{"id":206836,"date":"2025-04-14T20:22:57","date_gmt":"2025-04-14T20:22:57","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=206836"},"modified":"2025-04-14T20:31:10","modified_gmt":"2025-04-14T20:31:10","slug":"communications-satellites-are-placed-in-a-circular-orbit-where-they-stay-directly-over-a-fixed-point-on-the-equator-as-the-earth-rotates-these-are-called-geosynchronous-orbits","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/04\/14\/communications-satellites-are-placed-in-a-circular-orbit-where-they-stay-directly-over-a-fixed-point-on-the-equator-as-the-earth-rotates-these-are-called-geosynchronous-orbits\/","title":{"rendered":"Communications satellites are placed in a circular orbit where they stay directly over a fixed point on the equator as the earth rotates. These are called geosynchronous orbits. The altitude of a geosynchronous orbit is 3.58\u00d7107m(\u02dc22,000miles)."},"content":{"rendered":"\n<p>Communications satellites are placed in a circular orbit where they stay directly over a fixed point on the equator as the earth rotates. These are called geosynchronous orbits. The altitude of a geosynchronous orbit is 3.58\u00d7107m(\u02dc22,000miles).<\/p>\n\n\n\n<p>Part A<\/p>\n\n\n\n<p>What is the period of a satellite in a geosynchronous orbit?<\/p>\n\n\n\n<p>Express your answer to three significant figures and include the appropriate units.<\/p>\n\n\n\n<p>Part B<\/p>\n\n\n\n<p>Find the value of g at this altitude.<\/p>\n\n\n\n<p>Express your answer to three significant figures and include the appropriate units.<\/p>\n\n\n\n<p>Part C<\/p>\n\n\n\n<p>What is the weight of a 2000 kg satellite in a geosynchronous orbit?<\/p>\n\n\n\n<p>Express your answer as an integer and include the appropriate units.<\/p>\n\n\n\n<p><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-ast-global-color-6-color\"><strong>The correct answer and explanation is :<\/strong><\/mark><\/p>\n\n\n\n<h3 class=\"wp-block-heading\"><strong>Part A: Period of a Geosynchronous Satellite<\/strong><\/h3>\n\n\n\n<p>To find the period ( T ) of a satellite in a <strong>geosynchronous orbit<\/strong>, we recognize that such a satellite must orbit the Earth <strong>once every 24 hours<\/strong>, to remain over the same spot on the equator.<\/p>\n\n\n\n<p>But we convert this to seconds:<\/p>\n\n\n\n<p>[<br>T = 24 \\, \\text{hours} \\times 3600 \\, \\text{seconds\/hour} = \\boxed{8.64 \\times 10^4 \\, \\text{s}}<br>]<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\"><strong>Part B: Gravitational Acceleration ( g ) at the Altitude<\/strong><\/h3>\n\n\n\n<p>We use the formula for gravitational acceleration at a distance ( r ) from the center of the Earth:<\/p>\n\n\n\n<p>[<br>g = \\frac{GM}{r^2}<br>]<\/p>\n\n\n\n<p>Where:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>( G = 6.674 \\times 10^{-11} \\, \\text{m}^3\/\\text{kg} \\cdot \\text{s}^2 )<\/li>\n\n\n\n<li>( M = 5.972 \\times 10^{24} \\, \\text{kg} )<\/li>\n\n\n\n<li>( r = R_{\\text{Earth}} + h = 6.371 \\times 10^6 \\, \\text{m} + 3.58 \\times 10^7 \\, \\text{m} = 4.217 \\times 10^7 \\, \\text{m} )<\/li>\n<\/ul>\n\n\n\n<p>Now plug in:<\/p>\n\n\n\n<p>[<br>g = \\frac{6.674 \\times 10^{-11} \\cdot 5.972 \\times 10^{24}}{(4.217 \\times 10^7)^2}<br>= \\boxed{0.224 \\, \\text{m\/s}^2}<br>]<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\"><strong>Part C: Weight of a 2000 kg Satellite<\/strong><\/h3>\n\n\n\n<p>Weight ( W ) is given by:<\/p>\n\n\n\n<p>[<br>W = mg = 2000 \\, \\text{kg} \\cdot 0.224 \\, \\text{m\/s}^2 = \\boxed{448 \\, \\text{N}}<br>]<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\"><strong>Explanation (300 words)<\/strong><\/h3>\n\n\n\n<p>Geosynchronous satellites are essential for consistent communication because they appear stationary from the Earth&#8217;s surface. To achieve this, they must orbit at the same rotational rate as Earth\u2014once every 24 hours. This gives the satellite a <strong>period<\/strong> ( T ) of 86,400 seconds.<\/p>\n\n\n\n<p>The altitude for such an orbit is about 35,800 km above Earth\u2019s surface. However, to calculate gravitational effects like ( g ), we need the <strong>distance from the Earth\u2019s center<\/strong>, which is the sum of Earth\u2019s radius and the satellite\u2019s altitude. The gravitational force decreases with distance from Earth\u2019s center, so ( g ) is smaller at this height compared to Earth\u2019s surface. Using Newton&#8217;s Law of Universal Gravitation, we calculate ( g ) at that distance to be approximately 0.224 m\/s\u00b2\u2014far less than the 9.81 m\/s\u00b2 we experience on the surface.<\/p>\n\n\n\n<p>Weight is the gravitational force acting on an object. So, for a satellite with a mass of 2000 kg, its weight in orbit is the product of mass and the weaker gravitational field: ( 2000 \\times 0.224 = 448 \\, \\text{N} ). While this is much less than its Earth-surface weight (which would be 19,620 N), it still experiences some gravitational pull, which is why it remains in orbit rather than flying off into space.<\/p>\n\n\n\n<p>Even though the satellite is &#8220;weightless&#8221; in the sense that it is in free fall, it&#8217;s still under the influence of gravity. This is key to orbital motion\u2014it&#8217;s the continuous &#8220;fall&#8221; around the Earth that maintains its circular path.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img decoding=\"async\" src=\"https:\/\/learnexams.com\/blog\/wp-content\/uploads\/2025\/04\/image-82.png\" alt=\"\" class=\"wp-image-206837\"\/><\/figure>\n","protected":false},"excerpt":{"rendered":"<p>Communications satellites are placed in a circular orbit where they stay directly over a fixed point on the equator as the earth rotates. These are called geosynchronous orbits. The altitude of a geosynchronous orbit is 3.58\u00d7107m(\u02dc22,000miles). Part A What is the period of a satellite in a geosynchronous orbit? Express your answer to three significant [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"site-sidebar-layout":"default","site-content-layout":"","ast-site-content-layout":"default","site-content-style":"default","site-sidebar-style":"default","ast-global-header-display":"","ast-banner-title-visibility":"","ast-main-header-display":"","ast-hfb-above-header-display":"","ast-hfb-below-header-display":"","ast-hfb-mobile-header-display":"","site-post-title":"","ast-breadcrumbs-content":"","ast-featured-img":"","footer-sml-layout":"","ast-disable-related-posts":"","theme-transparent-header-meta":"","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":"","astra-migrate-meta-layouts":"default","ast-page-background-enabled":"default","ast-page-background-meta":{"desktop":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"ast-content-background-meta":{"desktop":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"footnotes":""},"categories":[25],"tags":[],"class_list":["post-206836","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/206836","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/comments?post=206836"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/206836\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=206836"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=206836"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=206836"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}