Unit 9 Gravitation 9.1Universal Gravitation 9.2Gravitational field 9.3Gravitational potential energy 9.4Satellite orbits 9.5 Launching a satellite 9.6 Mechanical energy of a satellite 9.7 Kepler’s laws 9.1 Gravitation Newton’s law of universal gravitation states that the gravitational force Fbetween any two bodies of mass m1and m2separated by a distance r, is described by 221rmmF∝. 1m2mr F F It is a center-to-center attraction between all forms of matter. The force of gravity between any two bodies varies directly in proportion to the product of their masses and inversely with their separation squared. F The proportional constant is referred to as the universal gravitation constant G. Its value is G = 6.67×10-11Nm2kg-2. Now we can write 221rmmGF=r Example Twin asteroids Xand Y, having the same mass (M= 3.5×1018kg) are located 3.00 km apart. Find the net gravitational force of the spaceship when it is located at positions Aand B, as shown in figure. Given that the mass of the spaceship is m = 2.50 ×107kg. 1
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