NEWTON'S LAWS OF MOTION and GRAVITY

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NEW TECHNOLOGY & NEW EVIDENCE

GALILEO Galilei (1564--1642) taught mathematics and astronomy at Padua.

He performed EXPERIMENTS: e.g., balls rolling down inclined planes and
learned about INERTIA.

Galileo Built a TELESCOPE in 1608. Instead of commercial or military use
GALILEO POINTED IT AT THE SKY and DISCOVERED:

  • The LUNAR TERMINATOR WAS IRREGULAR: it had MOUNTAINS
    and WASN'T A PERFECT SPHERE.
  • PLANETS LOOKED LIKE DISKS, STARS STILL LOOKED LIKE POINTS.
  • MILKY WAY IS COMPRISED OF MANY STARS --- many fainter stars could be seen
    between those visible to the naked eye
  • VENUS WENT THROUGH PHASES (including a Full phase, not
    possible in Ptolemaic model) --- reflecting light from the Sun
    A real proof that the Heliocentric Picture was better than the Geocentric!
  • THE SUN HAD SPOTS --- the most perfect of all heavenly bodies had blemishes.
    He could measure that the sun rotated using the spot motions.
  • JUPITER HAD FOUR MOONS --- something other than Earth had things
    going around it

    All of these discoveries, published in 1610 Sidereus nuncius,
    challenged the Aristotlean / Catholic picture of the Universe ---
    perfect spheres shining by themselves, perfect circular orbits,
    only the Earth at the center of everything.

    While he had already thought Copernicus' model was best Galileo felt
    this DATA had PROVEN it.

    While others in Germany, England, etc., confirmed these discoveries and accepted the
    HELIOCENTRIC PICTURE, the response in Rome wasn't very good: although Vatican
    astronomers confirmed his observations, they didn't accept his logic and demanded
    that Copernicus' model not be taught.

  • Galileo was ordered to stop supporting this view, and he became more circumspect,
    finally publishing a Dialog Concerning the Two Chief World Systems in Italian in 1632.
  • After facing the Inquisition and nominally renouncing his ideas,
    he was placed under house arrest in 1633.

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    MATHEMATICS AND UNDERSTANDING

    Isaac NEWTON (1642--1727) of Woolsthorpe, England is arguably
    the most important scientist in history.

    His work completely changed the way educated people looked at the world.

    Effectively, Newton was the founder of PHYSICS as well as
    THEORETICAL ASTRONOMY

    HE CO-INVENTED THE CALCULUS
    (but Leibnitz, who invented it independently, had better notation)

    HE DID PIONEERING WORK IN OPTICS: PRISM, REFLECTING TELESCOPE

    MECHANICS AND GRAVITY: his Philosophiae Naturalis Principia Mathematica,
    published in 1684, reflected work he'd mostly done in 1665-1666 when plague closed Cambridge.

    Newton was knighted, and became first president of the Royal Society,
    later Director of the Mint.

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    NEWTON'S LAWS OF MOTION

    1. An object at rest remains at rest and an object moving at a
    certain velocity retains that velocity unless a FORCE acts on it.

    Aristotle's view was that forces were needed merely to keep
    something moving at a constant speed, but Newton realized friction or air resistance
    were forces that slowed things down; Galileo had already understood this.

    2. The rate of change of velocity, or ACCELERATION, EQUALS FORCE DIVIDED BY MASS.

    The core of Newtonian mechanics, it allows trajectories of
    cannon balls, rockets, planets, comets, stars and galaxies to be computed.

  • F = m a
    is the most important relation in physics;
    one can equivalently write
  • a = F/m
  • This clearly says less massive objects obtain larger
    accelerations from the same force.

  • Think of stepping on the gas and going from 0 mph to 60 mph
    in 10 seconds: your acceleration is 6 mph/s (forwards)
  • Breaking takes you from 60 mph back to 0 in 6 seconds or a negative acceleration of 10 mph/s.
  • These are VECTOR equations -- with magnitude and direction
  • Velocity = distance/time -- both the Speed and Direction are needed
  • I.e. 50 mph to the East is the same speed, but different
    velocity    , from 50 mph to the North,
  • and going around a curve at a constant speed DOES involve an
    acceleration (you feel pushed to one side of the car, right?)

    3. EVERY ACTION (FORCE) HAS AN EQUAL AND OPPOSITE REACTION.

    Forces don't act in isolation:

  • the Earth pulls the Moon and the Moon pulls back on the Earth;
  • we push down and back on the ground with our muscles, it pushes us up and forward;
  • a rocket expels gases rearward and it flies forward.

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    NEWTON'S LAW OF GRAVITY

    The ATTRACTIVE FORCE OF GRAVITY IS DIRECTLY PROPORTIONAL TO THE
    PRODUCT OF THE MASSES AND INVERSELY PROPORTIONAL TO THE
    SQUARE OF THE DISTANCE BETWEEN THEM.

    or

    F = G m_1 m_2 / d^2

  • where G = 6.673 x 10^{-11} m^3 kg^-1 s^-2

    Combine with his SECOND LAW OF MOTION:
    the ACCELERATION DUE TO GRAVITY OF AN OBJECT IS PROPORTIONAL
    TO ITS MASS AND INVERSELY PROPORTIONAL TO THE
    SQUARE OF THE DISTANCE FROM ITS CENTER.

  • a = F/m
  • Here we call the acceleration due to gravity, g and
    g = F_grav/m_2 = G m_1 m_2 / (d^2 m_2)
    g = G m_1 / d^2

  • Example: if m_1 = M_E(arth) and d = R_E we have
    g = [6.673 x 10^{-11} m^3 kg^-1 s^-2] [5.974 x 10^{24} kg] / (6.378 x 10^6 m)^2
    g = 9.80 m s^{-2} (or 32 ft/s^2)
    YOU SHOULD VERIFY THIS CALCULATION!