This document discusses how Tycho Brahe's accurate astronomical observations and data collection paved the way for Johannes Kepler's discovery of the laws of planetary motion. Brahe made extensive measurements of the positions of planets and stars. Kepler used Brahe's data to discover that planets move in elliptical orbits with the sun at one focus, that they sweep out equal areas in equal times, and that the squares of their orbital periods are proportional to the cubes of their average distances from the sun.

2. In this lesson, you will be able to explain how
Brahe's innovations and an extensive collection of data in
observational astronomy paved the way for Kepler's
discovery of the laws of planetary motion.

4. 1. Kepler discovered that planets do not go around the Sun at a uniform
speed but it depends on its position relative to the Sun. What is its speed
when it is farther from the Sun?
A. faster
B. neither fast nor slow
C. slower
D. similar to the speed when it is closer to the Sun

5. 2. Based on Kepler's First Law, which of the figures below describes the
path of a planet as it moves around the Sun?

6. 3. The accurate measurement of the positions and distances of
stars and planets in the major contribution of _________ to the
field of astronomy.
A. Johannes Kepler
B. Tycho Brahe
C. Copernicus
D. Ptolemy

7. 4. Below is Brahe’s model of the universe. What is the implication of
Brahe’s model when it comes to the idea of the center of the
universe?
A. There are two centers the Earth and the Sun.
B. The Earth, not the Sun is the center of the universe.
C. The Sun, not the Earth is the center of the universe.
D. Neither the Earth nor the Sun is the center of the
universe

8. 5. The Copernican system is based on the model of _________
A. Heliocentric model
B. Geocentric Model
C. Geo-Heliocentric model
D. Neither of the two

9. The knowledge about the universe starting from the ancient time up
to the present has proven to be a dynamic one. The discoveries weakened
the foundation of a theory that thought to be correct and widely accepted
for quite a long time. And in the process of revolutionizing the idea, one
must be able to back the claim with proof. The best proof one could present
is data that is verified and tested several times. Just like the works of Tycho
Brahe.

10. Tycho Brahe’s Contribution
The timeline of some of the who’s who in the field of astronomy
and mathematics

11. What do you call the model which
believes that the sun is the center of
the solar system?

13. What do you call the model which
believes that the earth is the center
of the solar system?

14. Ptolemy placed
the Earth at the center of
his geocentric model.
Using the data he had,
Ptolemy thought that the
universe was a set of
nested spheres
surrounding the Earth. He
believed that the Moon
was orbiting on a sphere
closest to the Earth,
followed by Mercury, then
Venus and then the Sun.

16. Differentiate the Copernican
system from the Ptolemic System

17. Brahe's model of the
universe is also called
the Tychonic model. It is
considered as a hybrid
of geocentric and
heliocentric models of
the universe.

18. Is the Tychonic Model based on
the heliocentric model or the
geocentric model? Explain.

19. It was also during this time that Brahe met the young German
mathematician Johannes Kepler. Brahe hired Kepler as a sort of
"research assistant" primarily to prove that Brahe's model the
geoheliocentric model is the right model.

20. But Kepler failed to reconcile the data on hand with the model Brahe
proposed especially on the notion of the stationary Earth. It took
another brilliant mind and his invention of the telescope to prove that
Copernicus was right in proposing that Earth after all is not the center
of the universe.

21. Three Laws of Planetary Motion
But despite everything still, something good came out of his persistence,
after about 20 years or so working with the data he got from Brahe; the Three
Laws of Planetary Motion were published in two different years

22. The First law of Planetary Motion
Law of E_ _ _ _ _ _ _

23. The First law of Planetary Motion
Law of Ellipses

24. FIRST LAW OF PLANETARY MOTION
First Law: Law of
Elliptical Orbit or Law
of Ellipses (1609)- The
planets move in elliptical
orbits with the Sun at a
focus (F1). The other
focus (F2) is empty.

25. The Second law of Planetary
Motion
Law of E_ _ _ _
A _ _ _ _

26. The Second law of Planetary
Motion
Law of Equal Areas

27. SECOND LAW OF PLANETARY MOTION
Second Law: Law of
Equal Areas
(1609)-As the
planets orbit around
the sun, the planets
cover equal areas in
equal times.

29. The Second law of Planetary
Motion
Law of P_ _ _ _ _ _

30. The Second law of Planetary
Motion
Law of Periods

31. THIRD LAW OF PLANETARY MOTION
Third Law: Law of Periods (1619)-The ratio of the squares of the
periods (the time needed for one revolution about the Sun) of any
of the two planets revolving around the Sun is equal to the ratio of
the cubes of their mean distances from the Sun.

33. Based on the result of the calculation, do
you think this is also true for other planets
and heavenly bodies?

36. 1. Which of the following is also presented by the
Greeks to prove that the Earth is spherical?
A. solar eclipse
B. sunrise and sunset
C. ships sailing seemed to be gradually
disappearing in the horizon
D. passing of the comet in Earth’s orbit

37. 2. Aside from Aristotle who among the
philosophers below believed that Earth is
spherical?
A. Pythagoras and the Mesopotamians
B. Pythagoras and Plato
C. Plato and the Mesopotamians
D. Mesopotamians and Egyptians

38. 3. Which phase of the moon is shown in the
figure?
A. full moon
B. new moon
C. first quarter moon
D. last quarter moon

39. 4. The following are astronomical phenomena that
were already observed by the ancient people even
before the telescope was invented except
_______.
A. solar eclipse
B. phases of the moon
C. craters of the moon
D. planet like Venus

40. 5. Which of the statements below describes a lunar eclipse?
A. A lunar eclipse occurs when the Earth is behind the Sun and
the moon is in front of the Sun.
B. A lunar eclipse occurs when the moon is between the Earth
and the Sun
C. A lunar eclipse occurs when the moon is forming ninety
degree-angle with the Earth.
D. A lunar eclipse occurs when the Earth is between the moon
and the Sun.

41. 6. Refer to the figure below, “phases of the moon”. Which among
the numbered figure represents the full moon?
A. 1
B. 2
C. 3
D. 4

42. 7. The accurate measurement of the positions and distances of
stars and planets in the major contribution of _________ to the
field of astronomy.
A. Johannes Kepler
B. Tycho Brahe
C. Copernicus
D. Ptolemy

43. 8. Below is Brahe’s model of the universe. What is the implication of
Brahe’s model when it comes to the idea of the center of the
universe?
A. There are two centers the Earth and the Sun.
B. The Earth, not the Sun is the center of the universe.
C. The Sun, not the Earth is the center of the universe.
D. Neither the Earth nor the Sun is the center of the
universe

44. 9. Based on Kepler's First Law, which of the figures below describes the
path of a planet as it moves around the Sun?

45. 10. Kepler discovered that planets do not go around the Sun at a uniform
speed but it depends on its position relative to the Sun. What is its speed
when it is farther from the Sun?
A. faster
B. neither fast nor slow
C. slower
D. similar to the speed when it is closer to the Sun