Tycho Brahe

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1 Tycho Brahe At the time of Shakespeare and Elizabeth I and Champlain Lost part of his nose in a duel over who was the best mathematician At 27 he measured the distance of a supernova and a comet to be beyond the Moon in the immutable spheres Changes in the Perfect heavenly bodies

2 Triangulation Measure baseline & angles to find distance Scale diagram or use trigonometry Bigger baseline: more accuracy, bigger distances

3 Parallax Is the apparent motion of an object due to the motion of the observer Parallax of Moon using Earth s diameter is 2 Bigger baseline gives a bigger parallax Bigger distance smaller parallax

4 Stellar Parallax Apparent motion of a star measured from one side of Earths orbit to other Not observed until Bessel in 1838 Basis of the Cosmic Distance Scale

5 Stars within 30 light years Centered on Sun Includes Sirius, Procyon, Vega & Altair New 3 rd & 4 th nearest stars

6 Discovery of Eris = UB 313 Three pictures taken 21 October 2003 Find the moving object Eris--

7 Parallax is: a. The motion of your finger held in front of your face when you switch from looking with one eye and then the other eye b. Used by your brain to judge the distance to nearby objects c. Bigger if you use a bigger baseline d. The apparent motion of a star due to the motion of the Earth around the sun e. All of these

8 Given Island of Hveen Tycho s quadrant Measured 777 stars, moon, sun and planets Accurate to a few minutes of arc great improvement Planets showed large discrepancies with Ptolemaic Model

9 Tycho s Model No measurable stellar parallax so a stationary Earth Sun orbits Earth Other planets orbit sun No parallax for supernova or comet so they are beyond Moon Very complicated scientific theory Not favored by Occam s Razor

10 Tycho s Death Tycho moved to Prague 1588 to be mathematician to Rudolph II Tycho hired Kepler to calculate orbit of Mars Tycho died mysteriously in 1601 Probably mercury from his own medicine Kepler inherited/kept/stole Tycho s data

11 Kepler Given observations of Mars When Tycho died, Kepler became Imperial Mathematician Found planet positions from triangulation over baseline of part of Earth s orbit 1609 first two laws & 1619 third law

12 Kepler s 1 st Law 1609 Kepler found Planetary orbits are ellipses - NOT off center circles With the Sun off center at one focus - NOT geocentric Half distance from Perihelion to Aphelion is Semi-major Axis

13 Eccentricity of Orbits Eccentricity of a planet s orbit is small = near circular Eccentricity of a comet s orbit is large ~.9

14 Orbit of New Dwarf Planet Eris The orbit is very elliptical It has a large eccentricity The sun is at one focus Just like Kepler s 1 st law would predict

15 Earth s Speed at Perihelion 21 March to 21 Sept not equal to 21 Sept to 21 March 10+30Apr+31May+30Jun+31July+31Aug+21Sep=184 days 9+31Oct+30Nov+31Dec+31Jan+28Feb+21Mar=181 days Perihelion (close) is 4 January and Aphelion (far) is 4 July Earth moves faster at Perihelion than at Aphelion

16 Kepler s 2 nd Law 1609 Law of Equal Areas in Equal Time A line from the planet to the sun sweeps equal areas in equal time Not uniform motion on circular orbit as Aristotle/Ptolemy assumed Planets move more quickly at perihelion than at aphelion Just like Mercury moves faster than Venus, which is faster than Earth

17

18 Sidereal Orbital Period Sidereal period: the time for a planet to orbit the sun as seen from outside solar system Synodic period: time for a planet to come back to the same configuration ie. opposition to opposition. Planet Synodic Sidereal Mercury days Venus day Mars years Jupiter years Saturn years Uranus years Neptune years Pluto years

19 Kepler s 3 rd Law 1619 P 2 (years)=a 3 (AU) A planet s orbital period P squared equals its semimajor axis A cubed Jupiter s distance from sun is 5 AU. What is its orbital period? Saturn s orbital period is 30 years. What is its distance from the sun?

20 Regarding Kepler s three laws, which if any, of the following is NOT correct? a. A planet s orbit is an ellipse with the sun at one focus b. The planets move most quickly at perihelion c. The orbital period in years squared equals the semimajor axis in astronomical units cubed d. Kepler s laws are a scientific theory that makes predictions that have been shown to be true e. All of these are correct

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