{"id":265711,"date":"2025-07-22T08:26:52","date_gmt":"2025-07-22T08:26:52","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=265711"},"modified":"2025-07-22T08:26:54","modified_gmt":"2025-07-22T08:26:54","slug":"if-kepler-1606b-has-no-atmosphere-and-an-albedo-similar-to-the-earths-albedo-of-0-3-what-would-the-equilibrium-average-temperature-of-the-planet-be","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/07\/22\/if-kepler-1606b-has-no-atmosphere-and-an-albedo-similar-to-the-earths-albedo-of-0-3-what-would-the-equilibrium-average-temperature-of-the-planet-be\/","title":{"rendered":"If Kepler 1606b has no atmosphere and an albedo similar to the Earth&#8217;s (albedo of 0.3), what would the equilibrium average temperature of the planet be"},"content":{"rendered":"\n<p>If Kepler 1606b has no atmosphere and an albedo similar to the Earth&#8217;s (albedo of 0.3), what would the equilibrium average temperature of the planet be? Give your answer in \u00c2\u00b0C.<\/p>\n\n\n\n<p><em><strong><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-ast-global-color-1-color\">The Correct Answer and Explanation is:<\/mark><\/strong><\/em><\/p>\n\n\n\n<p>To find the equilibrium temperature of Kepler 1606b, we can use the Stefan-Boltzmann Law, which relates the energy received by a planet to its temperature. The equilibrium temperature is determined by balancing the energy absorbed from the star with the energy radiated by the planet. The formula is: Teq=((1\u2212A)S4\u03c3)1\/4T_{eq} = \\left( \\frac{(1 &#8211; A) S}{4 \\sigma} \\right)^{1\/4}Teq\u200b=(4\u03c3(1\u2212A)S\u200b)1\/4<\/p>\n\n\n\n<p>Where:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>TeqT_{eq}Teq\u200b is the equilibrium temperature of the planet,<\/li>\n\n\n\n<li>AAA is the albedo (reflectivity),<\/li>\n\n\n\n<li>SSS is the solar flux (energy per unit area received from the star),<\/li>\n\n\n\n<li>\u03c3\\sigma\u03c3 is the Stefan-Boltzmann constant, 5.67\u00d710\u22128\u2009W\/m2\u2009K45.67 \\times 10^{-8} \\, \\text{W\/m}^2 \\, \\text{K}^45.67\u00d710\u22128W\/m2K4,<\/li>\n\n\n\n<li>The factor of 4 accounts for the fact that only one side of the planet receives sunlight at any given time.<\/li>\n<\/ul>\n\n\n\n<p>The solar flux SSS at Earth&#8217;s distance from the Sun (which we assume is similar for Kepler 1606b) is approximately: S=1361\u2009W\/m2S = 1361 \\, \\text{W\/m}^2S=1361W\/m2<\/p>\n\n\n\n<p>We can now plug in the values:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Albedo A=0.3A = 0.3A=0.3,<\/li>\n\n\n\n<li>S=1361\u2009W\/m2S = 1361 \\, \\text{W\/m}^2S=1361W\/m2,<\/li>\n\n\n\n<li>\u03c3=5.67\u00d710\u22128\u2009W\/m2\u2009K4\\sigma = 5.67 \\times 10^{-8} \\, \\text{W\/m}^2 \\, \\text{K}^4\u03c3=5.67\u00d710\u22128W\/m2K4.<\/li>\n<\/ul>\n\n\n\n<p>First, calculate the term inside the parentheses: (1\u2212A)=1\u22120.3=0.7(1 &#8211; A) = 1 &#8211; 0.3 = 0.7(1\u2212A)=1\u22120.3=0.7 (1\u2212A)S4\u03c3=0.7\u00d713614\u00d75.67\u00d710\u22128\u22482.68\u00d7109\u2009W\/m2\\frac{(1 &#8211; A) S}{4 \\sigma} = \\frac{0.7 \\times 1361}{4 \\times 5.67 \\times 10^{-8}} \\approx 2.68 \\times 10^9 \\, \\text{W\/m}^24\u03c3(1\u2212A)S\u200b=4\u00d75.67\u00d710\u221280.7\u00d71361\u200b\u22482.68\u00d7109W\/m2<\/p>\n\n\n\n<p>Now, take the fourth root to find TeqT_{eq}Teq\u200b: Teq=(2.68\u00d7109)1\/4\u2248283.1\u2009KT_{eq} = \\left( 2.68 \\times 10^9 \\right)^{1\/4} \\approx 283.1 \\, \\text{K}Teq\u200b=(2.68\u00d7109)1\/4\u2248283.1K<\/p>\n\n\n\n<p>Finally, convert from Kelvin to Celsius: Teq=283.1\u2212273.15\u22489.96\u2009\u00b0CT_{eq} = 283.1 &#8211; 273.15 \\approx 9.96 \\, \\text{\u00b0C}Teq\u200b=283.1\u2212273.15\u22489.96\u00b0C<\/p>\n\n\n\n<p>Thus, the equilibrium average temperature of Kepler 1606b would be approximately <strong>10\u00b0C<\/strong>.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Explanation:<\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li>The albedo of 0.3 indicates that the planet reflects 30% of the incoming solar radiation and absorbs the remaining 70%.<\/li>\n\n\n\n<li>The equilibrium temperature is calculated by considering the balance between the absorbed radiation and the energy the planet radiates back into space.<\/li>\n\n\n\n<li>The result of around 10\u00b0C suggests that without an atmosphere, Kepler 1606b would have a temperate climate, similar to Earth&#8217;s average temperature, assuming it has an albedo close to Earth&#8217;s and the same solar flux.<\/li>\n<\/ul>\n\n\n\n<figure class=\"wp-block-image size-full\"><img decoding=\"async\" src=\"https:\/\/learnexams.com\/blog\/wp-content\/uploads\/2025\/07\/learnexams-banner6-1502.jpeg\" alt=\"\" class=\"wp-image-265713\"\/><\/figure>\n","protected":false},"excerpt":{"rendered":"<p>If Kepler 1606b has no atmosphere and an albedo similar to the Earth&#8217;s (albedo of 0.3), what would the equilibrium average temperature of the planet be? Give your answer in \u00c2\u00b0C. The Correct Answer and Explanation is: To find the equilibrium temperature of Kepler 1606b, we can use the Stefan-Boltzmann Law, which relates the energy [&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-265711","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/265711","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=265711"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/265711\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=265711"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=265711"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=265711"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}