Brahe and Kepler Law

• Eccentricity


  In an ellipse, the ratio of the distance between the foci to the major axis
• Ellipse


  A closed curve for which the sum of the distances from any point on the ellipse to two points inside (called the foci) is always the same
• Focus


  (Plural: foci) One of two fixed points inside an ellipse from which the sum of the distances to any point on the ellipse is constant
• Kepler's first law


  Each planet moves around the Sun in an orbit that is an ellipse, with the Sun at one focus of the ellipse
• Kepler's second law


  The straight line joining a planet and the Sun sweeps out equal areas in space in equal intervals of time
• Kepler's third law


  The square of a planet's orbital period is directly proportional to the cube of the semimajor axis of its orbit
• Major axis


  The maximum diameter of an ellipse
• Orbit


  The path of an object that is in revolution about another object or point
• Orbital period (P)


  The time it takes an object to travel once around the Sun
• Orbital speed


  The speed at which an object (usually a planet) orbits around the mass of another object; in the case of a planet, the speed at which each planet moves along its ellipse
• Semimajor axis


  Half of the major axis of a conic section, such as an ellipse
• Tycho Brahe


  • Danish astronomer and nobleman
  • Made accurate observations of the movement of celestial bodies
  • Invented different astronomical instruments
  • Made an extensive study of the solar system
  • Determined the position of 777 fixed stars accurately
• Johannes Kepler


  • Born to a poor German family
  • Studied as a scholar at the University of Tübingen in 1589
  • Worked as an assistant to Tycho Brahe
  • Interpreted Brahe's observations of Mars
  • Formulated the three laws of planetary motion
• When King Frederick II died

  Brahe moved to Prague where he was supported by Emperor Rudolf II
• Emperor Rudolf II

  Recommended Johannes Kepler to work for him as an assistant
• Brahe and Kepler had an unsteady working relationship
• Brahe mistrusted Kepler with his astronomical data in fear of being shadowed by his assistant
• Brahe's work with Kepler

  1. Brahe assigned to Kepler the interpretation of his observations of Mars

  2. Kepler was tasked to figure out what pattern the movement of Mars did not match Brahe's calculations
• 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
• Kepler's First Law

  • Planets follow an elliptical orbit
• Kepler's Second Law

  • When an imaginary line is drawn from the center of a planet to the center of the Sun, an equal amount of space is swept in equal amount of time
• Kepler's Third Law

  • The ratio of the squares of the period of two planets is equal to the ratio of the cubes of the planets' average distance from the Sun
• Brahe was able to determine the position of 777 fixed stars accurately
• 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 had an unsteady working relationship. Kepler was Brahe's assistant. However, 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, whose movement did not match Brahe's calculations. Kepler was tasked to figure out what path Mars followed as it revolved around the Sun
• Kepler postulated that there must be a force from the Sun that moves the planets. He 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. This table was known as Rudolphine Tables, named after the Roman emperor and was 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