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Chapter 3
                                                                                                  Gravitation
                       Gravitational force is known as universal force because it acts between any two bodies in
                  the universe. Figure 3.3 shows the gravitational force between the Sun, the Earth and the Moon.
                  How can the gravitational force between two bodies be explained?
                                                               The Earth

                                     Gravitational force between
                                     the Sun and the Earth
                                                                 Gravitational force  Gravitational force
                                                                 between the Earth
                                                                 and the Moon

                                       Gravitational force between  The Moon
                                       the Sun and the Moon
                                                                                 http://bt.sasbadi.com/p4079

                         The Sun

                            Figure 3.3 Gravitational force as a universal force

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                    In the year 1687, Isaac Newton presented two relationships that
                    involve gravitational force between two bodies:               Gravitational force exists
                    •  gravitational force is directly proportional to the product of   between two bodies.
                                                         m                        Both bodies experience
                      the masses of the two bodies, that is F ∝ m 1  2
                    •  gravitational force is inversely proportional to the square of the   gravitational force of the
                                                                     1             same magnitude.
                      distance between the centres of the two bodies, that is F ∝   2
                                                                    r
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                                                          Body 2
                               Body 1                                           Why does a fallen leaf move
                                                                                towards the ground?
                                      F              F
                                 m                         m
                                  1                          2

                                            Distance, r

                            Figure 3.4 Gravitational force between two bodies
                                                                                Both the leaf and the Earth
                       Th  e two relationships above are formulated in Figure 3.5 to   experience the same
                  obtain Newton’s Universal Law of Gravitation.                 gravitational force. This causes
                                                                                the leaf and the Earth to move
                                 F ∝ m m 2                                      towards one another. As the
                                      1
                                                          m m 2                 mass of the Earth is very much
                                                           1
                                                     F ∝    2                   larger than the mass of the leaf,
                                                           r
                                      1                                         gravitational force does not
                                  F ∝   2                                       have an apparent effect on the
                                      r
                                                                                Earth’s movement. As such,
                      Figure 3.5 Formulation of Newton’s Universal Law of Gravitation  we only observe the leaf falling
                                                                                to the ground.
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                   3.1.1
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