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Newton’s Law of Gravitation

Newton’s Law of Gravitation. 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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Newton’s Law of Gravitation

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  1. Newton’s Law of Gravitation

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

  3. Since Fr 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

  4. 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.

  5. Equation FG = Gm1m2/ r2 G = universal constant = 6.67 x 10-11 N m2/kg2

  6. 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?

  7. 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 1024 kg

  8. Acceleration Due to Gravity FG = Gm1m2/ r2 On the earth m2 is the mass of the earth and m1 the mass of the object FG = mg mg = Gm1m2/ r2 m1cancels (this is the mass of the object) g = Gm2/ r2

  9. Example 3 What is the acceleration due to gravity on the moon which has a mass of 7.4 x 1022 kg and a radius of 1750 km?

  10. 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?

  11. 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

  12. Perception of Weightlessness There is still gravity acting in a satellite (about 8.9 m/s2), so why do we feel weightless? In an free falling elevator, if the FA is equal to the FG, there is no FN No force is felt feel weightless – called apparent weightlessness

  13. 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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