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Universal Gravitation

Universal Gravitation. ISAAC NEWTON (1642 – 1727). The rate of acceleration due to gravity at the Earth’s surface was proportional to the Earth’s gravitational force on the Moon.

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Universal Gravitation

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  1. Universal Gravitation

  2. ISAAC NEWTON (1642 – 1727) • The rate of acceleration due to gravity at the Earth’s surface was proportional to the Earth’s gravitational force on the Moon. • The Earth’s gravitational force on the moon was inversely proportional to the square of the Earth’s distance from the moon. Fg 1/r2

  3. LAW OF UNIVERSAL GRAVITATION Fg = G (m1 m2) / r2 • m1 and m2 = masses of the 2 objects (kg) • r = center-to-center distance between the objects • G = universal gravitational constant • G = 6.67 x 10 -11 Nm2 / kg 2

  4. HENRY CAVENDISH (1731-1810) • 1798: Using a torsion balance, Cavendish measured the gravitational attraction between small objects, and calculated the value of the Universal Gravitational Constant.

  5. Gravity Near Earth’s Surface • The force of gravity is the weight of the object. Near Earth’s surface, Fg = G (m mE) / rE2 = mg G (mE) / rE2 = g • The mass of the Earth can be calculated from this: mE = g rE2/G

  6. Gravity Near Earth’s Surface • The value of g on Earth can vary due to: • Elevation and latitude (distance from center of Earth) • Variations in densities of rock. This may indicate the presence of mineral or oil deposits. • These variations are small, but can be measured with a gravimeter

  7. Satellites • Satellites are placed in orbit by “throwing” them with enough velocity that they fall around the earth. • If you give it enough speed, a satellite will escape, never to return (escape speed).

  8. TYCHO BRAHE (1546 - 1601) • Danish astronomer. • Became astronomer to the King of Denmark, and made highly detailed observations of planetary movements for over 20 years.

  9. JOHANN KEPLER (1571 - 1630) • German mathematician • 1609: Kepler publishes a book which describes the motion of the planets. • Kepler’s 1st Law: Planets move around the sun in elliptical orbits, with the sun at one focus.

  10. JOHANN KEPLER (1571 - 1630) • Kepler’s 2nd Law: A straight line connecting the sun and a planet sweeps out equal areas in equal time intervals.

  11. JOHANN KEPLER (1571 - 1630) • Kepler’s 3rd Law: The ratio of the squares of the periods T of any two planets revolving around the Sun is equal to the ratio of the cubes of their mean distances s from the Sun. (T1/T2)2 = (s1/s2)3 • Kepler’s 3rd law applies to any two bodies orbiting a common center.

  12. Kepler’s Laws and Newton’s Synthesis • Newton was able to show that: • Kepler’s Laws could be derived from universal gravitation and the laws of motion • Only an inverse-square relationship for gravitation would explain Kepler’s laws. • Deviations in the orbits predicted by Kepler’s laws (perturbations) can be used to locate undiscovered planets.

  13. Types of Forces in Nature • Four fundamental forces: • Gravitational • Electromagnetic • Strong nuclear • Weak nuclear • Physicists have unified the electromagnetic and the weak nuclear forces (electroweak force), but still seek a Grand Unified Theory • Everyday forces are due to electromagnetic and gravitational forces.

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