Tychonic System
image of Kepler book - New astronomyimage of marsimage of
aristarchuslink to IP fileimage of Ptolemaic system, Ptolemy; used
to make accurate predictions, even by Columbus to navigate to new
world and its accurate prediction of the date for an eclipse used
by him to impress local natives who were reluctant to provide his
crew food
Simulation of Ptolemaic retrograde motion in Mech Univ Episode
Apple and Moon starting at 8:13still used epicycles - even more so
than Ptolemy
Simulation of Coperican retrograde motion in Mech Univ Episode
Apple and MoonReymers/Ursus - rival to Brahe who published Brahe
model after visiting Hven, Brahe thought that Ursus stole the idea;
Kepler sent copies of book - Mysteries of the Cosmos - to Brahe and
Ursus with flattering letter so he could get a job! Ursus cited the
letter in his book that described the Tychonian model. Brahe hired
Kepler to analyze his data to show that the model was really his
because he could link the model to data, something that Ursus could
not do!Ptolemy and Copernicus wanted to describe motion of planets
- find a model to represent the motion and make predictions -
without any physical understanding or underlying causes; Kepler
wanted physical causes and put sun at center due to its size and
mass - it must the reason that planets move the way they do - this
lead to Newtons explanation using force of gravity; difference
between Newton and Kepler is former understood that the driving
force had to be centrally directed to make objects go in circles vs
latter who thought a tangential force pushed the planets around -
or the idea of inertia had not been developed sufficiently for
Kepler to understand the need for a centripetal force
Death of Brahe - 18 mo after Kepler hired - he clearly jealous
of Brahes data and upset he did not get ready access to it; Brahe
only gave limited access; Brahe died suddenly after overindulging
at dinner - supposedly his bladder burst; high level of mercury in
hair after body exhumed in early 20th century - but he was an
alchemist who probably used mercury in his experiments - like
Newton; recent book suggested that Kepler may have murdered Brahe
to gain access to the data?! but amateur historians unlike to be
accepted by mainstream historians!overview of analysisKeplers New
Astronomy - with 1st and 2nd laws: just one of many astronomy books
and this was hard to read and follow - so it had no major impact;
Galileo had copy but made no commentIf this cumbersome mode of
working displeases you, you may rightly pity me who had to apply it
at least seventy times with great loss of time. - quoted in I.
Peterson, Newtons Clock p 63looking for something to remain
constant - if not distance from sun (circles) or speed, then maybe
the combination or area/time
no reason behind this - later seen as angular momentum: L = rmv
= I or rotational inertia x rotational/angular velocity - again
inertia in motion but angular motion; units are rather than m/s for
motion but rv = m2/s or area per time = Keplers idea of what
remains constant as planets orbit the sun; note this is rotational
equivalent of Galileos idea of inertia - object move in straight
line in absence of outside forceLog-log plot = slope = 2/3 as
drawn; switch axes so period on Y-axis and slope = 3/2
"On the 8th of March of this year 1618, if exact information
about the time is desired, it appeared in my head. ... [but I]
rejected it as false. Finally, on May 15, it came again and ...
conquered the darkness of my mind, whereat there followed such an
excellent agreement between my seventeen years of work at the
Tychonic observations and my present deliberations ... it is
entirely certain and exact that the proportion between the periodic
times of any two planets is precisely one and a half times the
proportion of the mean distances."
Harmonice Mundi (Harmony of the World), completed in
1619http://www.fau.edu/~jordanrg/bios/Kepler/Kepler_bio.htm
Robin G Jordan Physics Dept (Florida Atlantic Univ)
In 1617 Kepler saw a copy of John Napier's famous work Mirifici
Logarithmorum Canonis Descripto on logarithms, which had been
published in 1614. He realized their importance immediately in
reducing the time-consuming tasks of computation in astronomy and
he thought that anyone using his Tables should have at their
disposal such aids. Accordingly, in 1621-1622 Kepler composed a
book that was eventually published in 1623, putting logarithm
tables in the form suitable for astronomical tables. (In fact, some
200 years later, the French mathematician Laplace said that ... by
shortening the labors, [logarithms] ... doubled the life of the
astronomer.")
- = attractive forced2 = inverse square law from Keplers 1st law
on elliptical orbits and Keplers 3rd lawradial = Keplers 2nd law -
central force does not exert a torque so angular momentum (area
swept out is constant)mM = Newtons 3rd law on equal & opposite
forces so exponents must be the same; must be equal to 1 to account
for Galileo observation that heavy objects fall at same rate at
light & Newtons 2nd lawG = constant of proportionality that
Newton never knew the value for?! Took 100 years to measure by
Henry Cavendish; Newtons calculations had to be based on ratios
& proportions"We may regard the present state of the universe
as the effect of its past and the cause of its future. An intellect
which at a certain moment would know all forces that set nature in
motion, and all positions of all items of which nature is composed,
if this intellect were also vast enough to submit these data to
analysis, it would embrace in a single formula the movements of the
greatest bodies of the universe and those of the tiniest atom; for
such an intellect nothing would be uncertain and the future just
like the past would be present before its eyes."
Hayleys comet - Image of Edmund Hayley, cometdiscovery of new
planets - Newton also saw effect of other planets on motion of
planets - perturbation theoryprecession of orbits - except part of
Mercury; gave rise to General relativity/Einstein
