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CHAPTER 8 NOTES

Dive into Kepler's Laws of Planetary Motion and Isaac Newton's Universal Gravitation. Understand the movements of planets in elliptical orbits and the gravitational forces between celestial bodies. Explore the Cavendish Experiment and Newton's approach to satellite motion.

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CHAPTER 8 NOTES

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  1. CHAPTER 8 NOTES KONICHEK

  2. I. Kepler's Laws of planetary motion. A. Was seeking an explanation of why Mars orbit was off of path of a circle as predicted by Brahe. B. Brought astronomy from a qualitative/ observational science to a quantitative/ measurement science

  3. KEPLER

  4. KEPLER’S FIRST LAW • The planets move in elliptical orbits with the sun as 1 foci

  5. Kepler’s second law-Law of areas • Planets will sweep equal area in equal times

  6. KEPLER’S THIRD LAW- The square of the periods is proportional to the cube of the average radius of the orbit

  7. B SAMPLE PROBLEM- The moon Io is 4.2 units from the center of Jupiter. It has a period of 1.8 days. The measurement of Ganymede’s orbit is 10.7 units, find the period

  8. II. UNIVERSAL GRAVITATION-Isaac Newton • A. Showed that if the planets are moving in elliptical orbits the net force acting on the planet must vary proportionally with the inverse square of the distance • 1. F 1/d2 d is the average distance between the 2 bodies • B. The product of the 2 masses involved also play a role. • 1. Noted the falling of an apple from a tree and surmised that the earth is attracting the apple, but the apple is also attracting the earth...even if it is very little • 2. Noted that the force of attraction is directly proportional to the product of the masses.

  9. C. Law of Universal Gravitation- The force of attraction is proportional to the product of the masses and inversely proportional to the square of the distance. • 1. F=G M1M2/r2 • a. G= 6.67x10-11NM2/Kg2 • b. Cavendish experiment determined the value of G

  10. CAVENDISH EXPERIMENT

  11. The apparatus constructed by Cavendish was a torsion balance made of a six-foot wooden rod suspended from a wire, with a 2 inch diameter 1.61 pound lead sphere attached to each end. Two 12 inch 348 pound lead balls were located near the smaller balls, about 9 inches away, and held in place with a separate suspension system. The experiment measured the faint gravitational attraction between the small balls and the larger ones.

  12. III. Using the law of universal gravitation • A. Planets and satellites • B. Newton reasoned if a bullet shot out of a gun with enough force from a high mountaintop it would go into orbit about the earth • 1. The parabolic motion of the projectile would be identical to the curvature of the earth. • 2. An object with a horizontal velocity of 8Km/s will keep the same altitude and circle the earth. • C. V= • D. Finding the velocity of a satellite-A satellite is 225Km above the earth’s surface. What is the orbital velocity? • E. Able to derive Keplers 3rd law

  13. PROBLEMS ARISE IN PARADISE-LETS INVESTIGATE • Theoretical concerns • There is no immediate prospect of identifying the mediator of gravity. Attempts by physicists to identify the relationship between the gravitational force and other known fundamental forces are not yet resolved, although considerable headway has been made over the last 50 years (See: Theory of everything and Standard Model). Newton himself felt the inexplicable action at a distance to be unsatisfactory (see "Newton's reservations" below).

  14. Newton's theory requires that gravitational force is transmitted instantaneously. Given classical assumptions of the nature of space and time before the development of general relativity, a propagation delay leads to unstable orbits.

  15. Disagreement with observation • Newton's theory does not fully explain the precession of the perihelion of the orbits of the planets, especially of planetMercury. There is a 43 arc second per century discrepancy between the Newtonian prediction, which arises only from the gravitational tugs of the other planets, and the observed precession

  16. The predicted deflection of light by gravity using Newton's theory is only half the deflection actually observed. General relativity is in closer agreement with the observations.

  17. The observed fact that gravitational and inertial masses are the same for all bodies is unexplained within Newton's system. General relativity takes this as a postulate. See equivalence principle

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