{"id":259080,"date":"2025-07-18T18:10:18","date_gmt":"2025-07-18T18:10:18","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=259080"},"modified":"2025-07-18T18:10:18","modified_gmt":"2025-07-18T18:10:18","slug":"the-gravitational-force-between-the-sun-mass-1-99-x-1030-kg-and-mercury-mass-3-30-x-1023-kg-is-8-99-x-1021-n-2","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/07\/18\/the-gravitational-force-between-the-sun-mass-1-99-x-1030-kg-and-mercury-mass-3-30-x-1023-kg-is-8-99-x-1021-n-2\/","title":{"rendered":"The gravitational force between the Sun (mass = 1.99 \u00d7 1030 kg) and Mercury (mass = 3.30 \u00d7 1023 kg) is 8.99 \u00d7 1021 N."},"content":{"rendered":"\n<p>The gravitational force between the Sun (mass = 1.99 \u00d7 1030 kg) and Mercury (mass = 3.30 \u00d7 1023 kg) is 8.99 \u00d7 1021 N. How far is Mercury from the Sun? 6.98 \u00d7 1010 km 6.98 \u00d7 107 km 4.87 \u00d7 1013 km 4.87 \u00d7 1024 km<\/p>\n\n\n\n<p><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><\/p>\n\n\n\n<p>To calculate the distance between Mercury and the Sun, we can use Newton&#8217;s Law of Universal Gravitation, which is given by: F=G\u22c5m1\u22c5m2r2F = \\frac{G \\cdot m_1 \\cdot m_2}{r^2}F=r2G\u22c5m1\u200b\u22c5m2\u200b\u200b<\/p>\n\n\n\n<p>Where:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>FFF is the gravitational force (8.99 \u00d7 10\u00b2\u00b9 N),<\/li>\n\n\n\n<li>GGG is the gravitational constant (6.67430\u00d710\u221211\u2009Nm2\/kg26.67430 \\times 10^{-11} \\, \\text{Nm}^2\/\\text{kg}^26.67430\u00d710\u221211Nm2\/kg2),<\/li>\n\n\n\n<li>m1m_1m1\u200b is the mass of the Sun (1.99 \u00d7 10\u00b3\u2070 kg),<\/li>\n\n\n\n<li>m2m_2m2\u200b is the mass of Mercury (3.30 \u00d7 10\u00b2\u00b3 kg),<\/li>\n\n\n\n<li>rrr is the distance between the two objects (Mercury and the Sun).<\/li>\n<\/ul>\n\n\n\n<p>We need to solve for rrr (the distance). Rearranging the equation: r=G\u22c5m1\u22c5m2Fr = \\sqrt{\\frac{G \\cdot m_1 \\cdot m_2}{F}}r=FG\u22c5m1\u200b\u22c5m2\u200b\u200b\u200b<\/p>\n\n\n\n<p>Now, plugging in the known values: r=(6.67430\u00d710\u221211)\u22c5(1.99\u00d71030)\u22c5(3.30\u00d71023)8.99\u00d71021r = \\sqrt{\\frac{(6.67430 \\times 10^{-11}) \\cdot (1.99 \\times 10^{30}) \\cdot (3.30 \\times 10^{23})}{8.99 \\times 10^{21}}}r=8.99\u00d71021(6.67430\u00d710\u221211)\u22c5(1.99\u00d71030)\u22c5(3.30\u00d71023)\u200b\u200b<\/p>\n\n\n\n<p>First, calculate the numerator: (6.67430\u00d710\u221211)\u22c5(1.99\u00d71030)=1.32619\u00d71020(6.67430 \\times 10^{-11}) \\cdot (1.99 \\times 10^{30}) = 1.32619 \\times 10^{20}(6.67430\u00d710\u221211)\u22c5(1.99\u00d71030)=1.32619\u00d71020 (1.32619\u00d71020)\u22c5(3.30\u00d71023)=4.37443\u00d71043(1.32619 \\times 10^{20}) \\cdot (3.30 \\times 10^{23}) = 4.37443 \\times 10^{43}(1.32619\u00d71020)\u22c5(3.30\u00d71023)=4.37443\u00d71043<\/p>\n\n\n\n<p>Now, divide by the gravitational force: 4.37443\u00d710438.99\u00d71021=4.86\u00d71022\\frac{4.37443 \\times 10^{43}}{8.99 \\times 10^{21}} = 4.86 \\times 10^{22}8.99\u00d710214.37443\u00d71043\u200b=4.86\u00d71022<\/p>\n\n\n\n<p>Now, take the square root: r=4.86\u00d71022\u22486.98\u00d71010\u2009mr = \\sqrt{4.86 \\times 10^{22}} \\approx 6.98 \\times 10^{10} \\, \\text{m}r=4.86\u00d71022\u200b\u22486.98\u00d71010m<\/p>\n\n\n\n<p>Since 1 km = 1000 m: r\u22486.98\u00d7107\u2009kmr \\approx 6.98 \\times 10^{7} \\, \\text{km}r\u22486.98\u00d7107km<\/p>\n\n\n\n<p>Thus, the correct answer is <strong>6.98 \u00d7 10\u2077 km<\/strong>.<\/p>\n\n\n\n<p>This result indicates that Mercury is about 69.8 million kilometers away from the Sun. This is a typical distance in our solar system and corresponds to Mercury&#8217;s semi-major axis, which defines its average orbital distance.<\/p>\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-banner6-914.jpeg\" alt=\"\" class=\"wp-image-259132\"\/><\/figure>\n","protected":false},"excerpt":{"rendered":"<p>The gravitational force between the Sun (mass = 1.99 \u00d7 1030 kg) and Mercury (mass = 3.30 \u00d7 1023 kg) is 8.99 \u00d7 1021 N. How far is Mercury from the Sun? 6.98 \u00d7 1010 km 6.98 \u00d7 107 km 4.87 \u00d7 1013 km 4.87 \u00d7 1024 km The Correct Answer and Explanation is: To [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"","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-259080","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/259080","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=259080"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/259080\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=259080"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=259080"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=259080"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}