So you’re interested in coming to help do some observations with the quadrant, but not sure if you can really help since you’re not a science person. This post should get you started!
Bit of History
First off, the instrument we’re using was built by this guy, Tycho Brahe.
Brahe was a Danish nobleman which meant that he was supposed to rule over some land given to him by the king. But Tycho wasn’t particularly interested in that. He wanted to study the sciences. However, because the king had a fondness for Tycho’s family, when he got word that Tycho was planning on running off to study elsewhere, the king made Tycho an amazing offer: His own island to be lord of, where he could set up his own scientific observatory with a generous royal allowance.
Tycho gratefully accepted and set up his own castle observatory of Uraniborg. His goal was to take the most accurate measurements of things in the sky to hopefully refine the competing models of geocentrism (Ptolemy) and heliocentrism (Copernicus).
To that end, over the next few decades, Tycho built numerous instruments to help measure the position of things in the sky and amassed a huge collection of data. The problem was that it didn’t help solve the problem between the competing models; neither one fit the data better than the other.
Tycho tried developing his own model which was hybrid of the two in which the earth was at the center, the sun went around the earth, and everything else went around the sun. But it didn’t work either.
Later, Tycho hired Johannes Kepler to help make his model work. Tycho died in 1601 and Kepler kept working but ultimately found Tycho’s model to be impossible to fit to the data, and so Kepler turned his attention to the Copernican heliocentric model, revising it to have elliptical orbits instead of circular ones, which made the model fit the data beautifully.
What are we trying to do?
To begin, the objective is to simply collect lots of data like Tycho did. This is the raw material to do anything else with. And there’s a few things that I’d like to get out of this data.
First, we know that Tycho’s instruments were impressively accurate. If we draw a circle across the whole sky, it would be 360º. If each degree is divided into 60 minutes of arc, and each minute divided into 60 seconds, Tycho’s best instruments were capable of measuring down to 40 seconds of arc, which is about 0.01º. Although the quadrant I’ve constructed is done using modern methods, this should still give a feel for how well constructed Tycho’s must have been in relation.
Second, shortly after Tycho’s death Johann Bayer published a star atlas known as the Uranometria.
Prior to this, star maps were not drawn using actual data. They were done as artist’s interpretations and hardly accurate. Collecting positions on enough stars to produce a detailed star map is another goal.
Third, as noted above, Kepler used Tycho’s data to refine the Copernican model. Specifically, he used Mars (which was the hardest to fit the data). This is another goal in the project and by far the hardest to achieve. The reason is that we can’t presume to know the orbit of earth. As such, only observations when Mars is directly opposite the earth from the sun can be used. This only happens about every 2 years. Thus, to have enough observations to accurately determine the orbit will require about a decade.
How does it work?
All of the objectives above center around one thing: Determining the positions of stars in the sky. In other words, we’re trying to find some sort of coordinates for each object. Just like in a graph from elementary school, we need two coordinates: a “left-right” and an “up-down”. Since stars are all so far away that we can’t perceive their distances without advanced equipment, we don’t need to worry about that.
For the “left-right” we find the point on the horizon directly below the star and measure that from north. So we start at north on the horizon, going through east, south, west, and back to north making a full 360º. Thus, north is 0º, east is 90º, south is 180º, and west is 270º. This is called the Azimuth.
For the “up-down” we start at the point on the horizon directly beneath the star, and measure the angle above the horizon. Thus if the star is on the horizon, it’s 0º and if it’s straight up, it’s 90º. This is called the Altitude.
The trouble with this? The sky rotates. This Alt-Az coordinate system is fixed to our horizon and doesn’t move with it. So what we really want is a coordinate system that rotates with the sky. Fortunately, we can use some equations to convert between the systems. It takes a few more pieces of information (specifically the latitude and something known as the sidereal time), but in short, what we’re after on a night-to-night basis is the altitude and azimuth.
But with the quadrant as designed, we actually eliminate one of these variables. Instead of swiveling the quadrant all around to chase stars at all sorts of different azimuths, we set the quadrant up so it’s aligned along the north-south line, known as the meridian, and wait for stars to rotate across this line. This means their azimuth will always be 0º if they’re in the north, or 180º if they’re in the south.
How to observe?
The operation of this instrument takes at least two people, preferably three. One person must be responsible for sighting the star. Other tasks involve taking the reading, and recording the observation.
While this project does have a list of target stars, we have found it most effective to simply target any star crossing the meridian. We do not initially worry about which star we’re observing, but instead, find it on a star chart and number it, and associate the measurement with the number. We can then look up the star after the fact.
For each star, there are a few important values to record: The altitude, the azimuth, and the sidereal time. The altitude is what we’re measuring. Since we’re only targeting stars on the meridian, the azimuth is either 0º (north) or 180º (south). The sidereal time we get from a phone app since getting it other ways is far more difficult and would require measuring the angle between the sun and Venus, and then Venus and the target star. Not only is this a difficult measurement to make, but it would also require a greater time commitment as it would require starting before sunset every time, and limit the window observations to only times when Venus was visible.
The most challenging of these jobs is being the one that sights the object. There’s several reasons for this. The first is that learning to know how to sight a star is challenging. While the quadrant does have sights, we have found that they are nearly impossible to see in the dark which makes them difficult to use.
Instead, we have found that it is best to bring your eye to a level where the star is just above the far end of the sighting arm. If you move your head down any, the star should disappear behind the arm.
From there, bring the near end of the arm up. You will see that the near end is fuzzy in your vision since you cannot focus on the near end at the same time as the far end. Bring this up until the star appears in the fuzz. From there, small adjustments will be necessary as moving the near end up moved the far end down, changing its relative position to the star. The objective is to get the star just above the far end and in the fuzz at the same time. It takes a bit of practice.
The second challenge is that many of the stars we observe are quite faint. Observing conditions at the site we have done most of our observing at (Brommelsiek Park) are reasonably good, the the limiting magnitude tends to be about 5. However, even then, most stars tend to disappear when you look at them due there actually being a hole in the back of the eye that the nerves go through. Thus, it is best to look slightly to the side of the star to see it better. This is known as “averted vision” but has the problem of being hard to focus on.
Lastly, the design of the quadrant is also an issue. The large base, while providing good stability for the instrument, gets in the way making looking at stars within about 25º of the zenith hard to target as it requires some impressive feats of contortion.
Meanwhile, being the recorder is far easier. reading the scale is very straightforward:
The thick black lines mark every 10º. Each thinner line is 1º, and the short thick is the 5º. The diagonal set of dots simply allows us to spread these out so they don’t overlap and each one marks $\frac{1}{10}$º. The wire hanging down indicates where the reading should be taken and is thin enough to appear between two of the dots, allowing for a reading of as low as 0.05º ($\frac{1}{20}$º).
The plumb is designed to help level the instrument as well as pull the wire taut and straight down. The reality is that this instrument moves a bit and thus, the plumb will sway a bit, so reading the scale often involves gently stabilizing the plumb.
When called for, the recorder should take the reading, and write it down with the azimuth and sidereal time.