THE NATURE OF LIGHT, Part 1

But first, some more important things about gravity and orbits:

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Weight is the force due to gravity acting on a mass (amount of matter)
so W = m g (special case of F = m a).

  • Since gravity gets weaker a greater distances, you actually
    weigh less at the top of a building than you do at its base,
    even though your mass hasn't changed.
  • Since Atlanta is about 300 m above sea level, you weigh a little less here
    than you would in Savannah -- at sea level, and closer to the center of the earth.
  • You weigh more in an elevator as it just accelerates to go up
    and less in one that acclerates to go down and
    you are weightless in one that is falling w/o support!

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    CIRCULAR VELOCITY AND ESCAPE VELOCITY

    You ARE responsible for material in this section.

    Newton also showed that the general shape of a BOUND ORBIT
    was an ELLIPSE (with a circle as a special situation)
    and that the general shape of an ESCAPE ORBIT was a
    HYPERBOLA (with a parabola as a special case).

    The simplest case: a CIRCULAR orbit, just skimming the earth
    v_cir^2/R_E = g = G M_E/R_E^2; cancel one R_E and get
    v_cir^2 = G M_E / R_E or

  • v_cir = [ G M_E/ R_E]^{1/2} = 7.90 km s^{-1}

  • v < v_cir : ellipse with center of Earth at far focus--suborbital
  • v = v_cir : circular orbit
  • v_cir < v < v_esc : elliptical orbit w/ center of E at near focus
  • v = v_esc = (2 G M_E / R_E)^{1/2} = 2^{1/2} v_cir :
    parabolic escape orbit -- reaches infinity with no energy left
  • v > v_esc : hyperbolic escape orbit -- reaches infinity still moving away
  • For earth, v_esc = 11.2 km/s, or about 25,000 mph!

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    NEWTON COULD DERIVE KEPLER'S LAWS from
    HIS BASIC PHYSICAL ONES

    I.e. the FUNDAMENTAL LAWS can explain the EMPIRIAL ONES.

    You are not responsible for the following details in this section
    but should understand the above concept.
    I didn't have time to cover this material in class in Spring 2003.

    Consider a general circular orbit of a low mass object
    around a much more massive one:

  • v = [G m/r]^{1/2}
  • P = 2 pi r / v = 2 pi [r^3 / (Gm)]^{1/2}
  • i.e., P propto r^3/2
  • This is Kepler's Third Law!

    THIS IS ALSO HOW WE "WEIGH" -- DETERMINE THE MASS OF --
    ALL ASTRONOMICAL BODIES

  • P^2 = 4 pi^2 r^3 / (G m)
    or
  • m(total) = 4 pi^2 r^3 / (G P^2)
  • For example to get the mass of the Sun + Earth (basically just Sun)
    m = [4 pi^2/ 6.67 x 10^{-11}] [(1.496 x 10^{11} m)^3] / (3.15 x 10^7 s)^2 m = 2.0 x 10^{30} kg

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    THE NATURE OF LIGHT

    Light is an ELECTROMAGNETIC WAVE

    Light is also a PARTICLE: the PHOTON

    This nominal contradiction is an example of
    COMPLEMENTARITY in QUANTUM MECHANICS.
    Depending on circumstances it is preferable to use one or the other point of
    view for light, electrons, protons, etc.