###### By Robert M. Hazen, Ph.D., George Mason University

## Danish astronomer Tycho Brahe designed and constructed greatly improved astronomical instruments. This increased the accuracy of measurements. Tycho’s assistant Johannes Kepler was a mathematician who used his observations of the heavens to validate the Copernican model.

### Tycho Rises to Fame and Favor

Tycho, as he is generally called, rose to great fame at an early age and enjoyed the favors of the Danish king, King Frederick II, who lavishly supported his astronomical research.

The young Tycho first came into prominence in 1572 at the age of 27 when he discovered a new bright star, a supernova, which is an exploding star. He discovered this in the constellation Cassiopeia, and for 18 months he detailed the gradual dimming of that star.

These observations demonstrated the then astonishing idea that the heavens themselves are not immutable, that they can change from year to year. This added new impetus to the idea that the heavens should be studied and that this should be an ongoing process as opposed to just taking everything that Aristotle had said on faith.

King Frederick II of Denmark and Norway rewarded him by giving him title to an island, the island of Hven, which is located between Denmark and Sweden. On that island, the king had a great castle and observatory built, as well as workshops for the construction of the new equipment that Tycho designed.

Tycho spent more than 20 years on the island constructing these astronomical instruments and making various astronomical observations.

Learn more about the study of astronomy.

### Improved Astronomical Instruments

Tycho Brahe’s principal task was in improving astronomical observations with new instruments and then using those instruments to test the Ptolemaic and Copernican systems. He designed devices called quadrants and sextants. These devices would locate the position of stars and planets in the heavens. They were quite different from modern telescopes and didn’t employ lenses. They were just basically glorified gun sights, but very beautifully crafted gun sights.

An angle around from the horizon would be measured and an angle up, and he would sight a particular object at a particular time and place. Tycho had very elaborate instruments, which were adjusted for thermal contraction of the cold night air. He had very accurate timepieces to make sure he knew exactly when he was making his measurements.

Before Tycho, the position of a dime at perhaps 20 feet away could be measured. By the time that Tycho Brahe was finished with his new instruments, the position of a dime at more than 100 yards away could be measured.

Tycho used his instruments to check the accuracy of the Ptolemaic and Copernican models for the movements of planets. For example, Tycho used both models to locate Mars, but the position of Mars was not exactly where either model predicted. So Tycho came up with his own model, which is a rather complex combination of Copernican and Ptolemaic ideas.

Tycho’s story reveals why improved instruments are so important in science. Often, it is an improved instrument with greatly reduced errors that provides new insight.

This is a transcript from the video series

The Joy of Science. Watch it now, on Wondrium.

### Kepler’s Laws of Planetary Motion

Upon Tycho Brahe’s death in 1601, his data fell into the hands of his mathematically gifted assistant, the German mathematician Johannes Kepler. Kepler had become Tycho’s assistant in about 1600, and he carried on the work at the observatories.

He kept making measurements of Mars and other planets, for example.

Kepler was a mathematician, and he was able to take those numbers and fit the path of the planets to a mathematical equation, and this is seen as Kepler’s great advantage. He saw a great harmony, a great order to the natural world, and he derived three great laws of planetary motion.

The first of these laws describes the shape of planetary orbits. Kepler says the planetary orbits are elliptical, with the Sun at one focus.

His second law is that the speed that the planet travels as it is going around the Sun is not constant. When it is close to the Sun, it travels very fast. When it is far away, it travels more slowly.

### Kepler’s Third Law in Practice

The third law is a mathematical relationship of exactly how fast a planet travels depending on its distance. Kepler’s third law is as follows: the square of a planet’s orbital period is proportional to the cube of the average distance from the Sun.

Kepler’s theories, in particular the third one, allowed people to learn many things about other planets. For example, how far away Jupiter is from the Sun can be calculated, just by knowing its orbital period. It takes Jupiter 12 years to travel from one part of the zodiac, all the way around back to the same part of the zodiac.

According to Kepler’s third law, the period squared (P^{2}) over the average distance cubed (D^{3}) for Earth will be the same as P^{2}/D^{3} for Jupiter. For the Earth, P^{2}/D^{3 }is 1. So, for Jupiter, P^{2} is 144, which is equal to D^{3}. So, the distance to Jupiter is the cubed root of 144, or 5.2 astronomical units, 5.2 times the distance from the Sun to the Earth.

Learn more about celestial and terrestrial mechanics.

### Logic in a Superstitious World

In the introduction to his 1619 work called *Harmony of the World*, which introduced the third law, Kepler says,

At last I have found it, and my hopes and expectations are proven to be true that natural harmonies are present in the heavenly movements—both in their totality and in detail—though not in a matter which I had previously imagined, but in another, more perfect manner.

In spite of this mathematical logic he had discovered in the heavens, Kepler still had to contend with a superstitious world. In 1615, even as he was writing *Harmony of the World*, he had to go to his mother’s hometown and testify and defend her at her trial.

Tycho had invented the fine instruments that Kepler had used to generate the equations that demonstrated how the planets moved in the skies, moving closer to a better and more scientific understanding of the world.

### Common Questions about Tycho Brahe and Johannes Kepler

**Q. How did Tycho Brahe become famous?**

Tycho Brahe first came into prominence in 1572 at the age of 27 when he discovered a new bright star, a supernova, which is an exploding star. He discovered this in the constellation Cassiopeia, and for 18 months he detailed the gradual dimming of that star.

**Q. What was Tycho Brahe’s contribution to astronomy?**

Tycho Brahe’s principal task was in improving astronomical observations with new instruments like quadrants and sextants.

**Q. Who was Johannes Kepler?**

Johannes Kepler was a German mathematician astronomer, who was an assistant to Tycho Brahe. He continued Tycho’s observations and used the notes of his senior to develop the laws of planetary motion.