Summary of Brahe's Contributions

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, although Brahe did not interpret the absence of parallax for stars correctly, as we discuss below.

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.

Now back to Galileo for just a bit:

Key among his investigations are:

• developed the concept of motion in terms of velocity (speed and direction) through the use of inclined planes.
• developed the idea of force, as a cause for motion.
• determined that the natural state of an object is rest or uniform motion, i.e. objects always have a velocity, sometimes that velocity has a magnitude of zero = rest.
• objects resist change in motion, which is called inertia.

Kepler's (1571-1630) laws of Planetary Motion:

Kepler developed, using Tycho Brahe's observations, the first kinematic description of orbits, Newton will develop a dynamic description that involves the underlying influence (gravity)

Note: It was crucial to Kepler's method of checking possible orbits against observations that he have an idea of what should be accepted as adequate agreement. From this arises the first explicit use of the concept of observational error .

• 1st law (law of elliptic orbits): Each planet moves in an elliptical orbit with the Sun at one focus.

Ellipses that are highly flattened have high eccentricity. Ellipses that are close to a circle have low eccentricity.
• 2nd law (law of equal areas): a line connection the Sun and a planet (called the radius vector) sweeps out equal areas in equal times

Objects travel fastest at the low point of their orbit, and travel slowest at the high point of their orbit.
• 3rd law (law of harmonics): The square of a planet's orbital period is proportional to its mean distance from the Sun cubed.

The 3rd law is used to develop a ``yardstick'' for the Solar System, expressing the distance to all the planets relative to Earth's orbit by just knowing their period (timing how long it takes for them to go around the Sun).