As the long term goal of my project is to collect measurements in order to produce a star catalog and determine planetary orbits, this will obviously require some way to collect these measurements.
The master instrumentationalist whose data Kepler used was Tycho Brahe. He had numerous devices and their meticulous crafting and exceptionally large sizes allowed for the most accurate measurements of the age.
But for me, one stood out: Tycho’s Great Quadrant which is the one I’ll be modeling my own after.
In essence, this piece is little more than an exceptionally large protractor for the altitude of objects in the sky. Objects are sighted along the arm to the right where there are two metallic rings at either end, which the observer would use to line up the target.
Notice that there is no scale along the horizontal, in the plane of the ground, by which to measure the azimuthal angle. This is because Brahe and many other astronomers tried to simplify their efforts by only worrying about objects that were directly on the meridian (the North-South line across the sky).
Yet obviously the central post is meant to rotate. I suspect this was due to the expectation that this piece would be frequently moved and allowing the central post to rotate would be much easier than trying to tweak the alignment of the entire base.
But how to align it? The easiest quick solution would be to simply find Polaris, the North Star. Unfortunately, Polaris isn’t perfectly centered on the North celestial pole (NCP). It makes a small circle around the pole, being 0.65º away. The width of the full moon is only about 0.5º, so this is 1.5x the width of the full moon. That’s pretty substantial and would introduce some definite error. But thinking qualitatively about it, since the stars reach their peak height (and minimum for circumpolar stars) as they cross the meridian and they have very little up and down motion at that point which is what we’re measuring. So how bad will it really be to be that far off?
As a quick test to see how much this might effect a measurement, I popped into Stellarium for here in St. Louis, and tried out a few objects with a .65º azimuthal error.
| Object | -0.65º azimuth | True | Error |
| Antares | 24º58m20s | 24º58m31s | 11s = 0.003º |
| Spica | 40º10m12s | 40º10m20s | 10s = 0.003º |
| Arcturus | 70º30m3s | 70º30m7s | 4s = 0.001º |
As we can see, because the stars are moving so horizontally as they prepare to cross the meridian, the error is tiny being measured in seconds of arc. Brahe’s instruments are often considered to have an error of a few minutes of arc, although averaging seems to have reduced the error to 1⁄3 to 1⁄2 an arcminute (20-30 arcseconds). Since my goal is not to create an instrument to the same scale as Brahe’s, being that I intend to be able to take this to events for teaching and need to fit it in my car, I’m hoping to achieve an accuracy of about 5-10 arcminutes. Thus, a discrepancy of 15 arcseconds would scarcely register and would be lost in the inherent nose.
But let’s say I really wanted to do better. I can still do this using Polaris simply by having an idea of where Polaris is in relation to the NCP. If I wanted to cheat, I could simply use Stellarium to quickly look up Polaris’ current azimuth but if I want to do it just based on the night sky, there’s a few hints there as well.
Since Polaris makes a circle around the NCP, it crosses the meridian twice in a 24 hour period. If I can catch one of those transits, then I’d definitely be right on target.But how to know when it crosses? Well, the geometry works out such that the NCP is always above the horizon by whatever your latitude is. Here in St. Louis I’m at 38.63ºN. Thus if Polaris is at that altitude ±0.65º, it’s on the meridian.
But tonight that happens around 12:30 in the morning. If I wait that long, I’ll have missed several hours of observing!
Fortunately, other positions give more hints. If it’s exactly at ~38.58º, then I know it’s directly East or West of the meridian and I’d need to correct my azimuth by 0.65º. Knowing which it is should be easy since Polaris is on the opposite side of the meridian as the Big Dipper. Thus, if I see the Big Dipper in the west, Polaris is to the East of the meridian and vice versa.
I’d need to do a bit of geometry to figure out the correction for the in between times, but that could easily be done ahead of time and a handy table kept with my observing logs.
So that was a lot of reasoning to say that proper alignment shouldn’t be a problem. Getting a well made instrument that’s well calibrated is the most important aspect. So next we’ll start looking at the design.