phy53 lect dr. brown 28 october 2010
exam remarks
range 9-107 encouragement for those who got lower grade on the exam... consider how you're studying
covered as example short answer #3 -- use as diagnostic about your approach to the problem
done with mechanics -- heading to gravitation, fluids, waves ...
Galileo -- using pulse observed pendulum had constant period for given length
-- got caught up in philosophical debate Capernicous (sp), Ptolemy
a=g
Newton -- F = ma = mg , F_{ij} = -F{ji}
-- apple
F proportional to product of masses and has some distance component
reasoning -- gravitation "stuff" passes through sphere ... geometry suggests the functional form is inverse square.. so,
F = \frac{G m_1 m_2}{r^2}
how can Newton test this? take ratio of accelerations of apple and moon
parallax used to find distance to moon -- with good value for distance to moon IT CHECKED!
First law of Nature -- Newton's law of gravitation -- properly "coordinitized" as vector equation
derived Keplers 3rd Law from newton's radius of orbit cubed is proportional to square of period
kepler's 1st = planets form elliptical orbits about the sun
kepler's 2nd = planets sweep out equal areas in equal times = angular momentum over 2m ; note radial force exerts zero torque and therefore angular momentum is constant
lots of evidence from Kepler for validity of Newtons law of gravitation
We still need to know G = 6.67 x 10^{-11} ! note 'tis SMALL
[Cavandish]