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Gravitation

Explore the fundamental concepts of gravity, orbits, and circular motion. Learn about Newton's Law of Universal Gravitation, elliptical and circular orbits, Kepler's laws, equations for orbital periods and speeds, and centripetal forces. Discover how objects move in space and the forces that govern their motion.

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Gravitation

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  1. Gravitation

  2. Gravitational Force • the mutual force of attraction between particles of matter • Newton’s Law of Universal Gravitation • Fg=G(m1*m2/r2) • G= 6.67x10-11 Nm/kg2

  3. Force • Force is proportional to the mass times mass • Force is inversely proportional to the distance squared or the radius squared

  4. Elliptical Orbits • http://spaceweather.com/swpod2007/23oct07/orbit.gif

  5. Elliptical orbits • Perigee greatest force • greatest velocity • smallest distance

  6. Elliptical orbits • Apogee least force • least velocity • greatest distance

  7. Circular orbits • distance is constant • velocity is constant • Fc is constant

  8. Kepler’s Laws • First Law Each planet travels in an elliptical orbit around the sun with the sun as one focal point • Second Law- An imaginary line drawn from the sun to any planet sweeps out equal areas in equal time intervals. • Third Law- The square of an orbital’s period is proportional to the cube of the average distance between the planet and the sun T2 is proportional to t3

  9. Equations • T=2π√(r3/Gm) • v=√(Gm/r)

  10. Circular Motion • = the movement of an object at constant speed around a circle with fixed radius • Axis – straight line around which rotation takes place • Rotation – object turns around an internal axis • Ex. Ice skater • Revolution – object turns around an external axis • Ex. Earth around the sun

  11. Rotational Speed • Linear speed – distance/time • Tangential speed – speed along a circular path • Rotational speed – number of rotations per unit of time • Example: Carousel horses travel at same rotational speed but different tangential speed

  12. Centripetal Force • Force that causes an object to follow a circular path • Ex. Force holding occupants safely in a rotating carnival ride • Fnet = mv2 r

  13. Centripetal Acceleration • Always points toward the center of the circular motion. • Period (T) = time needed for an object to make one complete revolution • Distance traveled = circumference • Circumference = 2πr = πd

  14. Other formulas • Centripetal Acceleration equals the velocity squared divided by the radius • Ac = v2/r • The number of revolutions equals the distance traveled divided by the circumference • Revolutions = distance/circumference

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