Universal Gravitation Sir Isaac Newton: The Universal Law of Gravitation


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Universal Gravitation

  • Sir Isaac Newton: The Universal Law of Gravitation


The Falling Apple

  • Newton reasoned the moon is falling for the same reason the apple falls – they are both pulled by the Earth’s gravity.



Newton’s Excellent Idea

  • Now came Newton's truly brilliant insight: if the force of gravity reaches to the top of the highest tree, might it not reach even further; in particular, might it not reach all the way to the orbit of the Moon! Then, the orbit of the Moon about the Earth could be a consequence of the gravitational force, because the acceleration due to gravity could change the velocity of the Moon in just such a way that it followed an orbit around the earth.



The Falling Moon

  • Newton’s First law:

    • An object (the moon) will remain in motion in a straight line unless acted on by an outside unbalanced force (gravitational attraction)
  • The force that pulls an apple to the ground also keeps the moon in orbit.



The Falling Earth

  • Newton’s theory of gravitation confirmed the Copernican theory of the solar system.

  • A planets tangential speed allows the planets to orbit the sun without being pulled into it.



Newton’s law of Universal Gravitation



The Gravitational Constant Henry Cavendish 1798

  • He used a device with two objects on a rod that was hung on a wire. These masses were attracted to two larger objects, twisting the rod slightly. The measurement of the masses, distance between them and the torque on the wire allowed G to be determined.



The Universal Gravitational Constant – A G-thing

  • G is a constant of proportionality.

  • The magnitude is the force exerted by two 1-kg masses 1 meter apart.

  • G = 6.67 x 10-11 Nm2/kg2



Weight and Mass



Gravity and Distance: The Inverse Square Law

  • A quantity varies as the inverse square of its distance from its source

  • A localized source spreads evenly throughout the surrounding space.



The Weight of an Apple?



Gravity and Orbits

  • Centripetal acceleration

    • ac= v2/r
  • Centripetal Force

    • Fc= mac
  • The force in circular motion is directed towards the center - centripetal



Why is the Earth round?

  • Because of gravitation – earth attracted itself together.

  • The deviation of a planet from its normal orbit is called a perturbation. It is caused by other planets.



Reviewing

  • Objects orbiting around the Earth are actually falling toward Earth but have great enough tangential velocity to avoid hitting the earth.

  • Everything pulls on everything else with a force that depends on the mass of the objects and distances between them.

  • Gravitation decreases according to the inverse square law.



Geosynchronous Orbits



GPS



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