A neat logarithm example for kids thanks to Chanda Prescod-Weinstein and Bruce Macintosh

A saw a really neat twitter thread last week thanks to a re-tweet from Chanda Prescod-Weinstein:

Thinking about brightness of a moving object in magnitudes is complicated, so here’s a brief tutorial with some calculations at the end. Imagine a telescope with one arcsecond pixels, excellent seeing, and some idealization, and a 4th magnitude satellite.

— Bruce Macintosh (@bmac_astro) May 26, 2019

The thread explained why thinking about the (astronomical) magnitude of an object moving through a telescope’s field of view is a little difficult. It was neat to learn that something I didn’t realize was hard is actually pretty hard (though it feels like basically everything in astronomy is like that!), but another thing that jumped off the page for me in that twitter thread was that it was an excellent example to show to kids learning about logarithms.

For reference, here’s the Wikipedia page we used in the project to learn about the concept of magnitude and also get a few examples:

Wikipedia’s page on Magnitude

My younger son (in 7th grade) is just learning about logarithms now and my older son (in 9th grade) has a bit more experience with them. We started by talking about the relative magnitude formula and working through a short calculation to show why the number 2.5 shows up in the formula:

Next we looked at the Wikipedia page linked above to get some examples of magnitudes of a few objects we recognize:

Now we talked through Bruce Macintosh’s twitter thread. I wanted to go through the thread carefully to make sure the kids had a basic understanding of the concepts he was discussing (arcseconds, for example). We talked about some of the calculations, but did not do any calculating ourselves in this part. One question for the kids here was why did Macintosh use a + sign in his formula when the Wikipedia page has a – sign in the formula?

Finally, we did the calculations and found the answer to the mystery of the + and – sign from the last video. Happily, we match the answers from Macintosh’s thread:

This project was really fun. It was a really happy accident that just as my younger son was learning about logs a neat (and “new to me”) example of where logs are used showed up in my twitter feed!