{"id":63383,"date":"2023-12-14T12:54:11","date_gmt":"2023-12-14T07:24:11","guid":{"rendered":"https:\/\/pwonlyias.com\/stage\/?post_type=ncert-notes&p=63383"},"modified":"2024-09-26T12:23:58","modified_gmt":"2024-09-26T06:53:58","slug":"newton-law-of-gravitation","status":"publish","type":"ncert-notes","link":"https:\/\/pwonlyias.com\/stage\/ncert-notes\/newton-law-of-gravitation","title":{"rendered":"Gravitation: Newton’s Laws & Universal Movement of Celestial Bodies"},"content":{"rendered":"

Newton’s Laws and Celestial Forces<\/b><\/span><\/h2>\n

Gravitation is the force responsible for the attraction between objects with mass. It’s responsible for the motion of celestial bodies and objects falling towards the Earth. <\/span>Sir Isaac Newton<\/b> established the concept of the gravitational force.<\/span><\/p>\n

Moon’s Motion<\/b>:<\/span> The Dance of Gravitational Forces<\/b><\/span><\/h3>\n
    \n
  • Revolution: <\/b>The moon revolves around the earth.<\/span><\/li>\n
  • Newton\u2019s View: <\/b>Newton postulated that the same force that causes an apple to fall to the ground also keeps the moon in its orbit around the Earth.<\/span><\/li>\n
  • Orbiting Earth: <\/b>Although the moon seems to orbit the Earth without falling towards it, that is where the concept of centripetal force comes into play.<\/span><\/li>\n<\/ul>\n

    Centripetal Force<\/b>:\u00a0<\/span><\/span><\/p>\n

      \n
    • When an object moves in a<\/span> circular path, <\/b>the force that keeps it moving along that path and prevents it from flying off in a straight line is called the centripetal force.\u00a0<\/span><\/li>\n
    • Without this force, an object in motion would continue in a straight line, tangent to the circular path.<\/span><\/li>\n<\/ul>\n

      Spiraling Secrets: Revealing the Centripetal Force Mystery<\/b><\/span><\/p>\n

        \n
      • The moon’s orbit<\/b> around the earth can be attributed to centripetal force.\u00a0<\/span><\/li>\n
      • This force is a result of the gravitational attraction between the Earth and the moon.\u00a0<\/span><\/li>\n
      • Without this gravitational force, the moon would not revolve around the Earth but would move in a straight line.<\/span><\/li>\n<\/ul>\n

        Gravity: Earth, Apple, and Newton’s Laws in Motion<\/b><\/span><\/p>\n

          \n
        • While it is evident that the earth attracts objects, like<\/span> an apple falling from a tree,<\/b> the opposite is also true.\u00a0<\/span><\/li>\n
        • According to <\/span>Newton’s third law,<\/b> the apple exerts an equal and opposite gravitational force on the earth.<\/span><\/li>\n
        • However, due to the enormous mass difference between the earth and an apple, the resulting acceleration of the earth towards the apple is minuscule and imperceptible.<\/span><\/li>\n<\/ul>\n

          Planetary Orbits and the Cosmic Dance of Celestial Bodies<\/b><\/span><\/p>\n

            \n
          • Planets in our solar system revolve around the Sun due to the gravitational pull the Sun exerts on them.\u00a0<\/span><\/li>\n
          • Newton deduced from these observations that all objects in the<\/span> universe exert gravitational forces <\/b>on each other, irrespective of their size.<\/span><\/li>\n<\/ul>\n
            \"gravitational
            The gravitational force between two uniform objects is directed along the line joining their centres<\/figcaption><\/figure>\n

            Universal Force: Bridging Celestial Force<\/b><\/p>\n

              \n
            • Gravitation is a universal force <\/b>that attracts objects with mass towards each other.\u00a0<\/span><\/li>\n
            • This force is crucial for the functioning of our universe, governing the movement of celestial bodies and determining how objects behave on the Earth.<\/span><\/li>\n<\/ul>\n

              Unlocking the Mysteries of Gravitation: The Universal Law Revealed<\/b><\/span><\/h2>\n
                \n
              • Understanding Concept: <\/b>Every object in the universe attracts every other object with a force that is directly proportional to the product of their masses and inversely proportional to the square of the distance between their centres.<\/span><\/li>\n
              • Mathematical Representation<\/b>: For two objects A and B of masses <\/span>M<\/span><\/i> and <\/span>m<\/span><\/i> respectively, separated by a distance <\/span>d<\/span><\/i>:\u00a0<\/span><\/li>\n<\/ul>\n

                F\u221d M \u00d7 m\u00a0<\/span><\/p>\n

                F\u221d 1 \/ d<\/span>2<\/span><\/p>\n

                Combining both we get:\u00a0<\/span><\/p>\n

                F \u221d M \u00d7 m \/ d<\/span>2\u00a0 <\/span>or F = G (M \u00d7 m \/ d<\/span>2 <\/span>),\u00a0<\/span><\/p>\n

                where <\/span>G<\/i><\/b> is the Universal Gravitational Constant.<\/b><\/p>\n

                  \n
                • Value of G<\/b>: The constant <\/span>G<\/span><\/i>, called the universal gravitational constant, has an accepted value of:\u00a0<\/span><\/li>\n<\/ul>\n

                  F \u00d7 d<\/span>2 <\/span>= G M \u00d7 m or,<\/span><\/p>\n

                  G= F \u00d7 d<\/span>2 <\/span>\/ M \u00d7 m<\/span><\/p>\n

                    \n
                  • This value was determined by <\/span>Henry Cavendish<\/b> using a sensitive balance.<\/span><\/li>\n
                  • Perceptibility<\/b>: While this law means there’s a gravitational force between any two objects (like you and your friend), it’s usually much too weak to be noticeable unless at least one of the objects has a very large mass, like a planet.<\/span><\/li>\n
                  • Universality<\/b>: The law is applicable universally, irrespective of the nature, size, or location of the bodies.\u00a0<\/span>\n
                      \n
                    • For instance, if the distance between two objects is doubled (increases by a factor of 2), the gravitational force between them becomes a fourth (1\/4) of its original value.<\/span><\/li>\n<\/ul>\n<\/li>\n<\/ul>\n\n\n\n
                      \n

                      Example: <\/b>The mass of the earth is 6 \u00d7 10<\/span>24<\/span> kg and that of the moon is 7.4 \u00d7 10<\/span>22<\/span> kg. If the distance between the earth and the moon is 3.84 \u00d7 10<\/span>5<\/span> km, calculate the force exerted by the earth on the moon. (Take G = 6.7 \u00d7 10<\/span>\u201311<\/span> N m<\/span>2<\/span> kg<\/span>-2<\/span>)\u00a0<\/span><\/span><\/p>\n

                      Solution:\u00a0<\/b><\/span><\/p>\n

                      The mass of the earth, M=6 \u00d7 10<\/span>24<\/span> kg\u00a0<\/span><\/span><\/p>\n

                      The mass of the moon, m=7.4\u00d710<\/span>22<\/span> kg<\/span>
                      \n<\/span>The distance between the earth and the moon,\u00a0<\/span><\/span><\/p>\n

                      d = 3.84\u00d710<\/span>5<\/span>km = 3.84\u00d710<\/span>5<\/span>\u00d71000m = 3.84 \u00d7 10<\/span>8<\/span> m\u00a0<\/span><\/span><\/p>\n

                      G= 6.7\u00d710<\/span>\u201311<\/span> N m<\/span>2<\/span> kg<\/span>\u20132<\/span>\u00a0<\/span><\/span><\/p>\n

                      The force exerted by the earth on the moon is F = G (M \u00d7 m \/ d<\/span>2<\/span>)<\/span><\/span><\/p>\n

                      = 6.7\u00d710<\/span>\u221211<\/span> N m<\/span>2<\/span> kg<\/span>-2<\/span> \u00d7 6 \u00d7 10<\/span>24<\/span> kg \u00d7 7.4 \u00d7 10<\/span>22<\/span> kg \/ (3.84 \u00d7 10<\/span>8<\/span> m)<\/span>2<\/span>\u00a0<\/span><\/span><\/p>\n

                      = 2.02 \u00d7 10<\/span>20 <\/span>N.<\/span>
                      \n<\/span>Thus, the force exerted by the earth on the moon is <\/span>2.02 \u00d7 10<\/b>20<\/b> N.<\/b>\u00a0<\/b><\/span><\/p>\n<\/th>\n<\/tr>\n<\/tbody>\n<\/table>\n","protected":false},"featured_media":0,"parent":0,"template":"","notes-subjects":[4568],"subject-chapters":[4704],"acf":[],"_links":{"self":[{"href":"https:\/\/pwonlyias.com\/stage\/wp-json\/wp\/v2\/ncert-notes\/63383"}],"collection":[{"href":"https:\/\/pwonlyias.com\/stage\/wp-json\/wp\/v2\/ncert-notes"}],"about":[{"href":"https:\/\/pwonlyias.com\/stage\/wp-json\/wp\/v2\/types\/ncert-notes"}],"wp:attachment":[{"href":"https:\/\/pwonlyias.com\/stage\/wp-json\/wp\/v2\/media?parent=63383"}],"wp:term":[{"taxonomy":"notes-subjects","embeddable":true,"href":"https:\/\/pwonlyias.com\/stage\/wp-json\/wp\/v2\/notes-subjects?post=63383"},{"taxonomy":"subject-chapters","embeddable":true,"href":"https:\/\/pwonlyias.com\/stage\/wp-json\/wp\/v2\/subject-chapters?post=63383"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}