{"id":190318,"date":"2025-02-12T06:18:30","date_gmt":"2025-02-12T06:18:30","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=190318"},"modified":"2025-02-12T06:18:33","modified_gmt":"2025-02-12T06:18:33","slug":"the-distance-from-earth-of-the-red-supergiant-betelgeuse-is-approximately-643-light-years","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/02\/12\/the-distance-from-earth-of-the-red-supergiant-betelgeuse-is-approximately-643-light-years\/","title":{"rendered":"The distance from Earth of the red supergiant Betelgeuse is approximately 643 light-years"},"content":{"rendered":"\n<p>The distance from Earth of the red supergiant Betelgeuse is approximately 643 light-years. If it were to explode as a supernova, it would be one of the brightest stars in the sky. Right now, the brightest star other than the Sun is Sirius, with a luminosity of 26LSunLSun and a distance of 8.6 light-years.<\/p>\n\n\n\n<p>How much brighter in our sky than Sirius would the Betelgeuse supernova be if it reached a maximum luminosity of 1.2\u00d71010 LSunLSun?<\/p>\n\n\n\n<p>Express your answer using two significant figures.<\/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<p>To find how much brighter the Betelgeuse supernova would appear in the sky than Sirius, we need to use the inverse square law for brightness. The apparent brightness ( b ) of a star depends on its luminosity ( L ) and the distance ( d ) to the observer. The formula for this relationship is:<\/p>\n\n\n\n<p>[<br>b = \\frac{L}{d^2}<br>]<\/p>\n\n\n\n<p>Where:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>( L ) is the luminosity of the star,<\/li>\n\n\n\n<li>( d ) is the distance to the star.<\/li>\n<\/ul>\n\n\n\n<h3 class=\"wp-block-heading\">Step 1: Calculate the brightness of Sirius<\/h3>\n\n\n\n<p>Sirius has a luminosity of ( L_{\\text{Sirius}} = 26 L_{\\odot} ) and a distance of 8.6 light-years. Using the inverse square law:<\/p>\n\n\n\n<p>[<br>b_{\\text{Sirius}} = \\frac{L_{\\text{Sirius}}}{d_{\\text{Sirius}}^2}<br>]<\/p>\n\n\n\n<p>Substitute the known values:<\/p>\n\n\n\n<p>[<br>b_{\\text{Sirius}} = \\frac{26 L_{\\odot}}{(8.6)^2} = \\frac{26 L_{\\odot}}{73.96}<br>]<\/p>\n\n\n\n<p>[<br>b_{\\text{Sirius}} \\approx 0.351 L_{\\odot} \\, \\text{per light-year squared}<br>]<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Step 2: Calculate the brightness of the Betelgeuse supernova<\/h3>\n\n\n\n<p>The luminosity of the Betelgeuse supernova is given as ( L_{\\text{Betelgeuse}} = 1.2 \\times 10^{10} L_{\\odot} ), and its distance is 643 light-years. Using the same formula:<\/p>\n\n\n\n<p>[<br>b_{\\text{Betelgeuse}} = \\frac{L_{\\text{Betelgeuse}}}{d_{\\text{Betelgeuse}}^2}<br>]<\/p>\n\n\n\n<p>Substitute the known values:<\/p>\n\n\n\n<p>[<br>b_{\\text{Betelgeuse}} = \\frac{1.2 \\times 10^{10} L_{\\odot}}{(643)^2} = \\frac{1.2 \\times 10^{10} L_{\\odot}}{413,649}<br>]<\/p>\n\n\n\n<p>[<br>b_{\\text{Betelgeuse}} \\approx 28,997 L_{\\odot} \\, \\text{per light-year squared}<br>]<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Step 3: Compare the brightness<\/h3>\n\n\n\n<p>To compare how much brighter the Betelgeuse supernova would be than Sirius, we take the ratio of the two brightnesses:<\/p>\n\n\n\n<p>[<br>\\frac{b_{\\text{Betelgeuse}}}{b_{\\text{Sirius}}} = \\frac{28,997 L_{\\odot}}{0.351 L_{\\odot}} \\approx 82,600<br>]<\/p>\n\n\n\n<p>Thus, the Betelgeuse supernova would appear about 82,600 times brighter in the sky than Sirius.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Final Answer:<\/h3>\n\n\n\n<p>The Betelgeuse supernova would be <strong>82,000 times<\/strong> brighter than Sirius (rounded to two significant figures).<\/p>\n","protected":false},"excerpt":{"rendered":"<p>The distance from Earth of the red supergiant Betelgeuse is approximately 643 light-years. If it were to explode as a supernova, it would be one of the brightest stars in the sky. Right now, the brightest star other than the Sun is Sirius, with a luminosity of 26LSunLSun and a distance of 8.6 light-years. How [&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-190318","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/190318","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=190318"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/190318\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=190318"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=190318"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=190318"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}