Z Ursae Majoris beginning to fade

Just over a week ago, one day after full moon on the 12th June 2025, we had some more clear weather which enabled me to get another view of the variable star Z Ursae Majoris. The twilight at about 22:00 UT (23:00 BST) is now very bright but Z remains pretty much near its peak and so determination of its magnitude is not too much of a problem. Using 10x50 binoculars my estimate was:-

Z UMa, 22:23 UT, chart 217.02, A(1)V(1)B, mag. 6.8

The star is now beginning to fade. At the present time (20th June 2025) it is about 7th magnitude. It looks like the peak in brightness is going to be sharp as I predicted but it may yet brighten again or slow down its fade. We shall see!

All text and images © Duncan Hale-Sutton 2025 

Z Ursae Majoris on the 30th May 2025

The recent weather has been far too cloudy for me to carry out any observations but, just over a week ago, on the 30th May I was able to make an observation of Z Uma. Even then the weather wasn't that clear as I had to observe through thin cloud. At that time the moon was 3 days after new and twilight was an issue as it always is in the middle of summer. My estimate was as follows:-

Z UMa, 22:20 UT, chart 217.02, A(3)V(7)B, mag. 6.6

From this observation it looks like Z is beginning to fade after its recent maximum. Looking at other data from the BAA, this now does seem to be the case.

All text and images © Duncan Hale-Sutton 2025 

Using a program to calculate the angular separation of Mizar and Alcor

In my last post I described a program that could be used to calculate the angular separation of two celestial objects using their equatorial coordinates. I now want to revisit my calculation of the separation of the double stars Mizar and Alcor. I previously gave the coordinates of Mizar A as RA 13h 23m 55.543s Dec. +54 deg. 55' 31.30" and Alcor as RA 13h 25m 13.538s Dec. +54 deg. 59' 16.65". I previously found that their separation to 4 decimal places was 0.1968 degrees. Now using my own program I find that inputting the same coordinates I get the separation as 0.196820915 degrees which to four decimal places is the same value as before.

Unfortunately, as often happens on the web, the tool that I used previously to calculate the separation of these two stars is no longer accessible and so I can't compare the values to higher decimal places.

However I have found some other online calculators. For example, inputting these coordinates in  Clear Sky Tonight I obtain the separation as 11 minutes and 48.56 seconds which corresponds to 0.196822222 in decimal degrees and this differs from mine at the 6th decimal place. Another online calculator is this one by the Russian-Turkish 1.5m telescope. If I enter the coordinates here I get a separation of 0.196837 degrees which differs from mine at the 5th decimal place.

To be honest, this is more than I expected, so rounding obviously is an issue. However, 1 arc second is 0.00028 degrees so we are talking about a tenth of an arc second error or so at most.

All text and images © Duncan Hale-Sutton 2025

 

A program to calculate the angular separation between two stars

I have previously written a program to calculate binary star orbits using the algorithm given in Practical Astronomy with your Calculator by Peter Duffet-Smith. I wrote the code for a programmable calculator (a Casio fx-4500P) and it makes predicting the positions of binary stars fairly straight forward. Recently I had been thinking it would be useful to have some code that could calculate the angular separation of any two stars (or any two celestial objects) as this is something that is always cropping up. For example, in May last year I took a photograph of the double star Mizar and Alcor and I used their angular separation to determine the resolution of my camera (in arc seconds per pixel) when it was at the prime focus of my Orion OMC-140 telescope.

So now I have used another algorithm in Peter's book to write some code for the Casio to do this (see section (31) on page 52). It is based on knowing the equatorial coordinates of the two objects (in other words their Right Ascension and Declination):-

"STAR 1"

Pause 3

A"H": B"M": C"S"

W = A + B/60 + C/3600

E"D": F"M": G"S"

X = E + F/60 + G/3600

D"SIGN +/-1"

D = -1 → X = XD ∆

"STAR 2"

Pause 3

H"H": I"M": J"S"

Y = H + I/60 + J/3600

L"D": M"M": N"S"

Z = L + M/60 + N/3600

K"SIGN (+/-1)"

K = -1 → Z = ZK ∆

U = 15(W - Y) 

S = cosˉ¹ (sin X x sin Z + cos X x cos Z x cos U) ▲

S > 0.1 → Goto 1 ∆

"RECALC"

Pause 3

T =  √((cos X x U)² + (X - Z)²) ▲

Lbl 1

 

Before running this program it is best to set the mode to degrees and to clear the memories. The Right Ascension coordinates of the two objects are entered in the hours, minutes, seconds format and for the Declination in degrees, minutes, seconds. The angular separation of the two objects, S, is given in decimal degrees.

 

Further execution of the program is possible for small angles (less than 0.1 of a degree). This is because there may be a limitation in the accuracy of the calculator to return an exact result due to its precision. T gives an alternative calculation of the angular separation which may be more accurate. 

All text and images © Duncan Hale-Sutton 2025

Z Ursae Majoris still exceptionally bright

Four days ago on the 20th May 2025 we had a clear evening here in Norfolk and I was again able to observe the long-period variable Z UMa. The moon was at last quarter and wouldn't rise until 01.38 UT on the 21st, however, it is now technically twilight all night. The skies were clear and the transparency was good but with some thin cloud in places.

Z was still bright and has not declined yet. In fact, I think it has increased in brightness again compared to my last estimate. This was what I saw with 7x50 binoculars:-

Z UMa, 22:27 UT, chart 217.02, =A, mag. 6.3

It seems that people at the BAA have finally woken up to the fact that Z appears to be exceptionally bright as John Toone sent out an alert yesterday that said "Since mid-May I have had Z UMa at 6.2mv, slightly brighter than comp star A. This is the brightest I have seen it since commencing monitoring in 1978."

 

All text and images © Duncan Hale-Sutton 2025

More variable star observations

A week ago (the 13th May 2025) we again had some very clear weather (the story of this spring here in the east of England) and I was able to get a few more estimates for some long-period variable stars even though the moon was one day after full and astronomical twilight didn't end until nearly midnight (23.45 BST). Here are my observations (using 10x50 binoculars):-

Z UMa, 21:52 UT, chart 217.02, A(1)V(4)B, mag. 6.5

RY UMa 22.09 UT, chart 217.02, 1(5)V(2)2, mag. 7.2

TX Dra, 22.25 UT, chart 106.04, K(5)V(2)N, mag. 7.5

AH Dra, 22.29 UT, chart 106.04, 1(1)V(2)2, mag 7.1 

The star Z UMa remains very bright and close to its maximum. There is no sign yet (as of May 20th) that its brightness is declining.

 

All text and images © Duncan Hale-Sutton 2025

More about Z Ursae Majoris

In the last week I have added another item on the BAA Forum about this star under the heading "What's happening to Z Ursae Majoris?". This is what I said:-

"You might have noticed that Z UMa has just recently reached a peak in its brightness and this peak was brighter than previous peaks for the last four years (see the attached screen shot from the BAAVSS database). I am going to stick my neck out here and make a bit of a prediction! I think we will see more of this in the next four years with more sharply defined peaks and troughs and a wider range in magnitudes. My reasoning is the interplay between the two periods of pulsation that this star shows. If you look back to 2016-2017 there was a period then when the amplitude of variation died away somewhat and there was evidence for double peaks in the pulsation prior to this. Then the variation recovered and there were more sharply defined peaks and troughs. I think we are now seeing a repeat of this behaviour.

Why do I think this? Well, I am not sure I believe that the second, less prominent, pulsation period in this star is dying away. I think that this modulation of the amplitude and the double peaks (see above) is evidence that the two pulsation periods in this star are still operating together and causing the modulations to the primary pulsation period that we see. Over the next four years we will probably see these sharply defined peaks because the two periods are acting in concert and then after this they will go out of phase and we will see the return of the double peaks and the lower amplitude range. We shall see! For more on this read my previous posts on this subject."

Well, interestingly my post elicited no response from other members at the BAA at all and sometimes I think I am just talking to myself. It is difficult to know whether they find what I am saying is interesting or whether they just think it is boring, or perhaps worse still, they think I am wrong but they are too polite to say! I will be interested to see if my prediction turns out to be true. If it is I think that John Greaves may be wrong in suggesting that the two periods of pulsation in this star are unifying to one and that it may be premature to say that this star is becoming more Mira like.

One of the projects I am thinking about starting is to see if I can process this data for myself. It will involve me trying to learn a new computer language like Python but I may try and see if I can use AI to construct it to save some time. The first job would be to bin up this data and see how well defined it is. For example, it may be easier to see how frequently the double peaks occur as I reckon these are indicative of dual periods in the pulsation. Watch this space!

All text and images © Duncan Hale-Sutton 2025 (except the images kindly provided by the BAA).