Tycho Brahe made highly accurate astronomical observations over many years from his observatory. When Johannes Kepler gained access to Brahe's data after his death, he was able to discover the three laws of planetary motion: 1) Planets orbit the sun in ellipses, 2) They sweep out equal areas in equal times, and 3) The squares of their orbital periods are proportional to the cubes of their average distances from the sun. Kepler's laws were only possible due to Brahe's extensive, precise observations over many years providing the data needed.

1. Tycho Brahe (1546–1601) and
Johannes Kepler (1571–1630).
BRAHE’S OBSERVATIONS AND KEPLER’S
LAWS OF PLANETARY MOTION

2. I. Learning Competency with Code
• 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)

3. II. Background Information for Learners
• While Copernicus conceptually studied that the planets revolve
around the Sun, it was Kepler who correctly defined planets’ orbit.
• At the age of 27, Kepler became the assistant of a wealthy
astronomer, Tycho Brahe, who asked him to study the orbit of
Mars.
• Brahe had collected a lifetime of astronomical observations, which,
on his death, passed into Kepler’s possession.
• (Brahe, kept his observations from Kepler on Earth-centered model
of the Universe at least in part because he doesn’t want Kepler to
use them to prove that his Copernican theory is true)
• Using these observations, Kepler found out that the orbits of the
planets followed three laws.

4. Tycho Brahe
❖ Tycho Brahe (1546-1601) – a Danish
Astronomer and a nobleman known for his
accurate and comprehensive astronomical
and planetary observation.
❖ Built an observatory financed by the king
of Denmark – King Frederick II. It is known
as a naked eye observatory with over-sized
instruments (mural gradient) since the
telescope had not yet been invented.
❖ He made detailed observations and
records of the planets.
❖ He was assisted by mathematician
named Johannes Kepler.

5. • The goal is to measure the position of planets with high
accuracy.
• These instruments allowed Brahe to calculate and measure
the position of planets with high accuracy.
• He noted that previous measurements of the planets, as
recorded in the texts of the time, were incorrect.
• He was able to record the position of the planets with the
best possible accuracy for naked eye observations – ten
times more accurate than people had been getting until
then.

6. • However, Brahe was not able to detect any changes in the
positions of the stars over the year, which should occur if the
Earth revolves around the Sun.
• If he had, this would have constituted direct proof of the
Earth’s motion.
• Brahe’s model includes all the planets except Earth orbiting
around the Sun. This model satisfies all the observations
because it corresponds to reality except that is viewed from
the point of view of someone on Earth.

7. Johannes Kepler (1571-1630)
❖ A German mathematician and astronomer who
used the planet data of Tycho Brahe and developed
Three Laws of Planetary Motion.
❖ He was mistrusted by Brahe because afraid to be
outshined..
❖ His work on Martian data allowed him to
formulate the correct laws of planetary motion, thus
eventually achieving a place in the development of
astronomy far surpassing that of Brahe.
❖ Brahe’s data was kept by his family from Kepler.
Eventually Kepler retrieved the data after the death
of Brahe.
❖ Based on Brahe’s data, he was able to realize that
the orbits of the planets were ellipses, thus 3 Laws of
Planetary Motion was formulated.

8. Kepler’s Laws of Planetary Motion

9. First Law: Law of Ellipses
➢ Planets move in an elliptical orbit with the
Sun at one focus.
➢ The orbits of the planets are elliptical.
➢ Circular and elliptical orbits having the
same period and focus.
➢ Motion is not uniformly circular.
➢ The shape of the orbit is elliptical and
the Sun at one focus (R to figure 3).

10. 2nd Law: The law of equal areas
➢ The radius vector describes an equal
area in equal times.
➢ The motion is uniform but in order
for an object along an elliptical orbit to
sweep out the area at a uniform rate,
the object moves faster when the
vector radius is short and slower when
the vector radius is long
(Refer see figure 4).
➢ Planets move faster when closer to
the sun and slower when farther from
the sun.
➢ The speed at which any planet moves
through space is constantly changing

11. 3rd Law: Harmonic Law
➢ The ratio of the squares of the revolutionary periods (P) for the two
planets is equal to the ratio of the cubes of their mean distances (R)
from the sun.
P12 / P22 = R13 / R23
➢ This law was published in 1619 in his book entitled Harmonices Mundi.
➢ The period for a planet to orbit the sun increases rapidly with the
radius of the orbit.