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I am reading a book on the Coopernican Revolution where the author states that Tycho Brahe was able to make twenty times more accurate measurements than any of his predecessors.
On the other hand, I remember having heard a lecture where the speaker said that Tycho did not significantly improve measurements since Ptolemy because no new equipment (telescope) had been invented.
So, which statement is correct?
Accuracy relative to other authors is hard to estimate.
However, here's a scholarly article that shows a modern determination of the actual accuracy of Brahe's measurements in absolute terms:
http://adsbit.harvard.edu/full/1978JHA.....9...42W
The conclusion is that it depends on the instrument and it depends on the actual measurement, but as a general rule he was able to obtain an accuracy better than 1 arc minute, often down to 0.5 arcmin.
For comparison, the resolving power of the healthy, young, average human eye is around 1 arcmin. So Brahe was able to somehow make measurements with an accuracy better than the smallest details resolved by the human eye, even though there were no magnifying instruments available in his time. I believe this was achieved by averaging multiple measurements.
In other words, he was very near the limit of what was theoretically achievable before the invention of the telescope. He was certainly the best of his era by a large margin, and far better than distant predecessors such as Ptolemy. What mattered here was the methodology, and the unprecedented scale of the instruments (the armillary sphere, etc).
I've read 10 fold, not 20 but I'm not sure which is more accurate. He didn't use a telescope but that doesn't mean he didn't have new equiptment. He had equipment specially built, some of it, 10 feet high.
This article describes some of his equipment. Nobody before him used equiptment this good.
He more accurately measured the placement and precise angles in the sky of many stars and planets with 10-20 times better accuracy than anyone before him. He didn't use a telescope but that didn't matter. He didn't look deeper into the solar-system or universe, but he mapped it more accurately.
It was Brahe's accurate placement of Mars that helped Kepler work out his laws. There was even a rumor that Kepler killed Brahe to get full time use of his observatory and his notes on Mars, but exhumation provided no evidence of that. Brahe was known for his voracious appetite and partying and is thought to have died from excessive drinking.
The telescope didn't really help Kepler with his work either though he used one. Kepler's skill was primarily in mathematics, which helped him work out the laws of orbits.
Galileo, who came about the same time as Kepler, but in a different part of Europe, built a better telescope, that was also a 10 fold leap forward. The Telescope was instrumental in some of his key discoveries like Jupiter's moons and the phases of Venus. I don't know if Kepler had access to Galileo's telescope. It was considered a military secret.
