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10.1Kepler’s Laws
Newton wouldn’t have been able to figure out why the planets move the
way they do if it hadn’t been for the astronomer Tycho Brahe (1546-1601)
and his protege Johannes Kepler (1571-1630), who together came up with
the first simple and accurate description of how the planets actually do
move. The difficulty of their task is suggested by the figure below, which
shows how the relatively simple orbital motions of the earth and Mars
combine so that as seen from earth Mars appears to be staggering in loops
like a drunken sailor.
sun
earth's orbit
Mars' orbit
Jan 1
Feb 1
Mar 1
Apr 1May 1
Jun 1
Jul 1
Aug 1
As the earth
and Mars
revolve around
the sun at different
rates, the combined
effect of their motions
makes Mars appear to
trace a strange, looped
path across the back-
ground of the distant
stars.
Brahe, the last of the great naked-eye astronomers, collected extensive
data on the motions of the planets over a period of many years, taking the
giant step from the previous observations’ accuracy of about 10 seconds of
arc (10/60 of a degree) to an unprecedented 1 second. The quality of his
work is all the more remarkable considering that his observatory consisted
of four giant brass protractors mounted upright in his castle in Denmark.
Four different observers would simultaneously measure the position of a
planet in order to check for mistakes and reduce random errors.
With Brahe’s death, it fell to his former assistant Kepler to try to make
some sense out of the volumes of data. Kepler, in contradiction to his late
boss, had formed a prejudice, a correct one as it turned out, in favor of the
theory that the earth and planets revolved around the sun, rather than the
earth staying fixed and everything rotating about it. Although motion is
relative, it is not just a matter of opinion what circles what. The earth’s
rotation and revolution about the sun make it a noninertial reference frame,
which causes detectable violations of Newton’s laws when one attempts to
describe sufficiently precise experiments in the earth-fixed frame. Although
such direct experiments were not carried out until the 19th century, what
Tycho Brahe made his name as an
astronomer by showing that the bright
new star, today called a supernova,
that appeared in the skies in 1572 was
far beyond the Earth’s atmosphere.
This, along with Galileo’s discovery of
sunspots, showed that contrary to Ar-
istotle, the heavens were not perfect
and unchanging. Brahe’s fame as an
astronomer brought him patronage
from King Frederick II, allowing him to
carry out his historic high-precision
measurements of the planets’ motions.
A contradictory character, Brahe en-
joyed lecturing other nobles about the
evils of dueling, but had lost his own
nose in a youthful duel and had it re-
placed with a prosthesis made of an
alloy of gold and silver. Willing to en-
dure scandal in order to marry a peas-
ant, he nevertheless used the feudal
powers given to him by the king to
impose harsh forced labor on the in-
habitants of his parishes. The result
of their work, an Italian-style palace
with an observatory on top, surely
ranks as one of the most luxurious
science labs ever built. When the king
died and his son reduced Brahe’s privi-
leges, Brahe left in a huff for a new
position in Prague, taking his data with
him. He died of a ruptured bladder af-
ter falling from a wagon on the way
home from a party — in those days, it
was considered rude to leave the din-
ner table to relieve oneself.
Chapter 10Gravity