One of the long term goals of this project is to collect enough data to derive the orbit of Mars. However, because Kepler didn’t know the orbit of Earth, he couldn’t use the observation on any given night. Instead, he only used observations from when Mars was at opposition1. This happened to be last night, so we packed up the quadrant and headed out.
Tonight I was joined by Slaine, Padrig, and Sarah. We got there a bit before 10pm to set up. The first thing that was done was changing out the line for the plumb. Previously I’d been using some waxed thread for doing leatherwork, but in the past week, I found a translation of Tycho’s description of the instrument I based this quadrant on and discovered they used copper wire. I wasn’t able to find any copper wire in a sufficiently high gauge, so I got some 26ga brass wire instead. It took a bit to swap the cords out, but eventually we did and I much prefer the wire. It frays less and will be less prone to knotting. In addition, it’s much thinner than the thread allowing more precise readings and even seems to sway less.
Last time, we also noticed that the central column had a tendency to rotate when we were trying to sight. This meant we frequently needed to realign on Polaris. To remedy this, I made another collar for the central column similar to the one that goes around it where it passes through the top of the base. But this one went at the very bottom and was clamped to the X shape supports. It worked beautifully and kept us aligned all night although there is still some play in the quadrant on the axle itself.
Once we were set up, the goal was to observe stars. However, the full moon, high humidity, and light clouds severely limited our options. At times, we estimate we could just make out some stars around magnitude 3.5, we weren’t always sure the stars we wanted to observe were the ones we were aiming at. Ultimately, we tried for 14 stars with the understanding that if any were significantly off, then we probably chose the wrong star since we didn’t have enough stars to properly orient ourselves sometimes, and that observation would be tossed out. Ultimately two stars that we attempted to observe were more than 3º off2.
We also slightly modified our procedure. Last time, we took our observations of altitude when the sidereal time matched the right ascension of the target object. This works because it means the hour angle is zero and thus, right ascension = sidereal time. However, it presupposes we know the right ascension. Since the purpose of this portion of the project is to derive the coordinates, we shouldn’t. Thus, we kept the knowledge of the right ascension and sidereal time from those of us doing the observations. Instead, we had to use our best judgement to determine when the target was in the sights and therefore on the meridian. This would introduce a new error, but one that is reasonable. For the altitude, it shouldn’t make much of a difference (as discussed in this post), but it may make a minute or two of difference in the azimuth. That being said, since Polaris is 0.7º off the actual north celestial pole, that could be an even larger source of error in the azimuth. But more on that shortly.
First, here’s the record from last night:
| Object | Alt | Az | ST |
| χ Dra | 55.2 | 0 | 18h24m |
| λ Sgr | 25.8 | 180 | 18h28m |
| φ Sgr | 24.2 | 180 | 18h46m |
| σ Sgr | 24.75 | 180 | 18h54m |
| ζ Sgr | 21.5 | 180 | 19h03m |
| π Sgr | 30.2 | 180 | 19h12m |
| δ Dra | 61.1 | 0 | 19h17m |
| δ Aql | 54.25 | 180 | 19h28m |
| γ Aql | 62.2 | 180 | 19h46m |
| α Aql | 60.05 | 180 | 19h48m |
| Mars | 26 | 180 | 20h30m |
| Mars | 25.85 | 180 | 20h31m |
As you can see, Sagittarius was the big target for the night. There were some other bright stars in Aquila and Vega, but we’ve discovered that anything much higher than about 80º is nearly impossible to sight, because it would require your head to be inside the box that holds the plumb weight. This will have to be solved by taking the quadrant to events at notably different latitudes. Unfortunately, to cover the whole sky, that would be several spread out across the year.
Upon getting home, I plugged these observations into a conversion program I wrote to get the RA/Dec.
| Object | RA | Dec | Dec Error |
| χ Dra | 18h24m | 73.52 | -0.80 |
| λ Sgr | 18h28m | -25.48 | 0.06 |
| φ Sgr | 18h46m | -27.08 | 0.1 |
| σ Sgr | 18h54m | -26.53 | 0.81 |
| ζ Sgr | 19h03m | -29.78 | -0.09 |
| π Sgr | 19h12m | -21.08 | 0.06 |
| δ Dra | 19h17m | 67.62 | 0.03 |
| δ Aql | 19h28m | 2.97 | .013 |
| γ Aql | 19h46m | 10.92 | -0.32 |
| α Aql | 19h48m | 8.77 | 0.13 |
| Mars | 20h30m30s | -23.35 | -0.26 |
Here, I’ve ignored the error for the RA. As I noted earlier, this is equal to the sidereal time, so really just an error in judgement about when it’s on the meridian. Since the quadrant is really designed to measure altitude, which translates as the declination, I’ve only shown the deviation there. As you can see, there’s definitely a bit of spread. The standard deviation came about to be 0.40 which is half what it was last time. I can’t say whether that’s due to improved familiarity with the instrument, a better wire to read the scale by, or the new collar to lock the column to prevent misalignment. Probably a combination of all three.
But even better, if the errors themselves are averaged, it ends up being -0.0150º which corresponds to -0.899 arcminutes or a mere -53.9 arcseconds. If the overall error is being driven by human error, this suggests that repeated measurements will average to cancel out a great deal of it, giving a very good overall accuracy. While this result is being best measured in arcseconds, that’s overly generous as the scale can only be read down to about 3 arcminutes (when the wire hangs between two of the dots on the scale), so anything more accurate than that, ends up losing meaning, but this is still indicating the accuracy may be at the present theoretical limit. This gives me encouragement to look further into creating a more well divided brass scale.
In the translation of Tycho’s description of the original instrument, he noted that the original instrument had divisions of $\frac{1}{6}$ of 1 minute of arc. So divisions every 10 arcseconds whereas mine only has marks every 10 arcminutes. Depending on exactly how he defined a cubit, his quadrant was slightly smaller or slightly larger than mine, so it should be possible to use the same divisions, if only I can get a scale made with similar accuracy.