{"id":88705,"date":"2025-06-01T07:18:44","date_gmt":"2025-06-01T07:18:44","guid":{"rendered":"https:\/\/exam.pscnotes.com\/mcq\/?p=88705"},"modified":"2025-06-01T07:18:44","modified_gmt":"2025-06-01T07:18:44","slug":"two-planets-orbit-the-sun-in-circular-orbits-with-their-radius-of-orb","status":"publish","type":"post","link":"https:\/\/exam.pscnotes.com\/mcq\/two-planets-orbit-the-sun-in-circular-orbits-with-their-radius-of-orb\/","title":{"rendered":"Two planets orbit the Sun in circular orbits, with their radius of orb"},"content":{"rendered":"

Two planets orbit the Sun in circular orbits, with their radius of orbit as R\u2081 = R and R\u2082 = 4R. Ratio of their periods (T\u2081\/T\u2082) around the Sun will be<\/p>\n

[amp_mcq option1=”1\/16″ option2=”1\/8″ option3=”1\/4″ option4=”1\/2″ correct=”option2″]<\/p>\n

\n
\n
This question was previously asked in<\/div>\n
UPSC NDA-2 – 2020<\/div>\n<\/div>\n
Download PDF<\/a>Attempt Online<\/a><\/div>\n<\/div>\n
\nThis problem can be solved using Kepler’s Third Law of planetary motion, which states that the square of the orbital period (T) of a planet is directly proportional to the cube of the semi-major axis (R) of its orbit: T\u00b2 \u221d R\u00b3. For circular orbits, the semi-major axis is simply the radius (R). Thus, (T\u2081\/T\u2082)\u00b2 = (R\u2081\/R\u2082)\u00b3. Given R\u2081 = R and R\u2082 = 4R, we have (T\u2081\/T\u2082)\u00b2 = (R \/ 4R)\u00b3 = (1\/4)\u00b3 = 1\/64. Taking the square root of both sides, T\u2081\/T\u2082 = \u221a(1\/64) = 1\/8.
\n<\/section>\n
\nKepler’s Third Law relates the orbital period and orbital radius of planets orbiting the same central body: T\u00b2 \u221d R\u00b3.
\n<\/section>\n
\nKepler’s Laws are empirical laws describing the motion of planets around the Sun. Newton’s Law of Universal Gravitation provides the theoretical basis for Kepler’s Laws. For circular orbits, the speed v is constant, and the period T = 2\u03c0R\/v. The gravitational force provides the centripetal force: GMm\/R\u00b2 = mv\u00b2\/R. Substituting v = 2\u03c0R\/T gives GMm\/R\u00b2 = m(2\u03c0R\/T)\u00b2\/R, which simplifies to T\u00b2 = (4\u03c0\u00b2\/GM) R\u00b3, confirming T\u00b2 \u221d R\u00b3.
\n<\/section>\n","protected":false},"excerpt":{"rendered":"

Two planets orbit the Sun in circular orbits, with their radius of orbit as R\u2081 = R and R\u2082 = 4R. Ratio of their periods (T\u2081\/T\u2082) around the Sun will be [amp_mcq option1=”1\/16″ option2=”1\/8″ option3=”1\/4″ option4=”1\/2″ correct=”option2″] This question was previously asked in UPSC NDA-2 – 2020 Download PDFAttempt Online This problem can be solved … <\/p>\n

Detailed SolutionTwo planets orbit the Sun in circular orbits, with their radius of orb<\/span><\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1094],"tags":[1288,1128,1435],"class_list":["post-88705","post","type-post","status-publish","format-standard","hentry","category-upsc-nda-2","tag-1288","tag-physics","tag-space","no-featured-image-padding"],"yoast_head":"\nTwo planets orbit the Sun in circular orbits, with their radius of orb<\/title>\n<meta name=\"description\" content=\"This problem can be solved using Kepler's Third Law of planetary motion, which states that the square of the orbital period (T) of a planet is directly proportional to the cube of the semi-major axis (R) of its orbit: T\u00b2 \u221d R\u00b3. For circular orbits, the semi-major axis is simply the radius (R). Thus, (T\u2081\/T\u2082)\u00b2 = (R\u2081\/R\u2082)\u00b3. Given R\u2081 = R and R\u2082 = 4R, we have (T\u2081\/T\u2082)\u00b2 = (R \/ 4R)\u00b3 = (1\/4)\u00b3 = 1\/64. Taking the square root of both sides, T\u2081\/T\u2082 = \u221a(1\/64) = 1\/8. Kepler's Third Law relates the orbital period and orbital radius of planets orbiting the same central body: T\u00b2 \u221d R\u00b3.\" \/>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/exam.pscnotes.com\/mcq\/two-planets-orbit-the-sun-in-circular-orbits-with-their-radius-of-orb\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Two planets orbit the Sun in circular orbits, with their radius of orb\" \/>\n<meta property=\"og:description\" content=\"This problem can be solved using Kepler's Third Law of planetary motion, which states that the square of the orbital period (T) of a planet is directly proportional to the cube of the semi-major axis (R) of its orbit: T\u00b2 \u221d R\u00b3. For circular orbits, the semi-major axis is simply the radius (R). Thus, (T\u2081\/T\u2082)\u00b2 = (R\u2081\/R\u2082)\u00b3. Given R\u2081 = R and R\u2082 = 4R, we have (T\u2081\/T\u2082)\u00b2 = (R \/ 4R)\u00b3 = (1\/4)\u00b3 = 1\/64. Taking the square root of both sides, T\u2081\/T\u2082 = \u221a(1\/64) = 1\/8. Kepler's Third Law relates the orbital period and orbital radius of planets orbiting the same central body: T\u00b2 \u221d R\u00b3.\" \/>\n<meta property=\"og:url\" content=\"https:\/\/exam.pscnotes.com\/mcq\/two-planets-orbit-the-sun-in-circular-orbits-with-their-radius-of-orb\/\" \/>\n<meta property=\"og:site_name\" content=\"MCQ and Quiz for Exams\" \/>\n<meta property=\"article:published_time\" content=\"2025-06-01T07:18:44+00:00\" \/>\n<meta name=\"author\" content=\"rawan239\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:label1\" content=\"Written by\" \/>\n\t<meta name=\"twitter:data1\" content=\"rawan239\" \/>\n\t<meta name=\"twitter:label2\" content=\"Est. reading time\" \/>\n\t<meta name=\"twitter:data2\" content=\"1 minute\" \/>\n<!-- \/ Yoast SEO Premium plugin. -->","yoast_head_json":{"title":"Two planets orbit the Sun in circular orbits, with their radius of orb","description":"This problem can be solved using Kepler's Third Law of planetary motion, which states that the square of the orbital period (T) of a planet is directly proportional to the cube of the semi-major axis (R) of its orbit: T\u00b2 \u221d R\u00b3. For circular orbits, the semi-major axis is simply the radius (R). Thus, (T\u2081\/T\u2082)\u00b2 = (R\u2081\/R\u2082)\u00b3. Given R\u2081 = R and R\u2082 = 4R, we have (T\u2081\/T\u2082)\u00b2 = (R \/ 4R)\u00b3 = (1\/4)\u00b3 = 1\/64. Taking the square root of both sides, T\u2081\/T\u2082 = \u221a(1\/64) = 1\/8. Kepler's Third Law relates the orbital period and orbital radius of planets orbiting the same central body: T\u00b2 \u221d R\u00b3.","robots":{"index":"index","follow":"follow","max-snippet":"max-snippet:-1","max-image-preview":"max-image-preview:large","max-video-preview":"max-video-preview:-1"},"canonical":"https:\/\/exam.pscnotes.com\/mcq\/two-planets-orbit-the-sun-in-circular-orbits-with-their-radius-of-orb\/","og_locale":"en_US","og_type":"article","og_title":"Two planets orbit the Sun in circular orbits, with their radius of orb","og_description":"This problem can be solved using Kepler's Third Law of planetary motion, which states that the square of the orbital period (T) of a planet is directly proportional to the cube of the semi-major axis (R) of its orbit: T\u00b2 \u221d R\u00b3. For circular orbits, the semi-major axis is simply the radius (R). Thus, (T\u2081\/T\u2082)\u00b2 = (R\u2081\/R\u2082)\u00b3. Given R\u2081 = R and R\u2082 = 4R, we have (T\u2081\/T\u2082)\u00b2 = (R \/ 4R)\u00b3 = (1\/4)\u00b3 = 1\/64. Taking the square root of both sides, T\u2081\/T\u2082 = \u221a(1\/64) = 1\/8. Kepler's Third Law relates the orbital period and orbital radius of planets orbiting the same central body: T\u00b2 \u221d R\u00b3.","og_url":"https:\/\/exam.pscnotes.com\/mcq\/two-planets-orbit-the-sun-in-circular-orbits-with-their-radius-of-orb\/","og_site_name":"MCQ and Quiz for Exams","article_published_time":"2025-06-01T07:18:44+00:00","author":"rawan239","twitter_card":"summary_large_image","twitter_misc":{"Written by":"rawan239","Est. reading time":"1 minute"},"schema":{"@context":"https:\/\/schema.org","@graph":[{"@type":"WebPage","@id":"https:\/\/exam.pscnotes.com\/mcq\/two-planets-orbit-the-sun-in-circular-orbits-with-their-radius-of-orb\/","url":"https:\/\/exam.pscnotes.com\/mcq\/two-planets-orbit-the-sun-in-circular-orbits-with-their-radius-of-orb\/","name":"Two planets orbit the Sun in circular orbits, with their radius of orb","isPartOf":{"@id":"https:\/\/exam.pscnotes.com\/mcq\/#website"},"datePublished":"2025-06-01T07:18:44+00:00","dateModified":"2025-06-01T07:18:44+00:00","author":{"@id":"https:\/\/exam.pscnotes.com\/mcq\/#\/schema\/person\/5807dafeb27d2ec82344d6cbd6c3d209"},"description":"This problem can be solved using Kepler's Third Law of planetary motion, which states that the square of the orbital period (T) of a planet is directly proportional to the cube of the semi-major axis (R) of its orbit: T\u00b2 \u221d R\u00b3. For circular orbits, the semi-major axis is simply the radius (R). Thus, (T\u2081\/T\u2082)\u00b2 = (R\u2081\/R\u2082)\u00b3. Given R\u2081 = R and R\u2082 = 4R, we have (T\u2081\/T\u2082)\u00b2 = (R \/ 4R)\u00b3 = (1\/4)\u00b3 = 1\/64. Taking the square root of both sides, T\u2081\/T\u2082 = \u221a(1\/64) = 1\/8. Kepler's Third Law relates the orbital period and orbital radius of planets orbiting the same central body: T\u00b2 \u221d R\u00b3.","breadcrumb":{"@id":"https:\/\/exam.pscnotes.com\/mcq\/two-planets-orbit-the-sun-in-circular-orbits-with-their-radius-of-orb\/#breadcrumb"},"inLanguage":"en-US","potentialAction":[{"@type":"ReadAction","target":["https:\/\/exam.pscnotes.com\/mcq\/two-planets-orbit-the-sun-in-circular-orbits-with-their-radius-of-orb\/"]}]},{"@type":"BreadcrumbList","@id":"https:\/\/exam.pscnotes.com\/mcq\/two-planets-orbit-the-sun-in-circular-orbits-with-their-radius-of-orb\/#breadcrumb","itemListElement":[{"@type":"ListItem","position":1,"name":"Home","item":"https:\/\/exam.pscnotes.com\/mcq\/"},{"@type":"ListItem","position":2,"name":"UPSC NDA-2","item":"https:\/\/exam.pscnotes.com\/mcq\/category\/upsc-nda-2\/"},{"@type":"ListItem","position":3,"name":"Two planets orbit the Sun in circular orbits, with their radius of orb"}]},{"@type":"WebSite","@id":"https:\/\/exam.pscnotes.com\/mcq\/#website","url":"https:\/\/exam.pscnotes.com\/mcq\/","name":"MCQ and Quiz for Exams","description":"","potentialAction":[{"@type":"SearchAction","target":{"@type":"EntryPoint","urlTemplate":"https:\/\/exam.pscnotes.com\/mcq\/?s={search_term_string}"},"query-input":"required name=search_term_string"}],"inLanguage":"en-US"},{"@type":"Person","@id":"https:\/\/exam.pscnotes.com\/mcq\/#\/schema\/person\/5807dafeb27d2ec82344d6cbd6c3d209","name":"rawan239","image":{"@type":"ImageObject","inLanguage":"en-US","@id":"https:\/\/exam.pscnotes.com\/mcq\/#\/schema\/person\/image\/","url":"https:\/\/secure.gravatar.com\/avatar\/761a7274f9cce048fa5b921221e7934820d74514df93ef195a9d22af0c1c9001?s=96&d=mm&r=g","contentUrl":"https:\/\/secure.gravatar.com\/avatar\/761a7274f9cce048fa5b921221e7934820d74514df93ef195a9d22af0c1c9001?s=96&d=mm&r=g","caption":"rawan239"},"sameAs":["https:\/\/exam.pscnotes.com"],"url":"https:\/\/exam.pscnotes.com\/mcq\/author\/rawan239\/"}]}},"amp_enabled":true,"_links":{"self":[{"href":"https:\/\/exam.pscnotes.com\/mcq\/wp-json\/wp\/v2\/posts\/88705","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/exam.pscnotes.com\/mcq\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/exam.pscnotes.com\/mcq\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/exam.pscnotes.com\/mcq\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/exam.pscnotes.com\/mcq\/wp-json\/wp\/v2\/comments?post=88705"}],"version-history":[{"count":0,"href":"https:\/\/exam.pscnotes.com\/mcq\/wp-json\/wp\/v2\/posts\/88705\/revisions"}],"wp:attachment":[{"href":"https:\/\/exam.pscnotes.com\/mcq\/wp-json\/wp\/v2\/media?parent=88705"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/exam.pscnotes.com\/mcq\/wp-json\/wp\/v2\/categories?post=88705"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/exam.pscnotes.com\/mcq\/wp-json\/wp\/v2\/tags?post=88705"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}