considered magnitudes

I've been thinking about magnitude. For a while but more so lately. The visual magnitude scale used with stars. How I interpret or use it. How perceptually different stars will appear at specific magnitudes. That the whole system is logarithmic. And I wondered if there were some tools to help with this...

More frequently, I have been estimating the magnitude differences of pairs of stars. But in the back of my mind I've been thinking that this is not scalar.

The observing sessions last week elevated things a bit more. Partly because I was trying to monitor VZ Cancri, a suggestion from the Turn Left at Orion book, wherein the author notes that the variable star "doubles in brightness" at maxima. When I looked up the details of the RR-type star in SkyTools, it showed the magnitude ranging from 7.18 to 7.91. On the face, that doesn't seem like much.

A quick search of the interwebs lead me to a long and interesting page. where I spotted a familiar diagram. The Star Magnitude infographic in the section Starlight Luminousity – How bright is your star looks like it is from All About Telescopes book. I link directly to the Millstone News site, their Night Sky News section, for the image:

The little box is filled chockablock with useful information such as the brightest star, the limits for the eye and typical instruments, naked eye limits for city and country locales, and the math tip for determining the difference between stars. All good stuff. But the diagram proper, with the circles, does not immediately convey the incredible differences in brightness; the circles are progressively larger or smaller. It feels like an arithmetic series, not a geometric.

One of the big takeaways is the difference for each magnitude value: 2.5. Technically, it is the fifth root of 100. Hence the TLAO reference. Going from magnitude 7 (rounded) to 8 would be a 2½ change in brightness.

And now that I think on it, perhaps what I have been doing with double stars is not incorrect. That is, if I was comparing a mag 7 and 9 pair as opposed to a mag 2 and 4 pair, the differences are the same, approximately 2.5² or 6.3.

Some easy to remember numbers are that if there's a five magnitude difference between stars, they are different by 100 times in brightness. And if ten mags different, then the brightness varies by 10 000 times.