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Newton’s Law of Gravitation

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Newton concluded that gravity was a force that acts through even great distances Newton did calculations on the a r of the moon and its F r Found the F r inversely proportional to the square of the radius of orbit

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Since F r is caused by gravity, the force of gravity is inversely proportional to square of radius Newton also realized that the force of gravity depends on the mass – directly proportional to the mass of the two objects being attracted

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Law of Universal Gravitation Every part in the universe attracts every other part with a force that is proportional to the product of their masses and inversely proportional to the square of the distance between them.

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Equation F G = Gm 1 m 2 / r 2 G = universal constant = 6.67 x 10 -11 N m 2 /kg 2

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Example 1 A 50 kg person and a 75 kg person are sitting on a bench so that their centers are about 50 cm apart. How much gravitational force is there between them?

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Example 2 What is the force of gravity acting on a 2000 kg spacecraft when it orbits two Earth radii from the Earth’s surface? Radius = 6380 km Mass of earth = 5.98 x 10 24 kg

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Acceleration Due to Gravity F G = Gm 1 m 2 / r 2 On the earth m 2 is the mass of the earth and m 1 the mass of the object F G = mg mg = Gm 1 m 2 / r 2 m 1 cancels (this is the mass of the object) g = Gm 2 / r 2

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Example 3 What is the acceleration due to gravity on the moon which has a mass of 7.4 x 10 22 kg and a radius of 1750 km?

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Example What is the acceleration due to gravity acting on a satellite orbiting at a distance of two earth’s radii from the earth’s surface?

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The velocity of a satellite keeps it in orbit Even when moving, the satellite is actually accelerating toward the Earth (this is what keeps it in its circular path) Its acceleration results in a curved path which is the same as the curve of the Earth Gravity is providing the centripetal force

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Perception of Weightlessness There is still gravity acting in a satellite (about 8.9 m/s 2 ), so why do we feel weightless? In an free falling elevator, if the F A is equal to the F G, there is no F N No force is felt feel weightless – called apparent weightlessness

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Weightlessness that you feel in a satellite is like the weightlessness in an elevator The satellite and everything on it are all accelerating toward the earth at the same rate

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