Omar Marcos - Total Solar Eclipse

TOTAL SOLAR ECLIPSE

April 6, 2024

❗ ❗  If you intend to watch the eclipse in person, use proper protective eyewear for yourself and protective filters for your camera & video gear!

Solar eclipse enthusiasm seems to have gripped the national consciousness as a result of the upcoming April 8, 2024 event, and that's not a bad thing, as there's a lot of cool phenomena involved. (Similar triangles, the varying elliptical axis of both the moon and earth, ephemerides, the magnitude of the moon, etc…)

I'm by no means an astronomy expert and the specifics of eclipse calculations were topics we only briefly touched on in school, so I took the liberty of perusing a corresponding forum for more info. (The formula below was posted by user "JustThinking", and I'm curious to know who actually came up with this math and how long ago it was discovered…) Multiple places including Discover Magazine detail how there are two different shadows of differing intensities cast on the earth during a total solar eclipse. The following equation below, however, determines the radius (R_u) of just the darkest part of the moon's shadow, the umbra, which moves along the much-talked about path of totality.

My final calculations for the radius ended up being 100.822754 and I almost lost sight of the fact that I had to double this value to get the diameter of the umbra. (Aren't you glad I don't work for NASA?!) So in effect, I ended up with 201.645508 km, and once I converted kilometers to miles, my final answer was approximately 125.3 miles for the size of the umbra. From what I've heard from the experts, the upcoming umbra is expected to be roughly 115 miles in diameter, so I'm assuming my approximated value for the Distance from the Sun to the Earth may have thrown off my result here. (…among other things!)

By this point, you may be asking why in the world I'm bothering with these equations, especially since much of this can be modeled in computer simulations nowadays. The short answer: Just because I'm a geek and in the rare event I have some free time, I sometimes enjoy breaking out the calculator to solve random or interesting formulas. 🤓
Since I'm crunched for time again, for the next update I'll recheck my math, finalize the rest of this post, and write about how a solar eclipse is akin to a photo-loving, scene-stealing pug!

UPDATED CALCULATIONS - 4.10.25

So I went back and looked up more accurate values for the distance of the moon & the distance of the sun from the earth, and lo and behold, the resulting answer was spot on with the announced size of the umbra's shadow on that mystical day in April 2024. [Note: I'll leave my previous erroneous calculations posted, if only to serve as reminder that while constants (such as the radius of the earth, moon & sun here) remain the same, it's crucial to obtain updated values for variables whenever you're crunching numbers! The distance from the moon to the earth will get you every time…]
Occasionally in math class someone would just spew out an answer without showing the step-by-step process, which could be very frustrating if you're only beginning to learn a concept. So this time I've also included more of the progressive calculations below, so you can follow along with the steps. In case you're interested. 🤓 😎