Parallax and Tycho Brahe

Tycho Brahe (1546-1601) proposed an experiment that would determine whether or not the earth goes around the sun. Basically, if the Earth orbits the sun, nearby stars should periodically "move" back and forth in their position with respect to more distant stars every 6 months. If the Earth was stationary (at the center of the Universe, this wouldn't occur.

Schematic Representation of stellar Parallax.

Distant stars act as a fixed reference coordinate system. "1" and "2" correspond to Earth's position relative to the Sun 6 months apart and circle in the center represents the Sun. Nearby stars, when observed at these two positions will show a small movement with respect to the background of fixed stars. At position 1, the nearby star would be viewed against a background that contained star B while 6 months later, at position 2, the nearby star would be viewed against a background that contained star A. This shift in the background position is measured in angles (theta) - a convenient way to measure distances projected on the sky (divide the sky into 360 degrees). The unit of measurement is an arcsecond, 1/3600th of a degree. Note, the nearer the star the bigger the shift the nearby star makes against the background. Note that the nearest stars produce parallax shifts less than 1". This means more distant stars produce smaller shifts.

A visualization of Parallax. Notice that the bigger the eye separation or "orbit", the bigger the shift.

He built a very elaborate observatory at Ven that made elaborate use of siting tubes but no telescopes since they hadn't been invented yet!

He essentially used a series of long "sextans" that could measure fairly accurately the angle of a star above the horizon. The azimuth (the direction parallel to the horizon) was measured in degrees from some starting point in this circular observatory out portals that were equally spaced around the floor.

His observatory allowed him to take relatively precise data for measuring the position of Mars night after night.

Upon failing to detect stellar parallax he proposed this strange hybrid model for the solar system which actually opens up more questions. Fortunately, this model didn't last very long.

Tycho Brahe's universe: The Earth is at the center; Planets orbit the Sun which in turn orbits the Earth.

1. He made the most precise observations that had yet been made by devising the best instruments available before the invention of the telescope.

2. His observations of planetary motion, particularly that of Mars, provided the crucial data for later astronomers like Kepler to construct our present model of the solar system.

3. He made observations of a supernova (literally: nova= "new star") in 1572 (we now know that a supernova is an exploding star, not a new star).

   This was a "star" that appeared suddenly where none had been seen before, and was visible for about 18 months before fading from view. Since this clearly represented a change in the sky, prevailing opinion held that the supernova was not really a star but some local phenomenon in the atmosphere (remember: the heavens were supposed to be unchanging in the Aristotelian view). Brahe's meticulous observations showed that the supernova did not change positions with respect to the other stars (no parallax). Therefore, it was a real star, not a local object. This was early evidence against the immutable nature of the heavens.

   

4. Brahe made careful observations of a comet in 1577. By measuring the parallax for the comet, he was able to show that the comet was further away than the Moon. This contradicted the teachings of Aristotle, who had held that comets were atmospheric phenomena ("gases burning in the atmosphere" was a common explanation among Aristotelians). As for the case of the supernova, comets represented an obvious change in a celestial sphere that was supposed to be unchanging; furthermore, it was very difficult to ascribe uniform circular motion to a comet.

5. He made the best measurements that had yet been made in the search for stellar parallax. Upon finding no parallax for the stars, he (correctly) concluded that either
   • the earth was motionless at the center of the Universe, or

   • the stars were so far away that their parallax was too small to measure.

   Not for the only time in human thought, a great thinker formulated a pivotal question correctly, but then made the wrong choice of possible answers: Brahe did not believe that the stars could possibly be so far away and so concluded that the Earth was the center of the Universe and that Copernicus was wrong.

6. Brahe proposed a model of the Solar System that was intermediate between the Ptolemaic and Copernican models (it had the Earth at the center). It proved to be incorrect, but was the most widely accepted model of the Solar System for a time.