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Unraveling Newton's Law of Gravitation: The Universal Force Behind Moon's Orbit

Delve into Sir Isaac Newton's groundbreaking insight on gravity, exploring its implications on celestial bodies like the Moon and Earth's orbit. Understand gravity's role in circular motion, planetary orbits, and the concept of weightlessness. Discover the gravity's mysterious force and its impact on the laws of physics.

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Unraveling Newton's Law of Gravitation: The Universal Force Behind Moon's Orbit

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  1. Gravity And---Sir Isaac Newton: The Universal Law of Gravitation

  2. 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.

  3. 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. Source: http://csep10.phys.utk.edu/astr161/lect/history/newtongrav.html

  4. 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.

  5. First, What is gravity? • An attractive force between two objects that depend upon the masses of the objects and the distance between them. • https://www.youtube.com/watch?v=mezkHBPLZ4A • https://www.youtube.com/watch?v=EwY6p-r_hyU

  6. 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.

  7. Newton’s law of Universal Gravitation First, let’s get some background information https://www.youtube.com/watch?v=7gf6YpdvtE0

  8. Newton’s law of Universal Gravitation

  9. 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.

  10. 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

  11. Weight and Mass

  12. 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.

  13. The Weight of an Apple?

  14. Gravity and Orbits • Centripetal acceleration • ac= v2/r • Centripetal Force • Fc= mac • The force in circular motion is directed towards the center - centripetal

  15. So why is the earth round? • Because of gravitation – earth attracted itself together. • https://www.youtube.com/watch?v=T4WjyTV98lg Is the Earth Flat? • https://www.youtube.com/watch?v=uFIs7AZ8pOw How do we know it is round.

  16. 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. • http://studyjams.scholastic.com/studyjams/jams/science/solar-system/sgravity-and-inertia.htm

  17. Weightlessness

  18. 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

  19. 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

  20. 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

  21. Circular Motion • When an object moves in a circle at constant speed, we describe it as undergoing uniform circular motion. • Its speed is constant, but its velocity is not because velocity includes direction and the object’s direction is clearly changing.

  22. Circular Motion • A changing velocity means acceleration. • The pull on the string is always directed perpendicular to the velocity. • The pull accelerates the ball into a circular path, even though the ball does not speed up or slow down. • The pull changes only the direction of the velocity, not the magnitude.

  23. Centripetal Acceleration • The acceleration arising from the change in direction of the velocity vector is called the centripetal acceleration and is determined mathematically by:

  24. Gravity can be a Centripetal Force

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