module 3

• Astronomical instruments


  Instruments used to study celestial bodies
• Tycho Brahe was able to determine the position of 777 fixed stars accurately
• Tycho Brahe


  Danish astronomer and nobleman who made accurate observations of the movement of celestial bodies
• Johannes Kepler


  German astronomer and mathematician who worked as an assistant to Brahe and formulated the three laws of planetary motion based on Brahe's extensive astronomical data
• When King Frederick II died, and the successor did not fully support Brahe's work, he moved to Prague in 1599 where he was supported by Emperor Rudolf II and worked as an imperial mathematician
• Emperor Rudolf II recommended Johannes Kepler to work for him as an assistant
• Kepler was born to a poor German family and studied as a scholar at the University of Tübingen in 1589
• Brahe and Kepler's working relationship


  Unsteady, Brahe mistrusted Kepler with his astronomical data in fear of being shadowed by his assistant
• Brahe assigned to Kepler the interpretation of his observations of Mars


  Kepler was tasked to figure out what path Mars followed as it revolved around the Sun
• Brahe gave this task to Kepler to keep him occupied and left Brahe to develop his laws of planetary motion
• Force from the Sun


  Kepler postulated that there must be a force from the Sun that moves the planets
• Kepler was able to conclude that this force would explain the orbit of Mars and the Earth, including all the other planets, moved fastest when it is nearest from the Sun and moved slowest when it is farthest from the Sun
• Brahe decided to give all his data to Kepler hoping that he would be able to prove his Tychonic system and put together new tables of astronomical data
• Rudolphine Tables


  Most accurate table known to the astronomical world, useful in determining the positions of the planets for the past 1000 years and the future 1000 years
• After Brahe died in 1601, Emperor Rudolf II assigned Kepler as the new imperial mathematician, and all of Brahe's writings, instruments, and the Rudolphine tables were passed on to him
• From Brahe's data, Kepler was able to formulate his laws of planetary motion: the law of ellipses, the law of equal areas, and the law of harmonies
• Kepler's First Law - Law of Ellipses

  Planets follow an oval or elliptical orbit, with the Sun at one focus of the ellipse
• Kepler's Second Law - Law of Equal Areas


  An imaginary line drawn from the center of the Sun to the center of a planet sweeps out an equal area of space in equal time intervals
• Kepler's Third Law - Law of Harmonies


  The square of a planet's orbital period (T2) is proportional to the cube of a planet's average distance from the Sun (R3)