Tycho Brahe

Cataloger of the Stars

(Image credit below)

Reconstructing Tycho

A detailed report on the construction of a star catalog, similar in nature and accuracy to Tycho's, using only angles to stars, as measured by an instrument of my own design.

David R. Skillman

Introduction and Summary

Reconstructing Tycho's Catalog

Tycho Brahe lived in Denmark in the 16th century. In the 1580s he constructed a star catalog, more accurate by a factor of 10 to 30 than the previous best catalogs available to him, those of Hipparchus and Ptolemy. He needed this catalog to provide a reference system for his other measurements of the planets, the Sun, and the Moon. His was the first improved star catalog in more than a thousand years. The high accuracy that he achieved allowed Kepler to determine the shape of the Solar System. Background on Tycho's catalog can be found here on his Wikipedia page.

When I first became aware of Tycho's work, I found myself very curious about the man and his efforts to improve astronomy. As I came to understand his star catalog efforts, which took 20 years to accomplish, I began to think about developing a project that would both honor the man and also let me experience at least part of the work he did. It made no sense to duplicate his instruments which were limited by the primitive technology of the time (late 1500s) but his observational and analysis techniques were sophisticated and could be used today. Reviewing his life's work, I was looking for 'intercept points' where I could parallel his efforts with my own tools and observations.

There were three possible intercept points: he developed his own instruments; he built his own observatory ('Uranienborg' in Danish); and he created a large data set of measurements of the stars. So that set my overall design goal of my project: build my own instrument, observatory, use them to create a data set similar to Tycho's, and produce a catalog of the stars from that data set. "Astronomy from the roots - Tycho style" as a friend put it.

Curiosity can take you to the oddest places.

Tycho was hobbled by the lack of accurate clocks. He had a set of the best clocks of the era, and they would often disagree by tens of minutes over a single day. Today, with the excellent clocks we have at our disposal, the problem of finding the east-west position of a star is almost trivial. If we set up a telescope that can only be pointed at the meridian (the circle on the sky that includes the north and south poles plus the zenith), then the east-west position (called 'right ascension') of a star on the meridian is simply related to the Universal Time (UT) on the clock.

Without good clocks, the key methodology of constructing a star catalog, in Tycho's time, was the measurement of angles and the application of spherical trigonometry. The two important classes of angles are the separation angle between two stars, and the altitude angle. Altitude angle is measured from the horizon to stars when they pass the observer's meridian (when the star is at maximum altitude).

Thus, my March 2019 goal:

Construct a star catalog, similar in accuracy to Tycho's, using only angles, as measured by an instrument of my own design.

To accomplish this goal I had to build a 4-axis telescope that could measure the separation of two stars, put it in an observatory that was convenient to use and that I could afford to maintain, perform the observations of Tycho's stars, and use this data to build a catalog 'Tycho style'. All on an amateur astronomer's budget.

I planned to reobserve the stars that Tycho included in his early catalog. The final catalog would thus be a list of about 700 stars, and their positions in the celestial coordinate system (right ascension and declination). It took about 14 months to ready the telescope and the observatory. Tentative observations started in June 2020, shortly after COVID arrived.

As the project progressed I had to make thousands of measurements of the Sun's limb in order to establish my latitude and the tilt of the Earth's axis, lots of engineering runs to learn the foibles of my instrument, thousands of measurements of meridian altitudes, and even more thousands of separation measurements. In parallel with the observational effort, I needed to develop tools to save the data, organize each night's observing plan, and monitor each night the overall progress of the data collection effort. If I missed significant data, I might have had to wait a year to reobserve a star. Tycho left few hints as to how he did the night's planning and estimating of the catalog's progress.

As a side benefit of my observations, I took advantage of my computer's clock to extract extra information from the data, information that Tycho would have loved to have but couldn't due to the poor clocks. From that I was able to make estimates of the Earth's rotation rate, Earth's orbital eccentricity, the length of the Earth's year, and the analemma.

There were a few complications that arose during the data collection: I had to avoid the region near the zenith; one of my encoders was slipping; eliminating power cables to the scope was critical; and getting a mercury mirror to provide a zenith reference, all offered challenges.

The data collection effort, which took about 18 months overall, ended in late 2021. I then needed to develop tools to turn the data into a catalog. The reduction was more complicated than I had thought, and I had to come up with iterative methods to extract the best value from the data. I did not use modern tools to create the catalog, although 'global least-squares' or 'annealing' algorithms could have done a better job than my techniques. Tycho again left no details as to how he built his catalog from his data, so I was on my own. The only tool I used that Tycho didn't have was modern spreadsheets. I used his formulas and data reduction techniques, but I ended up relying heavily on the ability of spreadsheets to 'sort' data. I don't know what Tycho did in its stead.

My catalog did finally emerge from the data in June 2022, and it was close to what Tycho had done. When checked against modern catalogs, my overall accuracy was a few arc minutes, similar to that of Tycho.

The catalog I have produced has no particular scientific value. Tycho's catalog has long been superseded in both accuracy and completeness. But it has given me a deep insight into Tycho's efforts. The point of such a project was simply to gain a better understanding of the work that went into his catalog, and to pay tribute to this man's energy, will power, and intellect from a vantage point 400 plus years later. My catalog might be the first catalog of this type built by an amateur astronomer.

To the reader: You may find this, my first try at a website, a bit awkward because I am aiming at two different audiences, the amateur astronomer and the Tycho enthusiast. Tycho himself sketched out in great detail the construction and testing of his many instruments. He also gave detailed explanations of the mathematical techniques he used in the designs. What he did not provide was a description of how he went about planning his observations, and how he took the large volume of data and turned it into a catalog. So this website contains a detailed description of the instrument I used to collect the data, my observational techniques, and a detailed look at the catalog construction process; perhaps more information than the average viewer will want.

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Below are some illustrations from Tycho's own books.

At right: Tycho pointing to a star, visible to him through a slit in a wall, directing his aides to measure the angle of the star above the horizon, using a giant protractor mounted on a wall, with no optical aid.

Lower left: Two assistants take simultaneous sightings of two different stars and measure the angle between the stars using this giant protractor, with no optical aid.

Upper left: Tycho's diagram of stars on the celestial sphere, where the separations of the stars, and their distances from the north celestial pole, are indicated.

Mid left: Tycho's calculated separations are converted to differences in right ascensions, and the sum around the globe's equator total to almost exactly 360 degrees.