BRAHE’S OBSERVATIONS AND KEPLER’S LAWS OF PLANETARY MOTION Tycho Brahe (1546–1601) and Johannes Kepler (1571–1630). 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) 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. 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. • 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. • 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. 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. Kepler’s Laws of Planetary Motion 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). 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 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.