If you're not already excited about the total solar eclipse that will be visible in the United States on August 21, maybe you haven't been paying attention. During a solar eclipse, the shadow of the moon falls on the Earth's surface—an event that hasn't been visible in the lower 48 states since 1979. And yes, it should be visible to just about everyone (wearing appropriate glasses), though you might not notice that big of a difference. Even with a little bit of sunlight going past the moon, the sky will appear to be pretty darn bright.
But if you want to experience the full power of the solar eclipse, you need to be in the region of total blackout (the umbra). The rest of the nation will just be in a partial shadow of the moon (the penumbra). When the moon completely covers the sun in this region, you will know it. It will be as dark as night. That's where I want to be—and where most of the country's eclipse nerds will, too. Which raises a question: Is it possible for everyone in the US to see the full solar eclipse? Could everyone get in their cars and drive to a place inside the path of the moon's shadow? Would there be enough room for all?
Let's begin with some crazy approximations. My general rule is that I don't want to look up things unless I absolutely have no choice. For everything else, I will just use my best judgement to get values.
There are two kinds of solar eclipses—annular and total. For an annular eclipse, the apparent angular size of the moon is a little bit smaller than the angular size of the sun. This means that in the best position, there is still a ring of fire (not really fire) around the shadow of the moon. For a total eclipse, the moon will completely cover the sun. This is much cooler to see.
The size of the moon's shadow depends on both the Earth-moon distance and the Earth-sun distance. Both of these distances change over the course of a year since neither the Earth's orbit nor the moon's are perfectly circular. OK, so say that the moon and the sun are at certain distances. How big would the moon shadow be? Let me start with a simplified diagram of the sun-moon-Earth system.
Of course this isn't drawn to scale—that's pretty much impossible. But for this calculation, focus on the white right triangle that I have included. This will have one side as the radius of the sun—but I will also need the radius of the moon and the distance from the sun to the moon. I am going to now just focus on the triangle (without showing the sun and moon).
I'll gloss over most of the details, but the key is to focus on the red and the green triangles in this diagram. These have to be similar triangles (based on the angles and stuff). Remember that for two similar triangles, the ratios of corresponding sides are the same. For the red triangle, the vertical side is equal to the difference between the radius of the moon and the sun. For the green triangle, the vertical side is the difference in the spot size (on the Earth) and the radius of the moon. It looks complicated, but once you have those two triangles, it's not too difficult to solve for the size of the spot. Note that I am assuming the Earth-moon distance includes the radius of the Earth (it doesn't). I am also assuming that the surface of the Earth is perpendicular to the spot shadow (which would be true near the equator). If the spot was near the North or South pole, it would be stretched out and not circular.
Now I just need the exact distances for the sun and moon. I will use this site for the Earth-sun distance and this site for the moon distance on a date very close to August 21. Plugging these values in (with the radius of the sun and moon), I get a spot radius of 53.7 km (that's a spot diameter of about 66 miles). I'm sure that's not the exact spot size, but it's close enough for me.
The question is not how many people can fit in the shadow, but how many people could view the total eclipse. Since this spot travels all the way across the US, it's like a really long and skinny rectangle. The width of this will be 107 km (I will just go with 100 km) and a length of perhaps 5,000 km. That gives a viewing area of 0.5 million km2.
How does this viewing area compare to the total area of the lower 48 states? Let me just approximate the US (lower 48—that's the last time I'm going to say it) as a giant rectangle that is 5,000 km by 2,000 km for a total area of 10 million km2. That means the viewing area is 5 percent of the total area. This is important for the next calculation.
This one is tough. It's not just about the available viewing area, it's also about parking. All of these people have to get into the viewing area somehow. They are going to have to drive—really, there's no other way. But how many parking spaces are there? I am just going to have to make three assumptions. First, the parking space density is uniform. This is obviously not true. There are probably more parking spaces in Nashville than there are in the middle of Oregon (although maybe there aren't many open parking spaces in Nashville). Second, there is one car for every two people in the USA. If there are 300 million humans, that would make 150 million cars. Third, there are four parking spaces for every car (yes, I just totally guessed). Obviously there are more spaces than cars—just look at all the empty parking lots on the weekend. That puts the total parking spaces at 600 million.
Now I can estimate the parking spaces in the viewing area. Since this is 5 percent of the total area, it would be OK to estimate that 5 percent of the parking spaces are in the viewing area. That would be 30 million spots for cars. If each car can carry five humans, that makes for 150 million viewers. That's a bummer for about half of the country's population. Who gets to be in the viewing area? How about a lottery system where everyone flips a coin? You get "heads," and congratulations, you get to see the total solar eclipse!
OK, this is just an estimation. I think it's possible I'm off by a factor of two, which means it's possible everyone could fit in this viewing area. But what would that be like? It would probably be hell on Earth. Traffic would completely suck. Think of the giant lines at Starbucks. What about the strain on the power grid and sewer systems? What about internet access? I think I would prefer to see the total eclipse from home and have the whole state to myself.
