At the time I could not get it to work. It seemed to me that something was missing. It was a nagging feeling as I left the web page.
Early today, I had a go using Beish's method, where he demonstrated using a custom bi-filar eyepiece with a micrometer. It got me thinking...
I returned to the British Astronomical Association web page with McCue's notes and diagrams. Built a spreadsheet (again, must have discarded the other) and hammered out the numbers.
Some light bulbs lit this time. I grokked the triangle formed by the initial cross-hair alignment and the second alignment. Trig at work. I started to get some good numbers.
I carefully read every-single-word. Spotted the remark about converting the seconds of time into seconds of angle by multiplying by 15. I did not recall seeing that before.
And then I tried working his sample values. Worked his numbers backwards. Things did not seem to align. And again, hit a roadblock. Again, it felt like something was missing. Or is McCue operating at a different level? Does "sin θ" mean something that I don't know, never learned, never understood?
I did some algebra and ended up with an equation which would solve the separation. And there it was! It worked! I had a value that matched his. Bit more brain-bending formulae and I got the separation! Holy Universe. It actually worked.
Tested it with three random doubles and was impressed. Pretty close on Albireo and HD 206224. A fair result with 94 Aquarii.
So let me try to explain the process and the maths is an obvious and easy way. McCue explanations, I feel, leave a lot to be desired.
- align cross-hair to EW or parallel to RA and drift a star across the field
- roughly estimate the position angle considering N and W in the field
- get time (t1) between primary and secondary stars drifting across the NS line, e.g. 1.93 seconds
- put the primary star at the centre
- align cross-hair through both stars
- get time (t2) of the secondary star drifting across the NS and EW lines, e.g. 3.04 seconds
- get the apparent/current declination (d) of the star, e.g. +28.0
- calculate the separation
- calculate the position angle
The formulae:
Hopefully I'm using the correct nomenclature here. To be clear, the sin-1 indicates the use of arcsine.
You should get a separation of 32.1" and a position angle of 53°.
Now, McCue explains that the initial PA can impact the final PA calculation. Again, I suggest you roughly estimate it at step 4 above. If the PA is between the degrees:
- 0 and 90, the primary will lead, and you do not need to modify the calculated value
- 90 and 180, the primary will lead, but use a final formula: 180 - your calculated PA
- 180 and 270, the secondary will lead, but use a final formula: 180 + your calculated PA
- 270 and 360, the secondary will lead, but use a final formula 360 - your calculated PA
McCue also cautions that if the PA is near zero or 180, timing is very difficult.
Notes:
- you need an equatorial mount where you can toggle sidereal tracking on and off, if that's not abundantly clear
- you'll want to work at a long focal length for greater resolution
- a stopwatch (app) with a lap timer will be very handy
- the alignment drifting and the timing runs should be done a few times, perhaps a dozen, to yield an average
- if you use an electronic spreadsheet such as Excel or Google Sheets, don't forget to convert to and from radians, as required
So, there you have it.
I really wanted to work through this, understand it. It is a proof of concept. It shows that if an observer really desires to measure doubles visually and has a cross-hair eyepiece, they are good to go.
With the dearth of astrometric eyepieces now, there are few options for the visual observer trying to save a few bucks...
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If you don't want to reinvent the wheel, ask me for my Excel workbook.
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Edited on 25 Aug to move "rough estimate" of PA earlier in the sequence. It's much more obvious after step 1.
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