{"id":26148,"date":"2025-06-19T10:40:29","date_gmt":"2025-06-19T10:40:29","guid":{"rendered":"https:\/\/gaviki.com\/blog\/?p=26148"},"modified":"2025-06-19T10:40:32","modified_gmt":"2025-06-19T10:40:32","slug":"calculate-the-angular-momentum-of-the-earth-in-its-orbit-around-the-sun","status":"publish","type":"post","link":"https:\/\/gaviki.com\/blog\/calculate-the-angular-momentum-of-the-earth-in-its-orbit-around-the-sun\/","title":{"rendered":"Calculate the angular momentum of the Earth in its orbit around the Sun."},"content":{"rendered":"\n

Calculate the angular momentum of the Earth in its orbit around the Sun. Compare this angular momentum with the angular momentum of Earth on its axis.<\/p>\n\n\n\n

The Correct Answer and Explanation is:<\/mark><\/strong><\/p>\n\n\n\n

To calculate and compare the angular momentum of Earth in two scenarios \u2014 orbiting the Sun and rotating on its axis \u2014 we use the following physics principles:<\/p>\n\n\n\n

\n\n\n\n

1. Angular Momentum of Earth in Its Orbit Around the Sun<\/strong><\/h3>\n\n\n\n

This motion can be treated as circular:<\/p>\n\n\n\n

Formula:<\/strong>
Lorbit=mvrL_{\\text{orbit}} = mvrLorbit\u200b=mvr<\/p>\n\n\n\n

Where:<\/p>\n\n\n\n

    \n
  • mmm = mass of Earth = 5.97\u00d71024\u2009kg5.97 \\times 10^{24} \\, \\text{kg}5.97\u00d71024kg<\/li>\n\n\n\n
  • vvv = orbital speed of Earth \u2248 2.98\u00d7104\u2009m\/s2.98 \\times 10^4 \\, \\text{m\/s}2.98\u00d7104m\/s<\/li>\n\n\n\n
  • rrr = average distance from Sun = 1.496\u00d71011\u2009m1.496 \\times 10^{11} \\, \\text{m}1.496\u00d71011m<\/li>\n<\/ul>\n\n\n\n

    Calculation:<\/strong>Lorbit=(5.97\u00d71024)(2.98\u00d7104)(1.496\u00d71011)Lorbit\u22482.66\u00d71040\u2009kg\u22c5m2\/sL_{\\text{orbit}} = (5.97 \\times 10^{24})(2.98 \\times 10^4)(1.496 \\times 10^{11}) \\\\ L_{\\text{orbit}} \u2248 2.66 \\times 10^{40} \\, \\text{kg} \\cdot \\text{m}^2\/\\text{s}Lorbit\u200b=(5.97\u00d71024)(2.98\u00d7104)(1.496\u00d71011)Lorbit\u200b\u22482.66\u00d71040kg\u22c5m2\/s<\/p>\n\n\n\n

    \n\n\n\n

    2. Angular Momentum of Earth Spinning on Its Axis<\/strong><\/h3>\n\n\n\n

    We treat Earth as a rotating solid sphere:<\/p>\n\n\n\n

    Formula:<\/strong>
    Lspin=I\u03c9L_{\\text{spin}} = I \\omegaLspin\u200b=I\u03c9
    Where:<\/p>\n\n\n\n

      \n
    • I=25mr2I = \\frac{2}{5}mr^2I=52\u200bmr2<\/li>\n\n\n\n
    • \u03c9=2\u03c0T\\omega = \\frac{2\\pi}{T}\u03c9=T2\u03c0\u200b, with T=86400\u2009sT = 86400 \\, \\text{s}T=86400s (1 day)<\/li>\n<\/ul>\n\n\n\n

      Using Earth’s radius:
      r=6.371\u00d7106\u2009mr = 6.371 \\times 10^6 \\, \\text{m}r=6.371\u00d7106mI=25(5.97\u00d71024)(6.371\u00d7106)2\u22489.72\u00d71037\u2009kg\u22c5m2I = \\frac{2}{5}(5.97 \\times 10^{24})(6.371 \\times 10^6)^2 \u2248 9.72 \\times 10^{37} \\, \\text{kg} \\cdot \\text{m}^2I=52\u200b(5.97\u00d71024)(6.371\u00d7106)2\u22489.72\u00d71037kg\u22c5m2\u03c9=2\u03c086400\u22487.27\u00d710\u22125\u2009rad\/s\\omega = \\frac{2\\pi}{86400} \u2248 7.27 \\times 10^{-5} \\, \\text{rad\/s}\u03c9=864002\u03c0\u200b\u22487.27\u00d710\u22125rad\/sLspin=(9.72\u00d71037)(7.27\u00d710\u22125)\u22487.07\u00d71033\u2009kg\u22c5m2\/sL_{\\text{spin}} = (9.72 \\times 10^{37})(7.27 \\times 10^{-5}) \u2248 7.07 \\times 10^{33} \\, \\text{kg} \\cdot \\text{m}^2\/\\text{s}Lspin\u200b=(9.72\u00d71037)(7.27\u00d710\u22125)\u22487.07\u00d71033kg\u22c5m2\/s<\/p>\n\n\n\n

      \n\n\n\n

      3. Comparison<\/strong><\/h3>\n\n\n\n
        \n
      • Angular momentum in orbit: \u22482.66\u00d71040\u2009kg\u22c5m2\/s\\approx 2.66 \\times 10^{40} \\, \\text{kg} \\cdot \\text{m}^2\/\\text{s}\u22482.66\u00d71040kg\u22c5m2\/s<\/li>\n\n\n\n
      • Angular momentum on axis: \u22487.07\u00d71033\u2009kg\u22c5m2\/s\\approx 7.07 \\times 10^{33} \\, \\text{kg} \\cdot \\text{m}^2\/\\text{s}\u22487.07\u00d71033kg\u22c5m2\/s<\/li>\n<\/ul>\n\n\n\n

        Conclusion:<\/strong>
        Earth\u2019s angular momentum due to orbiting the Sun is about a million times greater<\/strong> than its rotational angular momentum. This shows that the bulk of Earth\u2019s angular momentum is tied to its motion through space rather than its spinning motion. These values help scientists understand planetary dynamics, gravitational interactions, and conservation of momentum in celestial systems.<\/p>\n\n\n\n

        \"\"<\/figure>\n","protected":false},"excerpt":{"rendered":"

        Calculate the angular momentum of the Earth in its orbit around the Sun. Compare this angular momentum with the angular momentum of Earth on its axis. The Correct Answer and Explanation is: To calculate and compare the angular momentum of Earth in two scenarios \u2014 orbiting the Sun and rotating on its axis \u2014 we […]<\/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-26148","post","type-post","status-publish","format-standard","hentry","category-quiz-questions"],"_links":{"self":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/26148","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=26148"}],"version-history":[{"count":1,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/26148\/revisions"}],"predecessor-version":[{"id":26158,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/26148\/revisions\/26158"}],"wp:attachment":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/media?parent=26148"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/categories?post=26148"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/tags?post=26148"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}