Johannes Kepler (1571-1630) discovered a set of laws that accurately described the motions of the planets.

1
Johannes Kepler (1571-1630) discovered a set of
laws that accurately described the motions of the
planets.
2
(No Transcript)
3
(No Transcript)
4
Kepler was a great mathematician, but he had very
poor eyesight. This made it difficult to plot
the locations of the planets for his studies.
5
Kepler knew where to find extensive information
on the locations of planets which had been kept
for several decades.
6
These documents had been prepared and were in the
possession of Tycho Brahe.
7
Tycho Brahe (1546-1601) was born in Denmark and
was very well educated. He was very rude and
insulting to everyone.
8
He lost his nose in a duel while still a student.
After that, he wore a gold and silver
replacement which he glued in place.
9
(No Transcript)
10
(No Transcript)
11
Tychos rudeness forced him to leave Denmark in
1597 after becoming the enemy of almost everyone
important in the entire country.
12
He moved to Prague, which is close to Graz,
Austria, where Kepler just happened to be living.
Kepler came to work with Tycho in 1600.
13
They worked together trying to find a theory
explaining Tychos data. Tycho died a year
later, and Kepler inherited Brahes data (he
really stole it).
14
While Kepler was a Copernican, Brahe believed
that the Sun orbited the Earth, but that the
planets orbited the Sun.
15
Kepler set to work trying to find a principle
that would explain the observed motions of the
planets. This work would take most of the last 29
years of his life.
16
He used triangulation to plot the orbits of the
planets from Tychos data. After many years of
work he summarized the motions of the planets in
three simple laws.
17
Keplers Laws of Planetary Motion -1. The
orbital paths of the planets are elliptical,
with the Sun at one focus.
18
2. An imaginary line connecting the Sun to any
planet sweeps out equal areas of the ellipse in
equal intervals of time.
19
3. The square of a planets orbital period is
proportional to the cube of its orbital
semi-major axisP(years)2 a(a.u.)3
20
1. The planets orbits are ellipses with the Sun
at one focus.
21
The eccentricity is the ratio of the distance
between the foci to the length of the major axis.
22
Perihelion - closest approach to the
Sun.Aphelion - greatest distance from the Sun.
23
None of the planets orbits are as eccentric as
these pictures. Except for Mercury and Pluto it
would be difficult to tell that the orbit wasnt
a circle.
24
The substitution of the ellipse for the circle
was a BIG DEAL. The circle was Aristotles baby
and even Galileo was a believer in circular
motion.
25
2. An imaginary Sun to planet line sweeps out
equal areas in equal times.
26
The planets move faster when close to the Sun
and slower when farther away.
27
These two laws explained all the motions without
the need for epicycles.
28
Kepler published the first two laws in Astronomia
Nova (The New Astronomy) in 1609 proving the
laws only for Mars.
29
In 1619 he wrote Harmonice Mundi (The Harmony of
the Worlds) where he proved the first two laws
for all the known planets and added his third law.
30
3. The square of a planets orbital period is
proportional to the cube of its orbital
semi-major axis. The time taken for a planet to
orbit the Sun increases more rapidly than the
size of its orbit (measured in astronomical
units).
31
One astronomical unit is a measure of distance
equal to the average distance of the Earth from
the Sun, or the length of the semi-major axis of
Earths orbit.
32
(No Transcript)