I will briefly describe a technique that I’ve used to observe variable stars. It was invented by Herschel, and refined by Argelander in the middle of XIX century. This is the technique used by the French Association of Variable Stars (AFOEV).
Here is how it works. You’ve already chosen you star, and now you have to pick two stars, NOT variable ones, to use as standards for comparison. Try to choose your standards as close to the variables as possible. Let’s say that your star changes its magnitude from 2.3 to 4.1. In this case pick one brighter standard (2.2 or brighter) and one fainter (4.2 or fainter). In some cases you do not have a lot of stars to choose from, so try to find some that are close to the magnitude range of your star. Also, if your star jumps more than a few magnitudes (for example from 3.5 to 7.1) you would need to pick more than two standards (something like that: one 2.9, another 5.2, and third 7.5) for better accuracy of your observations.
You have your variable stars and two (or more) standards. What to do next? Compare. Go outside, or on your balcony as I did sometimes. Make sure that there are no bright streetlights that would impair your vision. Wait around 15 minutes for your eyes to accommodate. Well, 30 minutes is recommended, but few of us will sit every night and wait that long before start observing. I wasn’t one of those few, anyway ☺. The next step is to look at your variable star, than shift your gaze to one of the standards, than back to your star again. Repeat that multiple times with each standard. Now you have to determine how many “degrees” your star is fainter than the bright standard, let’s call it “c”, and how many “degrees” brighter than the fainter standard, let’s call it “d”. Here is how to do that using the five “degree” scale:
- If at first sight, the stars appear to be equally bright and you recognize after a close examination and repeated passages from “c” to “v” (where “v” is the variable star) and from “v” to “c” that, except at rare moments, “v” is brighter than “c”, you should say that “c” is 1 “degree” brighter than “v” and you should write
c 1 v
- If, although they seem to shine equally bright at first sight, star “c” appears, on closer examination, to be without hesitation brighter than “v”, you estimate the difference to be 2 “degrees” and you should write
c 2 v
- A difference that is obvious at first sight, this is equivalent to 3 “degrees” and is written as
c 3 v
- An even more obvious difference between the two stars represents 4 “degrees” and is noted
c 4 v
- Finally, if a real disproportion exists between the two stars, this difference is equivalent to 5 “degrees”
c 5 v
Beyond 5 “degrees” your observations will not be precise (that’s why this is 5 degree system), and you’ll need to use third standard. Now, do the same with the fainter, “d” standard, and you will end up something of the sort:
c 1 v 3 d
Now apply one of these formulae:
mv = mc + [(md-mc)/(x+y)] * x
mv = md – [(md-mc)/(x+y)] * y
where mv is the magnitude of your variable star, mc the magnitude of the “c” standard, md the magnitude of the “d” standard, x is the “degrees” between “c” and “v” (1 in the example above), and y is the “degrees” between “v” and “d” (3 in the example above). Always round your final magnitude to the first number after the decimal point (if you’ve calculated 2.873…, use 2.9). This technique has 0.1-magnitude accuracy due to limitations of your eyes. Only CCD photometry of variable stars could get better accuracy!
You are not done yet! Do that every clear night, if possible, and take notes: names of your variable star and standards, magnification used (if you’ve used a binocular), quality of the sky (1 good, 2 fairly good, 3 poor), and any other information you think is important. Here is more information about this technique.
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