Predicting the relative positions of the binary star Xi Bootis

In my previous post I described an observation of the binary star Xi Bootis that I made on the 1st May. From a photograph I was able to make a measurement of the separation and position angle (PA) of the pair and found this to be about 5.5 +/- 0.4 arcseconds and 291 +/- 3 degrees, respectively. This has lead me to wonder if I could get a prediction for these quantities using measured orbital properties of the binary. In my copy of Norton's 2000.0 star atlas and reference handbook (Longman Scientific and Technical 1989 edited by Ian Ridpath, 18th edition) there is a table of elements of some visual binaries (p146, table 46) and in this list is an entry for Xi Bootis (ADS number 9413 in the New General Catalogue of Double Stars). The orbital parameters are as follows:-

Orbital Period P (years) : 151.505

Date of periastron T : 1909.361

Semi-major axis of orbit a (arc seconds): 4.904

Eccentricity of orbit e : 0.512

Inclination of orbit to plane of sky i (degrees) : 140.04

Argument of periastron ω (degrees) : 203.92

PA of ascending node Ω (degrees) : 348.1

The first thing to note is the date of periastron which is when the two stars are closest. The last periastron was in 1909, the next one will be in 1909.361 + 151.505 = 2060.866 which I reckon is the 11th November 2060.

So how do you predict the relative position of these stars using this data? Well, there is a computer program written in Basic that you could use written on page 145 of Norton's 2000.0 but the alternative is to search the web for someone who has provided an online calculator. Such a person is Roger Wesson who is an astronomer at Cardiff University and his calculator can be found here. Unfortunately, Roger does not list the orbital parameters for Xi Boo in his star name look up but you can type in the orbital parameters given here.

The 1st May 2024 as a fraction of a year is, I think, (31 + 29 + 31 + 30 + 1)/366 = 122/366 = 1/3 (or 0.3 recurring as a decimal), so we can write this date approximately as 2024.333. Using Roger's calculator the predicted separation and PA of Xi Boo on this date was 4.81 arcseconds and 289.8 degrees, respectively. The PA is in good agreement with what I observed but the predicted separation is marginally smaller than what I saw but I wouldn't read a lot into this.

If you look at the bottom of Roger's page there is a nice little animation that you can play which shows how Xi Boo B moves around A. I have used the calculator to predict the separation and PA of this binary for the next 150 years in 10 year intervals starting at 2024.0. The plot is shown below:-

As you can see from the graph, Xi Boo B is moving round from a westerly position to a more southerly one over the next 30 years. Also, the PA and separation are decreasing more rapidly over this period (in 2064.0 the separation is just 2.16 arcseconds). As a result, it is a good time to start observing this pair as the changes will become more noticeable!

The question remains as to how reliable are the parameters for the orbit for Xi Boo? I have found another website by Gianluca Sordiglioni which lists these quantities for this binary and they are a little different to the ones presented here. However, I don't expect the predictions for separation and PA to be radically different. 

Here are the tabulated values for the points in the graph above using the oribtal parameters listed here.

2024.0 : 4.85 : 290.4

2034.0 : 3.90 : 270.5

2044.0 : 3.08 : 238.7

2054.0 : 2.63 : 191.3

2064.0 : 2.16 : 125.5

2074.0 : 2.76 : 53.5

2084.0 : 4.23 : 21.3

2094.0 : 5.47 : 5.2

2104.0 : 6.36 : 354.4

2114.0 : 6.92 : 346.0

2124.0 : 7.19 : 338.5

2134.0 : 7.20 : 331.2

2144.0 : 6.96 : 323.8

2154.0 : 6.50 : 315.5

2164.0 : 5.83 : 305.6

2174.0 : 4.98 : 292.7

All text and images © Duncan Hale-Sutton 2024

Double Stars - Xi Bootis (1st May 2024)

Xi Bootis is my fifth and final double star observation from the night of the 1st May (see my previous post for a discussion of this). Here is my image:-

 

This was a 5s exposure at ISO 1600 on a Nikon D90 at the prime focus of a 140mm Maksutov Cassegrain (an Orion OMC-140). The picture can be better seen by 'clicking' on it. The image is being viewed at full scale (in other words it has not been binned up). Xi Boo A and B are marked and these two stars are visual magnitude 4.70 and 6.97 respectively (actually A is a BY Draconis variable and ranges in brightness from 4.52 to 4.67). The image scale is 0.5859 arcseconds per pixel and this is a 1200x800 pixel crop of the original.

My method for orientating the image has been described in a previous post. Using this I have made some measurements of the separation and position angle (PA) of Xi Bootis (for a discussion of PA and how it is measured please again refer to my previous post). Three measurements of the separation gave me 5.6, 5.8 and 5.0 arcseconds which gives an average of 5.5 +/- 0.4 arcseconds. Again three measurements of PA gave 288.4, 294.0 and 290.6 degrees which averages to 291 +/- 3 degrees. 

This is probably the most interesting of the five double stars I photographed that night because this pairing is a proper binary system with an orbital period of 151.5 years. I have in my possession an old copy of the Webb Society's double star catalogue (The Webb Society Observer's Handbook, Vol. I Double Stars, London 1975) and this star is listed on pages 89 and 109 (STF 1888). The average separation and PA between 1964 and 1974 was 7.1 arcseconds and 342 degrees. So in the 50 odd years since those observations were made the system has changed quite a bit (as you would expect). In 2019 the separation and PA were 5.2 arcseconds and 298 degrees. My measurement of the separation is in good agreement but I think the PA has decreased even further since that date.

All text and images © Duncan Hale-Sutton 2024

 

Double Stars - Nu Draconis (1st May 2024)

Nu Draconis is my fourth double star observation from the night of the 1st May (see my previous post for a discussion of this). Here is my image:-

 

This was a 5s exposure at ISO 1600 on a Nikon D90 at the prime focus of a 140mm Maksutov Cassegrain (an Orion OMC-140). The picture can be better seen by 'clicking' on it. The image is being viewed at full scale (in other words it has not been binned up). Nu 1 and 2 Dra are marked and these two stars are equal in brightness both being visual magnitude 4.88. The image scale is 0.5859 arcseconds per pixel and this is a 1600x1067 pixel crop of the original.

My method for orientating the image has been described in a previous post. Using this I have made some measurements of the separation and position angle (PA) of Nu Draconis (for a discussion of PA and how it is measured please again refer to my previous post). A couple of measurements of the separation gave me 106.65 and 107.71 pixels. This averages to 107.18 pixels and, at 0.5859 arcseconds per pixel, this is 62.8 arcseconds. Again a couple of measurements of PA gave 311.2 and 310.8 degrees which averages to 311.0 degrees. The published separation and PA for this double star is 62.3 arcseconds and 311 degrees, so in very good agreement.

All text and images © Duncan Hale-Sutton 2024

 

Double Stars - Kappa Bootis (1st May 2024)

Kappa Bootis is my third double star observation from the night of the 1st May (see my previous post for a discussion of this). Here is my image:-

 

This was a 5s exposure at ISO 1600 on a Nikon D90 at the prime focus of a 140mm Maksutov Cassegrain (an Orion OMC-140). The picture can be better seen by 'clicking' on it. The image is being viewed at full scale (in other words it has not been binned up). Kappa 1 and 2 Boo are marked and Kappa 1 magnitude is 6.69 whereas Kappa 2 is a Delta Scuti variable ranging in brightness from 4.50 to 4.58. The image scale is 0.5859 arcseconds per pixel and this is a 1200x1200 pixel crop of the original.

My method for orientating the image has been described in my last post. Using this I have made some measurements of the separation and position angle (PA) of Kappa Boo (for a discussion of PA and how it is measured please again refer to my previous post). A couple of measurements of the separation gave me 23.60 and 23.02 pixels. This averages to 23.31 pixels and, at 0.5859 arcseconds per pixel, this is 13.7 arcseconds. Again a couple of measurements of PA gave 233.6 and 235.6 degrees which averages to 234.6 degrees. The published separation and PA for this double star is 13.5 arcseconds and 235 degrees, so in very good agreement.

All text and images © Duncan Hale-Sutton 2024

Double stars - 54 Leonis (1st May 2024)

54 Leonis is my second double star observation from the night of the 1st May (see my previous post for a discussion of this). Here is my image:-

This was a 5s exposure at ISO 1600 on a Nikon D90 at the prime focus of a 140mm Maksutov Cassegrain (an Orion OMC-140). The picture can be better seen by 'clicking' on it. The image is being viewed at full scale (in other words it has not been binned up). 54 Leo A and B are marked and are magnitude 4.48 and 6.29 respectively. The image scale is 0.5859 arcseconds per pixel and this is a 1200x1200 pixel crop of the original.

I now have a better method for orientating the image. I have posted this observation at the BAA. If you view this and then click on the link which says 54-Leo under the heading 'Objects' you will come to a page that lists all the observations of this double star and some additional information about the object. Again, if you click on the link which says In-The-Sky.org (a button in green) you will come to a very useful website run by BAA member Dominic Ford. This particular page has a finder chart on it and if you click on the magnifier in the corner you get another scalable view of this chart. Reducing the field of view to about 1 degree gives a nice plot of double star and the field stars around it.

I exported the chart as a PNG image and then opened it in Photoshop. At the same time I opened my original image of the double star and located the two reasonably bright field stars you can see in the chart near 54 Leo. Photoshop can be used to determine the angle between a line and the horizontal. Drawing a line between the two field stars on the chart gave me one angle. Repeating this for a line drawn between the same stars on my image gave me another. The difference between these two angles is how much I would need to rotate my image so that the two field stars in my image are in the same orientation as in the chart.

Having done this I could make some measurements of the separation and position angle (PA) of 54 Leo. A couple of measurements of the separation gave me 10.77 and 11.18 pixels. This averages to 10.98 pixels and, at 0.5859 arcseconds per pixel, this is 6.4 arcseconds. PA is a measurement of the angle of the fainter star relative to the brighter one. Imagine a line drawn from one to the other. The angle is measured from due north anticlockwise (through east) to the line. Again a couple of measurements gave 111.8 and 116.6 degrees which averages to 114 degrees. The published separation and PA for this double star is 6.6 arcseconds and 113 degrees, so in very good agreement.

All text and images © Duncan Hale-Sutton 2024

Double stars - Mizar and Alcor (1st May 2024)

Having got my telescope set up correctly on this evening (see previous post) unfortunately the weather wasn't going to play ball and it was pretty hazy. So I decided to observe something where the weather didn't matter too much and these were double stars. The SynScan handset of the HEQ-5 has a number of double stars preprogrammed into it and so I began to take a tour of them and to photograph them as I went. The first was Mizar and Alcor. This is an extremely wide but very well-known pairing but the interesting part is that Mizar is itself a double which I had only realized recently. Here is my photograph:-

This was a 1s exposure at ISO 1600 on a Nikon D90 at the prime focus of a 140mm Maksutov Cassegrain (an Orion OMC-140). The picture can be better seen by 'clicking' on it. The image is being viewed at full scale (in other words it has not been binned up). Mizar A and B are marked and are magnitude 2.23 and 3.88 respectively. Off to the left is Alcor which is magnitude 3.99. The other star, Sidus Ludoviciana is magnitude 7.58.

To get an idea of the image scale here we can determine the angular separation of Mizar A and Alcor using their coordinates. Mizar A is at RA 13h 23m 55.543s Dec. +54 deg. 55' 31.30" and Alcor is RA 13h 25m 13.538s Dec. +54 deg. 59' 16.65". Using the tool here, the separation is found to be 0.1968 degrees. Their separation in pixels is 1209.25 which gives 0.5859 arcseconds per pixel. 

It should be noted that this image here has been cropped and is 1600x1066 pixels. The full image is 4288x2844 pixels and this corresponds to 0.698x0.463 degrees. To get the right orientation with North upwards and West to the right I used this article for reference (the article is worth a read in itself) where there is a diagram showing the relative positions of the stars relative to North and South. I then rotated my image so that the stars were orientated correctly.

For a double star, a couple of measurements are given. The first is their separation of their components in arcseconds and the second is their position angle. The latter gives the position of the fainter star relative to the brighter and is an angular measure from the north anticlockwise through the east. I measured the separation of Mizar A and B to be 25.08 pixels which corresponds to 14.7 arcseconds. I must be to within about a pixel so + or - 0.59 arcsecond. The measured value is 14.4 arcseconds which is fortuitously close. The measured postion angle is 153 degrees and so by my image I don't think I am too far off in my orientation.

As a footnote, if you read Bob King's article highlighted above, you will discover that all three stars Alcor, Mizar A and Mizar B are doubles in themselves making this a sextuple system and all bound together gravitationally (in the case of Mizar and Alcor, just!).

All text and images © Duncan Hale-Sutton 2024

Telescope set up on a HEQ-5 mount (1st May 2024)

On Wednesday this week I was anticipating that it might be clear in the evening and I thought it would be a good opportunity to try and set up my 140mm Maksutov Cassegrain correctly on my HEQ-5 mount. I now have three stone blocks set up in the garden to rest the feet of my tripod on. Recently, I have been having trouble with polar aligning the scope and so, idly searching the net for help, I came across this video which gave me some ideas about how I could do things better.

I will describe what I did so that it may be of use to others. Firstly, I placed the tripod on the stone blocks in roughly the right position for true north. Although the three blocks are roughly levelled between themselves I adjusted the tripod legs so that top of it, using a spirit level, was properly level. I marked the location of the legs on the stone blocks so that I could replace the tripod in exactly the same place on another night.

Next I attached the HEQ-5 head and then made sure the azimuth adjustment screws were screwed in equally on both sides, so that the head was centred. I added the counterweight, then the telescope, DSLR camera and red dot pointer. I had been using a 50mm finder with crosshairs but I found it too heavy and it was awkwardly messing up the balance of the scope. The red dot pointer is much lighter and smaller. I then balanced the telescope in RA and Dec by adjusting the position of the telescope in the dovetail slot and by moving the counterweight.

I then waited until the stars were visible, lined up on Arcturus and made sure that the red dot pointer and telescope were aligned. I did need to take the camera off briefly to do this and replace it with a star diagonal and eyepiece but once the camera was back on I could focus the camera by using liveview and seeing the star on the screen.

Now, something perhaps I have not been careful about before was putting the telescope in the 'park' position before switching on the drive. This means that the counterweight is at its lowest position and the scope is pointing roughly in the direction of the pole. This helps when carrying out the alignment. Next came entering the usual date, time and location information on the handset (sometimes I get the date format wrong which can lead to all sorts of trouble!). When this is done the handset shows the location of polaris in the polar finder. This is in the format of HH:MM. From what I understand this is a 12 hour pointing system with 12 pointing directly up, 6 pointing directly down and the other locations increasing clockwise as on a face of a clock).

If you look through the polar finder you will see a small circle marked where you have to place polaris (northern hemisphere only). Suppose the handset said a time of 03:00, then you would rotate the polar scope until that circle is at the 3 o'clock position. Now using the azimuth and altitude adjustments on the HEQ-5 head only, move the head until polaris is seen in that small circle. Don't move the feet of the tripod as you might mess up the levelling you did earlier.

You should be roughly polar aligned. Then carry out a 3 star alignment. Not a 1 star or 2 star but a 3 star. This is something else I have learned. Do a 3 star as it is much more likely that the telescope will more reliably point to an object. Another thing I have learned is that you can do this ok with the camera in position. Just use liveview to centre the stars each time. Then you can be sure that the telescope remains well balanced.

I found that carrying this all out was entirely sufficient for my needs. Each time I used the controller to send the telescope to a new object it was reliably in the centre of the field. The video goes on to show how you can improve the polar alignment using certain functions on the controller which I might try sometime.

Finally, when dismounting the telescope I made a note of where the telescope was in the dovetail connection and where the counterweight was on its arm. When releasing the head from the tripod I undid the azimuth screws equally by one full turn each. Also I left the adjusted feet of the tripod as they were. Hopefully, this means that on another night when I go to set up I can return the telescope to exactly the same place and level and have the axis of the mount pointing in the same direction. It should speed up the whole set up process.

All text and images © Duncan Hale-Sutton 2024