(^44) Kinematics and Dynamics of a Point Mass
The basic ideas of modern astronomy go back to the Polish astronomer
NICOLAUS COPERNICUS (1473-1543) and his heliocentric theory of the solar
system. Copernicus was a canon (in modern terms, senior manager) of the
cathedral at the town of Prauenburg (now Frombork) in northern Poland,
and observed the stars and planets from his home. Around 1530, he came
to the conclusion that planets in our solar system revolve around the Sun.
He was hesitant to publish his ideas, both for fear of being charged with
heresy and because of the numerous problems he could not resolve; his
work, titled De revolutionibus orbium coelestium ("On the Revolutions of
the Celestial Spheres") was finally published in 1543, apparently just a few
weeks before he died.
It took some time to formalize the heliocentric ideas mathematically,
and the key missing element was the empirical data. The main instrument
for astronomical observations, the telescope, was yet to be invented: it was
only in 1609 that Galileo Galilei made the first one. Without a telescope,
collecting the data required a lot of time and patience, but the Danish
scientist TYCHO BRAHE (1546-1601) had both. Brahe was the royal as-
tronomer and mathematician to Rudolf II, the emperor of the Holy Roman
Empire. At the observatory in Prague, the seat of the Holy Roman Empire
at that time, Brahe compiled the world's first truly accurate and complete
set of astronomical tables. His assistant, German scientist JOHANN KEPLER
(1571-1630), had been a proponent of the heliocentric theory of Coperni-
cus. After inheriting the position and all the astronomical data from Brahe
in 1601, Kepler analyzed the data for the planet Mars and formulated his
first two laws in 1609. Further investigations led him to the discovery of
the third law in 1619.
Kepler's First Law: The planets have elliptical orbits with the Sun at
one focus.
Kepler's Second Law: The radius vector from the Sun to a planet
sweeps over equal areas in equal time intervals.
Kepler's Third Law: For every planet p, the square of its period Tp of
revolution around the Sun is proportional to the cube of the average distance
Rp from the planet to the Sun. In other words, T% = KsRl, where the
number Ks is the same for every planet.
A planetary orbit has a very small eccentricity and so is close to a
circle of some mean radius R. Kepler speculated that a planet is held
in its orbit by a force of attraction between the Sun and the planet, and
Newton quantified Kepler's qualitative idea. In modern terms, we can
coco
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