Basic data sets

To construct the full catalog we need several different data sets; (1) the primary stars, altitudes and separations to each other, both well sampled; (2) the secondary star altitudes and separations to the primary stars; (3) zenith stars tied to the primaries, separations only; and (4) Polaris, which stands by itself.

I had to eliminate a number of Tycho's stars for various reasons. A few were too far south to clear my tree-lined horizons, Tycho could see them from his observatory even though he was 15 degrees further north than I am. For stars that were close in magnitude and position to each other, I eliminated those that didn't have some clear asterism that would allow me to identify them in the pitch FOV where the star fields were rotated to unfamiliar orientations. I did find that the SIMBAD website has a very useful finder tool that allows a quick check on a star field. I started with about 780 stars and eventually obtained reasonable positions for about 734 of them.

The 100 primary stars were broken down into about 380 pairs and about five separations were measured for each pair, producing about 1900 separation measurements for the primaries. These form the backbone of the catalog positions.

The ~640 secondary stars were each linked to two primary stars and those two separations were measured 2 or 3 times, producing about 3300 separation measurements. These flesh out the catalog by tying all the remaining stars to the brighter primaries.

Additional separations were measured for special needs, such as the zenith stars, or stars with noisy data, or for engineering tests. The final list of measured separations runs about 6300 measurements. That list can be found here. This list is sorted first by the ra of the first star, then by the ra of the second star.

About 3200 altitudes were measured for the 740 stars, with the primaries getting more coverage than the secondaries. That list can be found here. This list is in ra order. The different methods of determining the meridian altitude are indicated in the 'obstype' column and are either the maximum altitude or the altitude at az=180 degrees.

The 30 zenith stars presented a number of observing problems. Since I could not measure reliable altitudes for stars between 36 and 42 degrees declination, I had to create special triplets of separations between these zenith stars and the primary stars, as detailed before. Unfortunately, 5 of these zenith stars were themselves primaries, thus I had unreliable altitudes for them which needed repair. They required extra observing in order to have altitudes as reliable as the other primaries, which then permitted them to be used in the triplets for the remaining zenith stars. I didn't pay adequate attention at first to forming these triplets, and I managed to generate several triplets that were almost collinear, violating one of my criteria for measuring separations.

Polaris was a special case because it lies so close to the pole that the standard triangle method does not work well. For this case, it was easier to monitor the path of Polaris during a long night, and then fit a circle to its path. The radius of that circle would be the co-declination of Polaris and thus its altitude would be 90 degrees minus the co-dec. I eventually had enough pairs that I could get a rough right ascension for Polaris.

To give an idea of the activity of the scope, here is a plot of all my altitude data as a function of MJD. It shows my early attempts to measure altitudes of the primary stars by holding the az to 180 degrees while allowing the altitude axis to go through and past the zenith. That was advantageous in that no az slewing was necessary to reach stars that passed north of the zenith. This mode was shown to be problematical due to mount axes misalignment and tube flexure. Past MJD 480 (early April 2020) this mode was abandoned and stars that culminated north of the zenith were observed by slewing az to the zero position.

After the axes' misalignment problem was fully recognized, meridian altitudes near the zenith were simply avoided. Altitudes of stars that fell in this region (36 to 42 degrees dec) were found by a different method, mentioned above. After enough data on the zenith triplets had been gathered, the spherical triangles were solved to determine the declinations and thus the meridian altitudes. Because the zenith star data had been collected over a few months, the solutions were assigned an arbitrary MJD of 700 and entered into the altitude history file.

I first started observing in June of 2020 and spent about 8 months shaking out the instrument, observing only the primary stars, and developing observing strategies and tools. In early February of 2021 I began to take data in earnest. By observing both in the evening and in the early morning I was able to complete the full sky in about 9 months. Tycho was able to observe for many years more than I did but he also observed the Sun, the Moon, the planets, eclipses, novae, and comets, and did so much more thoroughly than I did. The man amazes me.

To show you how hectic Tycho's observing schedule must have been, here is a note I sent to Dr. Rosa about some of my efforts:

From: David Skillman

Sent: Thursday, September 30, 2021 10:33 PM

To: M Rosa

Subject: a busy day for Tycho

Michael,

I send this because you are probably the only other person on the planet who can see the parallels. No need to reply.

We've had a string of good weather lately. Lots of clear nights. I am exhausted (a bit).

Last evening, just post-sunset, I tried to measure the sep of Venus and alphaSco even though they were at a very low altitude (~10 deg). Was able to do it, to my surprise.

But it began to worry me that I only have a good horizon to the west. not the east. This apparition of Venus is very unfavorable and I'm realizing that the spring apparition is not much better - probably not observable to my east.

This leaves me the problem of how to transfer the solar RA to a target star if I can't use Venus.

I went to bed at a normal time, even though it was clear, so as to get some sleep for late night work. I've mined the early evening sky pretty cleanly so most of the new work is toward the east. Checked out Jupiter (mag -2) as a possible alternate to Venus in the spring.

Got up at midnight - I have the automatic wake-up system of an old man. Did seps and merids until the sun stopped me at 6:30 am.

Did a Horizons prep for a Sun-to-alphaCMa sep test in the later morning. Got a bit of sleep, back up at 9am. Was able to get the Sun in the direct channel, through the trees to the east, and also Sirius through the pitch channel. Sep was 85 degrees(!). Was able to get a good sep in case all the planetary offsets fail.

Back for a couple of hours sleep and then up at 12:15pm to start my solar preps. Got a solar meridian passage but had to fight a lot of clouds. Couldn't get a sep to Venus because it was low in the east and I couldn't see it through the trees.

Couple more hours of sleep and up at 3:30pm to get the transit of Venus. That worked well, again through clouds, and I added a Sun-to-Venus sep measurement in case it can be of use.

Will try the Venus-Antares pair this evening before starting the cycle all over again.

I could use a few more instruments and assistants,

Dave

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