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UNIVERSAL GRAVITATION Law of Universal gravitation “The force of gravitational attraction between any two objects is directly proportional to the product of the masses of the objects, and inversely proportional to the square of the distance between their centres.” As A Diagram Universal Gravitation The Law of Universal Gravitation is concerned with the force of attraction between bodies. FG = G m1m2 r2 Where: G = 6.67 x 10-11 Nm2/Kg2 (universal gravitational constant) m1 = mass of one object m2= mass of a second object r = distance between the centres of the Objects (assumed to be spherical) Note: For force of attraction to be noticeable, at least one of the objects must be very large. Force of attraction diminishes rapidly as the two objects move apart. But FG never equals zero, every object exerts a force of attraction on every other object. The law only applies to two spherical objects (such as earth & sun), to two objects whose sizes are much smaller than their separation distance, or to a small object and a very large sphere. Example Earth: If we replace m1 with 1kg, m2 with the mass of the Earth, and r with the radius of the Earth, what do we get for FG? m1 = 1kg m2 = 5.9742 x 1024 Kg r = 6.3781 x 106 m G = 6.67 x 10-11 Nm2/Kg2 Example - Earth: If we repalce m1 with 1kg, m2 with the mass of the Earth, and r with the radius of the Earth, what do we get for FG? m1 = 1kg m2 = 5.9742 x 1024 Kg r = 6.3781 x 106 m G = 6.67 x 10-11 Nm2/Kg2 F G = G m 1m 2 r2 Example Earth: If we repalce m1 with 1kg, m2 with the mass of the Earth, and r with the radius of the Earth, what do we get for FG? m1 = 1kg m2 = 5.9742 x 1024 Kg r = 6.3781 x 106 m G = 6.67 x 10-11 Nm2/Kg2 F G = G m 1m 2 R2 = (6.67 x 10-11)( 1)(5.9742 x 1024) (6.3781 x 106)2 Example Earth: If we repalce m1 with 1kg, m2 with the mass of the Earth, and r with the radius of the Earth, what do we get for FG? m1 = 1kg m2 = 5.9742 x 1024 Kg r = 6.3781 x 106 m G = 6.67 x 10-11 Nm2/Kg2 F G = G m 1m 2 R2 = (6.67 x 10-11)( 1)(5.9742 x 1024) (6.3781 x 106)2 = 9.8 N Notice that this is the same as Fg = mg = (1 x 9.8) = 9.8 N