/>\n<meta name=\"author\" content=\"Parikshit Padole\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:label1\" content=\"Written by\" \/>\n\t<meta name=\"twitter:data1\" content=\"Parikshit Padole\" \/>\n\t<meta name=\"twitter:label2\" content=\"Estimated reading time\" \/>\n\t<meta name=\"twitter:data2\" content=\"6 minutes\" \/>\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\"@context\":\"https:\/\/schema.org\",\"@graph\":[{\"@type\":\"Article\",\"@id\":\"https:\/\/blogs.imperial.ac.uk\/parikshit\/2024\/09\/23\/solar-radiation-pressure-satellites\/#article\",\"isPartOf\":{\"@id\":\"https:\/\/blogs.imperial.ac.uk\/parikshit\/2024\/09\/23\/solar-radiation-pressure-satellites\/\"},\"author\":{\"name\":\"Parikshit Padole\",\"@id\":\"https:\/\/blogs.imperial.ac.uk\/parikshit\/#\/schema\/person\/3446e4644294882b7a20ed3ffcdf67fe\"},\"headline\":\"How Solar Radiation Pressure Affects Satellites: Calculating Instantaneous Force and Acceleration\",\"datePublished\":\"2024-09-23T03:34:48+00:00\",\"dateModified\":\"2024-09-23T04:04:49+00:00\",\"mainEntityOfPage\":{\"@id\":\"https:\/\/blogs.imperial.ac.uk\/parikshit\/2024\/09\/23\/solar-radiation-pressure-satellites\/\"},\"wordCount\":899,\"image\":{\"@id\":\"https:\/\/blogs.imperial.ac.uk\/parikshit\/2024\/09\/23\/solar-radiation-pressure-satellites\/#primaryimage\"},\"thumbnailUrl\":\"http:\/\/blogs.imperial.ac.uk\/parikshit\/files\/2024\/09\/Untitled-design.png\",\"articleSection\":[\"Maths and Physics\"],\"inLanguage\":\"en-GB\"},{\"@type\":\"WebPage\",\"@id\":\"https:\/\/blogs.imperial.ac.uk\/parikshit\/2024\/09\/23\/solar-radiation-pressure-satellites\/\",\"url\":\"https:\/\/blogs.imperial.ac.uk\/parikshit\/2024\/09\/23\/solar-radiation-pressure-satellites\/\",\"name\":\"How Solar Radiation Pressure Affects Satellites: Calculating Instantaneous Force and Acceleration Parikshit Padole\",\"isPartOf\":{\"@id\":\"https:\/\/blogs.imperial.ac.uk\/parikshit\/#website\"},\"primaryImageOfPage\":{\"@id\":\"https:\/\/blogs.imperial.ac.uk\/parikshit\/2024\/09\/23\/solar-radiation-pressure-satellites\/#primaryimage\"},\"image\":{\"@id\":\"https:\/\/blogs.imperial.ac.uk\/parikshit\/2024\/09\/23\/solar-radiation-pressure-satellites\/#primaryimage\"},\"thumbnailUrl\":\"http:\/\/blogs.imperial.ac.uk\/parikshit\/files\/2024\/09\/Untitled-design.png\",\"datePublished\":\"2024-09-23T03:34:48+00:00\",\"dateModified\":\"2024-09-23T04:04:49+00:00\",\"author\":{\"@id\":\"https:\/\/blogs.imperial.ac.uk\/parikshit\/#\/schema\/person\/3446e4644294882b7a20ed3ffcdf67fe\"},\"description\":\"Discover how solar radiation pressure influences satellite motion and orbit deviations over time. 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