{"id":38156,"date":"2025-06-26T08:29:05","date_gmt":"2025-06-26T08:29:05","guid":{"rendered":"https:\/\/gaviki.com\/blog\/?p=38156"},"modified":"2025-06-26T08:29:07","modified_gmt":"2025-06-26T08:29:07","slug":"calculate-the-gravitational-acceleration-at-jupiters-surface-technically-jupiter-is-a-gas-cloud-so-it-doesnt-have-a-surface-per-se-given-that-jupiters-radius-is-6-9x104-km","status":"publish","type":"post","link":"https:\/\/gaviki.com\/blog\/calculate-the-gravitational-acceleration-at-jupiters-surface-technically-jupiter-is-a-gas-cloud-so-it-doesnt-have-a-surface-per-se-given-that-jupiters-radius-is-6-9x104-km\/","title":{"rendered":"Calculate the gravitational acceleration at Jupiter&#8217;s surface (technically Jupiter is a gas cloud, so it doesn&#8217;t have a surface per se), given that Jupiter&#8217;s radius is 6.9&#215;10^4 km"},"content":{"rendered":"\n<p>Calculate the gravitational acceleration at Jupiter&#8217;s surface (technically Jupiter is a gas cloud, so it doesn&#8217;t have a surface per se), given that Jupiter&#8217;s radius is 6.9&#215;10^4 km. Express this acceleration as a fraction of the Earth&#8217;s gravitational acceleration at the surface. If your body mass was 60 kg, what would be the force of gravity on you if you happened to be on Jupiter&#8217;s surface?<\/p>\n\n\n\n<p><strong><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-vivid-cyan-blue-color\">The Correct Answer and Explanation is:<\/mark><\/strong><\/p>\n\n\n\n<p>To calculate the <strong>gravitational acceleration<\/strong> at Jupiter\u2019s surface, we use the <strong>universal law of gravitation<\/strong>:g=G\u22c5MR2g = \\frac{G \\cdot M}{R^2}g=R2G\u22c5M\u200b<\/p>\n\n\n\n<p>Where:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>ggg is the gravitational acceleration,<\/li>\n\n\n\n<li>GGG is the gravitational constant =6.674\u00d710\u221211\u2009N\\cdotpm2\/kg2= 6.674 \\times 10^{-11} \\, \\text{N\u00b7m}^2\/\\text{kg}^2=6.674\u00d710\u221211N\\cdotpm2\/kg2,<\/li>\n\n\n\n<li>MMM is the mass of Jupiter =1.898\u00d71027\u2009kg= 1.898 \\times 10^{27} \\, \\text{kg}=1.898\u00d71027kg,<\/li>\n\n\n\n<li>RRR is the radius of Jupiter =6.9\u00d7104\u2009km=6.9\u00d7107\u2009m= 6.9 \\times 10^4 \\, \\text{km} = 6.9 \\times 10^7 \\, \\text{m}=6.9\u00d7104km=6.9\u00d7107m<\/li>\n<\/ul>\n\n\n\n<h3 class=\"wp-block-heading\">Step 1: Compute Jupiter\u2019s surface gravity<\/h3>\n\n\n\n<p>gJ=6.674\u00d710\u221211\u00d71.898\u00d71027(6.9\u00d7107)2g_J = \\frac{6.674 \\times 10^{-11} \\times 1.898 \\times 10^{27}}{(6.9 \\times 10^7)^2}gJ\u200b=(6.9\u00d7107)26.674\u00d710\u221211\u00d71.898\u00d71027\u200bgJ=1.266\u00d710174.761\u00d71015\u224826.6\u2009m\/s2g_J = \\frac{1.266 \\times 10^{17}}{4.761 \\times 10^{15}} \\approx 26.6 \\, \\text{m\/s}^2gJ\u200b=4.761\u00d710151.266\u00d71017\u200b\u224826.6m\/s2<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Step 2: Express Jupiter\u2019s gravity as a fraction of Earth\u2019s<\/h3>\n\n\n\n<p>Earth\u2019s surface gravity: gE=9.8\u2009m\/s2g_E = 9.8 \\, \\text{m\/s}^2gE\u200b=9.8m\/s2gJgE=26.69.8\u22482.71\\frac{g_J}{g_E} = \\frac{26.6}{9.8} \\approx 2.71gE\u200bgJ\u200b\u200b=9.826.6\u200b\u22482.71<\/p>\n\n\n\n<p>So, gravity on Jupiter is <strong>about 2.71 times<\/strong> stronger than on Earth.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Step 3: Calculate the gravitational force on a 60 kg person<\/h3>\n\n\n\n<p>Using Newton\u2019s second law F=m\u22c5gF = m \\cdot gF=m\u22c5g:F=60\u2009kg\u00d726.6\u2009m\/s2=1596\u2009NF = 60 \\, \\text{kg} \\times 26.6 \\, \\text{m\/s}^2 = 1596 \\, \\text{N}F=60kg\u00d726.6m\/s2=1596N<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\">Explanation<\/h3>\n\n\n\n<p>Gravitational acceleration is the rate at which an object speeds up due to gravity. It depends on two factors: the mass of the planet and the square of the distance from the planet\u2019s center. Using Newton\u2019s law of gravitation, we can find the acceleration due to gravity on Jupiter even though it does not have a solid surface. Scientists often define a notional &#8220;surface&#8221; at the point where atmospheric pressure equals 1 bar (same as Earth\u2019s sea level).<\/p>\n\n\n\n<p>We start by plugging values into the gravitational formula. Jupiter is much more massive than Earth, and while it is also larger in radius, the increase in mass has a stronger effect than the increase in radius. This results in a stronger gravitational pull.<\/p>\n\n\n\n<p>After performing the calculation, we find that gravity on Jupiter is about <strong>2.71 times<\/strong> that on Earth. This means that if you weigh 60 kg on Earth, you would feel significantly heavier on Jupiter due to the increased gravitational force. Specifically, your weight (which is the force of gravity on you) would be about 1596 newtons, compared to 588 newtons on Earth.<\/p>\n\n\n\n<p>Even though you would still have the same <strong>mass<\/strong> of 60 kg, the gravitational force acting on that mass would be much higher. This distinction between mass (which stays constant) and weight (which changes depending on gravity) is crucial in physics. Jupiter\u2019s immense gravity makes it an extreme environment, and this is one reason why sending humans or probes near its surface presents such technical challenges.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"852\" height=\"1024\" src=\"https:\/\/gaviki.com\/blog\/wp-content\/uploads\/2025\/06\/learnexams-banner8-1008.jpeg\" alt=\"\" class=\"wp-image-38170\" srcset=\"https:\/\/gaviki.com\/blog\/wp-content\/uploads\/2025\/06\/learnexams-banner8-1008.jpeg 852w, https:\/\/gaviki.com\/blog\/wp-content\/uploads\/2025\/06\/learnexams-banner8-1008-250x300.jpeg 250w, https:\/\/gaviki.com\/blog\/wp-content\/uploads\/2025\/06\/learnexams-banner8-1008-768x923.jpeg 768w\" sizes=\"auto, (max-width: 852px) 100vw, 852px\" \/><\/figure>\n","protected":false},"excerpt":{"rendered":"<p>Calculate the gravitational acceleration at Jupiter&#8217;s surface (technically Jupiter is a gas cloud, so it doesn&#8217;t have a surface per se), given that Jupiter&#8217;s radius is 6.9&#215;10^4 km. Express this acceleration as a fraction of the Earth&#8217;s gravitational acceleration at the surface. If your body mass was 60 kg, what would be the force of [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1],"tags":[],"class_list":["post-38156","post","type-post","status-publish","format-standard","hentry","category-quiz-questions"],"_links":{"self":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/38156","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/comments?post=38156"}],"version-history":[{"count":1,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/38156\/revisions"}],"predecessor-version":[{"id":38174,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/38156\/revisions\/38174"}],"wp:attachment":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/media?parent=38156"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/categories?post=38156"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/tags?post=38156"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}