{"id":44086,"date":"2025-06-30T13:03:08","date_gmt":"2025-06-30T13:03:08","guid":{"rendered":"https:\/\/gaviki.com\/blog\/?p=44086"},"modified":"2025-06-30T13:03:09","modified_gmt":"2025-06-30T13:03:09","slug":"the-mass-of-saturn-is-5-68-x1026-kg","status":"publish","type":"post","link":"https:\/\/gaviki.com\/blog\/the-mass-of-saturn-is-5-68-x1026-kg\/","title":{"rendered":"The mass of Saturn is 5.68 x1026 kg"},"content":{"rendered":"\n<p>The mass of Saturn is 5.68 x1026 kg. The radius is 5.85 x 107 m. Find the density of Saturn in kg\/m3, then convert to g\/cm3. Compare with the density of water, 1 g\/cm3. If we could provide an ocean large enough, would Saturn sink or float?<\/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 density of Saturn, we need to use the formula for density:Density=MassVolume\\text{Density} = \\frac{\\text{Mass}}{\\text{Volume}}Density=VolumeMass\u200b<\/p>\n\n\n\n<p><strong>Step 1: Calculate the Volume of Saturn<\/strong><\/p>\n\n\n\n<p>Since Saturn is roughly spherical, we can calculate its volume using the formula for the volume of a sphere:V=43\u03c0r3V = \\frac{4}{3} \\pi r^3V=34\u200b\u03c0r3<\/p>\n\n\n\n<p>Given:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>The radius of Saturn, r=5.85\u00d7107\u2009mr = 5.85 \\times 10^7 \\, \\text{m}r=5.85\u00d7107m<\/li>\n<\/ul>\n\n\n\n<p>Plugging the radius into the formula:V=43\u03c0(5.85\u00d7107)3V = \\frac{4}{3} \\pi (5.85 \\times 10^7)^3V=34\u200b\u03c0(5.85\u00d7107)3V\u22488.50\u00d71022\u2009m3V \\approx 8.50 \\times 10^{22} \\, \\text{m}^3V\u22488.50\u00d71022m3<\/p>\n\n\n\n<p><strong>Step 2: Calculate the Density of Saturn<\/strong><\/p>\n\n\n\n<p>Now that we have the volume, we can calculate the density using the mass of Saturn m=5.68\u00d71026\u2009kgm = 5.68 \\times 10^{26} \\, \\text{kg}m=5.68\u00d71026kg:Density=5.68\u00d71026\u2009kg8.50\u00d71022\u2009m3\\text{Density} = \\frac{5.68 \\times 10^{26} \\, \\text{kg}}{8.50 \\times 10^{22} \\, \\text{m}^3}Density=8.50\u00d71022m35.68\u00d71026kg\u200bDensity\u22486.67\u00d7103\u2009kg\/m3\\text{Density} \\approx 6.67 \\times 10^3 \\, \\text{kg\/m}^3Density\u22486.67\u00d7103kg\/m3<\/p>\n\n\n\n<p><strong>Step 3: Convert the Density to g\/cm\u00b3<\/strong><\/p>\n\n\n\n<p>To convert the density from kg\/m3\\text{kg\/m}^3kg\/m3 to g\/cm3\\text{g\/cm}^3g\/cm3, we use the conversion factor:1\u2009kg\/m3=0.001\u2009g\/cm31 \\, \\text{kg\/m}^3 = 0.001 \\, \\text{g\/cm}^31kg\/m3=0.001g\/cm3<\/p>\n\n\n\n<p>Thus:Density&nbsp;in&nbsp;g\/cm3=6.67\u00d7103\u2009kg\/m3\u00d70.001\\text{Density in g\/cm}^3 = 6.67 \\times 10^3 \\, \\text{kg\/m}^3 \\times 0.001Density&nbsp;in&nbsp;g\/cm3=6.67\u00d7103kg\/m3\u00d70.001Density\u22486.67\u2009g\/cm3\\text{Density} \\approx 6.67 \\, \\text{g\/cm}^3Density\u22486.67g\/cm3<\/p>\n\n\n\n<p><strong>Step 4: Compare with the Density of Water<\/strong><\/p>\n\n\n\n<p>The density of water is 1 g\/cm\u00b3, which is much higher than the density of Saturn at 0.00667 g\/cm\u00b3.<\/p>\n\n\n\n<p><strong>Conclusion: Will Saturn Sink or Float?<\/strong><\/p>\n\n\n\n<p>Since the density of Saturn is much less than that of water, if we could somehow provide an ocean large enough to contain the entire planet, Saturn would float. This is because objects with a density lower than the fluid they are placed in float on that fluid, similar to how ice floats on water.<\/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-banner8-1460.jpeg\" alt=\"\" class=\"wp-image-44094\" srcset=\"https:\/\/gaviki.com\/blog\/wp-content\/uploads\/2025\/06\/learnexams-banner8-1460.jpeg 852w, https:\/\/gaviki.com\/blog\/wp-content\/uploads\/2025\/06\/learnexams-banner8-1460-250x300.jpeg 250w, https:\/\/gaviki.com\/blog\/wp-content\/uploads\/2025\/06\/learnexams-banner8-1460-768x923.jpeg 768w\" sizes=\"auto, (max-width: 852px) 100vw, 852px\" \/><\/figure>\n","protected":false},"excerpt":{"rendered":"<p>The mass of Saturn is 5.68 x1026 kg. The radius is 5.85 x 107 m. Find the density of Saturn in kg\/m3, then convert to g\/cm3. Compare with the density of water, 1 g\/cm3. If we could provide an ocean large enough, would Saturn sink or float? The Correct Answer and Explanation is: To calculate [&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-44086","post","type-post","status-publish","format-standard","hentry","category-quiz-questions"],"_links":{"self":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/44086","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=44086"}],"version-history":[{"count":1,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/44086\/revisions"}],"predecessor-version":[{"id":44095,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/44086\/revisions\/44095"}],"wp:attachment":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/media?parent=44086"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/categories?post=44086"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/tags?post=44086"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}