Well the previous post on July 28 presented the first measurement estimate of motion of Polaris about the north celestial pole. There was some operator error (Resident Astronomer George) in doing the least squares curve fit of the data to the apparent circular motion and we show here the latest, updated, motion measurement. Also, it became apparent that it was not obvious what direction to change the scope pointing angle so that instead of being centered on Polaris is centered on the north celestial pole (NCP) instead.
The previous estimate of the location of the NCP in the camera frame was based on the six measurements of the position of Polaris. If the camera frame was centered on the NCP then the six measurements should all lie on a circle centered at the same pixel locations as the camera frame center. But this was not the case.
The analysis used to find the center of the circular movement of Polaris was not done correctly. I had just used a trial and error approach to minimize the square error among all the six measurements and this didn't work correctly. I used the trial and error method because I couldn't remember how to do least squares estimation for two variables. Later on while considering whether to go back and use Matlab or Mathematica to do the analysis, I remembered how to use Solver in Excel to minimize the error based on adjusting two variables and just reran the data using that. The new estimate for the NCP location in the camera frame is shown at location (3685, 1655) and the minimum error is 7.83 and the estimated radial distance offset for Polaris is 41.1 arc minutes, which is much closer to the actual published location.
The key reason for knowing the actual location of Polaris is to more accurately setup the telescopes initial polar alignment. If you just use Polaris as the NCP, then you will be off by about 40 arc minutes.
|Revised curve fit for measured Polaris movement around the north celestial pole (Source: Palmia Observatory)|
Ok, so during the last observing session, the hand controller was used to show the current position of Polaris (See below). So, since, I had Polaris pretty much centered in the camera frame , I assumed I should just move the camera down and to the right so that Polaris was not moved off center and up and to the left/ But is this the right assumption? As it turns out, I had not read the instruction manual (duh?). To my (partial) credit I hadn't read the polar scope manual, first of all because I'm not even sure if there is such a thing, and, secondly, I am not able to even begin to see Polaris through the polar scope in these bright city lights observing sessions.
|Hand controller displays Polaris position as part of alignment process|
Assuming that I understood what the hand controller display was telling me, I adjusted the alignment knobs to move the image of Polaris up and to the left of the screen. Well as we can see by examining the spreadsheet, the position of the north celestial pole, the point from which the radius to Polaris is being measured, is quite a bit off center. So, this alignment change did not get me closer to the NCP, but further away!
Ok, let's take a look at an IPhone app that also shows the current position of Polaris (See below). Yep, it shows Polaris off center to the upper left of the display. This pretty much agrees with the image shown on the hand controller, but I was still a bit suspicious if I was interpreting the diagrams correctly or not because both of these images are supposed to be what you would see while using the polar scope, which in this case is built into the scope mount aligned with the right ascension axis. But the polar scope, like most small refractors, will invert the image!
|Screenshot of Apple app for Polaris position|
So, not knowing still how to use the polar scope and the app images, I consulted another application, Sky Safari Pro, to see how the current position of Polaris would be shown there. Wow, (see below), this application shows Polaris just as it would be seen if you looked at it with your own eyeballs. Note how Polaris is shown down and to the right of the NCP. So, yes, the previous applications seem to show the position of Polaris differently than I had previously assumed.
|Screenshot from Sky Safari Pro showing actual position of Polaris|
The direction to move so that you are more aligned to the north celestial pole rather than Polaris depends on whether your scope inverts the image or not. My refractor scope when used with the camera works so that my camera images, and images seen on the Liveview screen are all upright just the same as if you were looking at the object with your own eyeballs. So, now I can see what direction to move the scope pointing angle to align it closer to pointing at the NCP. I should have moved the scope alignment up and to the left by 40 arc minutes radial distance. At other alignment times, the direction to Polaris will be different, but you always move so that you are centered on the NCP.
Ok, now I am ready to try this whole measurement of the motion of Polaris out again. If successful, the technique of finding Polaris in city bright skies and knowing the change in direction required to get polar aligned, can be used in future observing session also. I know that in my previous setups, I wouldn't have taken the difference in Polaris's position into account.
Now if I can just find some good weather to try this out again. The forecast for this week does not look to good, but at least if it stays fair I should be able to redo the Polaris measurement and offset measurement and measure how close the adjust to the scope pointing is to the north celestial pole.
|Check the weather forecast as part of observation planning|
Until next time,
Resident Astronomer George