This for study purpose only

2. explain how Brahe’s innovations and
extensive collection of data in
observational astronomy paved the
way for Kepler’s discovery of his laws
of planetary motion
(S11/12PS-IVb-44)

5.  Danish nobleman known for
his accurate and
comprehensive
astronomical and planetary
observations.
 Born in Danish peninsula of
Scania.
 Well known in his lifetime as
an astronomer, astrologer,
and alchemist.

7. Became famous in his time because of
his improvement of celestial
knowledge.
Persuaded King Frederick II of
Denmark to give him funds and the
Hven as the site for the finest
observatory of its time.

9. Accurate measurements to about 1 minute
of arc (1/15 the diameter of the moon)

10. Stjerneborg
An observatory
means “castle of
the stars”.

11. Intended to
determine of angular
distances between
celestial bodies.

12. Measure the correct
elevation and
declination, or latitudes
and longitudes with
respect to the ecliptic.

13. Sept 10, 2003
Astronomy 100 Fall 2003

14. An astrolabe is an ancient
tool used in solving problems
that involve time and the
position of the Sun and stars.
Astrolabes can be used in timekeeping,
surveying, geography, and astronomy to
name a few disciplines. One of its most
well-known uses is navigation

15. A sextant is a doubly
reflecting navigation
instrument that measures the angular
distance between two visible objects.
The primary use of a sextant is to measure
the angle between an astronomical object
and the horizon for the purposes of celestial
navigation.

16. A quadrant is an
instrument that is used
to measure angles up to 90°. Different
versions of this instrument could be
used to calculate various readings, such
as longitude, latitude, and time of day.
It was originally proposed by Ptolemy as
a better kind of astrolabe.

17. Using the
instruments,
Brahe
continuously
recorded every
data and
deduced
results.
Most of
his
findings
were more
accurate

18. Brahe modified the geocentric
model.
He proposed an arrangement
that saved Earth at the center,
but the other planets orbited
around the sun, which also
revolved around Earth.

19. The Copernican model
was rejected by Brahe
because he felt that
Earth is not moving
around the sun.

20. It was in Prague when
Brahe met Johannes Kepler
who became his student.
Kepler inherited Brahe’s
volume of data and utilized it
to simplify the description of
planetary motion.

21. All of the planets
orbited the sun, and
the sun and the moon
orbited the Earth.
His model allowed the
path of the planet mars to cross
through the path of the sun
http://es.rice.edu/ES/humsoc/Galileo/People/tycho_brahe.html

22. Sept 10, 2003
Astronomy 100 Fall 2003

23. Sept 10, 2003
Astronomy 100 Fall 2003

24. Shows the deferent
Shows the deferent
movement and epicycle of a
movement and epicycle of a
planet as it moves around
planet as it moves around
the earth
the earth

25. Shows that the sun is
the center of the solar
system and all planets
revolve around the sun.

26. Depicts Earth in the
center. All other planets
revolve around the sun,
which also revolve around
the Earth.

27. Tycho died after two years and Kepler
inherited his data and his title:
imperial mathematician to the
emperor Rudolf II.
Kepler dutifully attempted to reconcile
the mars data using models of
Ptolemy,Copernicus, and Tycho.
None were successful at representing
Tycho’s accurate data for mars.

30. Johannes Kepler came from a poor
Protestant family in Germany.
He became aware of Copernicus’
work at the University of Tubingen,
where he completed a master’s
degree.
He then began studying theology,
but before finishing his degree he
was offered a job teaching
mathematics at a ( Lutheran) school
in Austria.
Sept 10, 2003

31. Tycho died after two years and kepler
inherited his data and his title: imperial
mathematician to the emperor Rudolf II.
Kepler dutifully attempted to reconcile
the mars data using models of
Ptolemy,Copernicus, and Tycho.
None were successful at representing
Tycho’s accurate data for mars.

32. After six years of work he gave up
attempting to use circles for the
planetary orbits.
Kepler realized Mars moves in an ellipse
around the sun.
In his Astronomia Nova (1609) he
presented his first two laws of planetary
motion.

33. E
A
S
T
W
E
S
T

34. a

35. Not a
perfect
circle, but
ellipses with
varying
eccentricity.

36. perihelion
aphelion
So, planet moves
faster at perihelion.

37. Example: Note the inequality of the
seasons: spring & summer have 93 days,
autumn has 90 days, and winter has 89
days
Earth moves faster during autumn and
winter (when it’s closer).

38. Now we need to define the often used term
Astronomical Unit or AU. This is simply the
average distance of the Earth to the Sun,
which is also about the Earth’s Semi-Major
axis. It is equal to 1.5 x 108
km. Then, we
can say that Jupiter for example is 5.2 AU
from the Sun, or 5.2 times the distance
away as the Earth. Just an easier unit.

39. Planet P (yr) a (AU) P2
a3
Mercury 0.24 0.39 0.06 0.06
Venus 0.61 0.72 0.37 0.37
Earth 1.00 1.00 1.00 1.00
Mars 1.88 1.52 3.5 3.5
Jupiter 11.86 5.20 141 141
Saturn 29.46 9.54 868 868
P2
= a3
P x P = a x a x a
Where P is in years and
a is in AU.

40.  In symbolic form: P² x a³ .
 If two quantities are proportional, we can insert
a proportionality constant, k, which depends on
the units adopted for P and a, and get an
equation:
 P²= ka³ .

41. • Kepler was a committed Pythagorean, and he
searched for 10 more years to find a
mathematical law to describe the motion of
planets around the Sun.
• In harmony of the world (1619) he enunciated
his Third Law:
• (period of orbit)² propprtional to (semi-major
axis of orbit)³

42. Works for Satellites, Moons, Comets, Asteroids,
Binary Stars… (a caveat)
Halley’s Comet returns every 76 years. What is
its semimajor axis?
P2
= a3
or a3
= 762
= 5776
so a = (5776)1/3
= 18 AU
Sept 10, 2003
Astronomy 100 Fall 2003

43. The farther away from the Sun, the longer it takes
for the planet to orbit AND the slower it’s average
orbit speed.

44. A group in Munich
is using Kepler’s
Laws to
determine the
mass of the black
hole in the center
of our galaxy
using deep near-
infrared
observations.
http://www.mpe.mpg.de/www_ir/GC/intro.html

45. By using the deepest
images of stars toward the
Galactic Center, they have
been able to detected a full
orbit of a star with a period
of 15.2 years and
Semimajor axis of 950 AU.
That means that the black
hole is about 2.6 million
solar masses!!!

47. First to systematically use the telescope (but did not invent it).
 Moon has mountains and valleys
 Milky Way consists of faint stars
 Saturn is elongated
 Venus shows phases
 Jupiter has moons (now called Galilean moons)
Sept 10, 2003
Astronomy 100 Fall 2003
Wow! Big
stuff. The
moons of
Jupiter did not
orbit the Earth!

48. Sept 10, 2003
Astronomy 100 Fall 2003
http://photojournal.jpl.nasa.gov/catalog/PIA01299
Geocentric Cosmology was still preferred model of the
Universe and Galileo was declared a Heretic and spent years
under house arrest.

49. What was the
problem? Galileo’s
observations
directly challenged
the Geocentric view
that was held by the
church. And there
was still no why.
Sept 10, 2003
Astronomy 100 Fall 2003
http://antwrp.gsfc.nasa.gov/apod/ap010116.html

50. Could not be explained with the Geocentric model
Sept 10, 2003
Astronomy 100 Fall 2003
http://www.calvin.edu/academic/phys/observatory/images/venus/venusb.html

51. Compare the Heliocentric to Geocentric
models to explain the phases of Venus.
http://www.astro.ubc.ca/~scharein/a310/SolSysE
x/phases/Phases.html
Sept 10, 2003
Astronomy 100 Fall 2003

52.  Disproved Ptolemaic system
 Rome bullied him into recanting (cleared
in 1992)
 Now we understand the motions and the
fact that the solar system MUST be
Heliocentric, but now we need a reason
why?
Sept 10, 2003
Astronomy 100 Fall 2003

53. Kepler discovered these patterns in nature by
using the data that Tycho collected, BUT the
world had to wait until someone could
understand the Natural Law that predicts
Kepler’s Laws.
The real problem: On Earth we’re use to things
that move but always come quickly to a rest. Why
didn’t the planets stop?
Sept 10, 2003
Astronomy 100 Fall 2003

54.  Gave us a reason
why-- GRAVITY.
 Developed
fundamental laws
of nature.
 Kepler’s 3rd
law
now became a way
to probe the
structure of the
Universe!
Sept 10, 2003
Astronomy 100 Fall 2003