How did Tycho Brahe measure time?

[jaqob]

I could have formulated this in a few different ways, and posted it in different parts of the forum, but I think this is the most fitting one, even if I think that my question is more about time keeping.

I recently watched an episode of Cosmos about Edmond Halley where parallax measurements where discussed. This got me interested, and I started to read more, especially about Tycho Brahe and his measurements. (I really appreciated this text http://cseligman.com/text/history/braheastro.htm).

Everywhere you read you find references to how he was extremely accurate, measuring the stars placement down to 2 minutes of arc (1/30 of a degree). I (think I) understand the mathematics behind the parallax measurements, and if I do, the timing of the measurement must be critical. (In the simplest case, the Earth should be facing in the exact same direction for the measurements to be directly comparable).

Attempting to summarize my question, was Tycho Brahe, around year 1600, able to measure the time of day (or night) with the needed precision to be able to compare measurements in a correct way? (Since Kepler was able to use his measurements for very impressive calculations, I assume that the answer is yes, and then my second question is how?)

(One possibility is that he "only" measured the relative position between stars, but I guess this would defeat the purpose of using parallax measurements if you believe that the distance to all stars are equal, I.e. that they are positioned on the same sphere)

 

[jbriggs444]

Everywhere you read you find references to how he was extremely accurate, measuring the stars placement down to 2 minutes of arc (1/30 of a degree). I (think I) understand the mathematics behind the parallax measurements, and if I do, the timing of the measurement must be critical. (In the simplest case, the Earth should be facing in the exact same direction for the measurements to be directly comparable).

If you want to measure a distance of one parsec using parallax, you obviously need to be able to detect an angular difference of one arc second. Let's do the math.

There are 360 degrees times 60 minutes per degree times 60 arc seconds per minute = 1.296 million arc seconds in a complete circle
There are 24 hours times 60 minutes per hour times 60 seconds per minute = 86400 seconds in a solar day.

Ignoring the discrepancy between the sidereal day and the solar day, the ratio between the two is 360/24 = 15 arc seconds per second.

The idea that Tycho Brahe was able to make celestial observations that depended on comparing celestial angles to the local vertical with a timekeeping accuracy of 1/15th of a second is... far fetched.

(One possibility is that he "only" measured the relative position between stars, but I guess this would defeat the purpose of using parallax measurements if you believe that the distance to all stars are equal, I.e. that they are positioned on the same sphere)

Yes. He measured relative positions. The negative results of Tycho's parallax measurements disprove the hypothesis that novae are near-earth phenomena.

 

[Vanadium 50]

To answer the title question, he used a clock. This is a clock that dates two centuries before Tycho.

To answer questions on parallax, one needs to use relative parallax - how much one star shifts with respect to the others.