A total eclipse photographed from Easter Island on July 11, 2010
By Ryan Bradley
May 1, 2014

Their stories are different, of course, but they all recall the moment itself with the same eerie clarity. The sky dimmed, birds flew back to their nests, dogs began to howl, the temperature dropped, flowers closed up, and they got chills and goose bumps and watched day become night. In the umbra — the black shadow cast on the earth’s surface by the moon as it passed in front of the sun — they watched the eclipse in its totality. That’s how they got hooked and became full-fledged eclipse chasers.

There are about 50,000 umbraphiles worldwide (about 80% are men). They follow closely the orbital cycles and travel to the ends of the earth for a chance to see a total eclipse, that rare astronomical event when the moon passes between earth and the sun. “It’s like a first love,” says the Slovak astronomer Vojtech Rusin, who has seen 20 eclipses (his first: 1973, Niger). “It’s indescribable,” says Rick Brown, a Long Island-based commodities and futures trader who also arranges eclipse trips (1970, Virginia Beach). Fred Espenak, a retired NASA astrophysicist based in Portal, Ariz., known as “Mr. Eclipse,” recalls driving 600 miles to see his first at age 18, just a few weeks after he earned his driver’s license. Espenak, 61, had been tearing through books about eclipses since he was 8, but the real thing “didn’t look anything like what you see in books. You can’t put words to it. As soon as it was over I thought, ‘I’ve got to see another.’ ” So he did, in eastern Canada, in 1972. Drove for days, but it was clouded out, which happens. The next year he traveled to the Sahara. He estimates he’s seen 90% of all total eclipses since 1970 — there have been 21. The few he has missed have been due to budgetary realities. For example, he could either buy a new car after his old one died or see another eclipse. He had to be practical, but still, missing one always hurts.

MORE: Eclipses from around the world

The rarity of an eclipse is certainly one draw — in 100 years, there are about 75 eclipses — along with the sheer spectacle. But since eclipses often occur in unfamiliar places, they also offer a unique way to see the world. Eclipse chasing is, in part, “the allure of odd travel,” says Rob Arnott, the renowned quantitative investor whose Newport Beach, Calif.-based Research Affiliates manages some $150 billion. His first eclipse was in Mazatlán, Mexico, in 1991. The longest possible eclipse lasts seven minutes, 32 seconds exactly, and occurs once every 1,000 years. In 1991 it wasn’t quite as long — five minutes, 48 seconds — though the moon at that time was farther away from the earth than usual, creating a tiny ring surrounding the blackness. As Arnott stared up, he saw luminous bursts of light, growing dimmer and dimmer, trailing off into the darkness. He was looking at the sun’s corona, a superheated, flaring and flaming plasma field that extends millions of miles from the sun’s surface out into space.

Arnott realized he was on his way to obsession after he missed an eclipse at the Taj Mahal, in 1994. A crowd of 500,000 assembled in Agra to watch it. It lasted 15 seconds. “I’ve been kicking myself ever since missing that,” he says. The next year an eclipse passed through central Siberia; Arnott went online afterward and found pictures of people with icicles on their mustaches and giddy grins on their faces. He’s since been to every eclipse but two.

The reason eclipses appear in odd, very specific places has to do with the moon’s shadow and where it is cast upon the earth. It’s possible to see a full eclipse in totality only within this point, which moves across the earth in funny patterns, as if you were to take a piece of cooked spaghetti and throw it onto a globe. Next year, on March 20, the shadow of a total eclipse will pass between the Faroe Islands and Svalbard, two extremely remote Scandinavian territories way up near the Arctic. They are also very foggy places — the best-laid eclipse-chasing plans can be thwarted by weather — but plenty of eclipse chasers have booked hotels and are planning trips all the same (the three hotels in Longyearbyen, a tiny village of 2,800 on Spitsbergen in Svalbard, are already mostly booked). Arnott, however, has a foolproof plan to glimpse it: He’ll be up in the air, at 30,000 feet, in a Boeing 757 chartered by a group from the University of California at Berkeley, watching the eclipse out of the window with 95 others onboard. That’s two passengers per row, or one at each window, because everything they’re paying for is happening outside. Arnott says he paid about $6,500 for his seat, which is “pretty reasonable.”

It won’t be the most extreme — or expensive — eclipse expedition Arnott has undertaken. Five years ago he spent four weeks in Antarctica aboard a Russian research vessel chartered by Quark Expeditions, an outfitter that plans eclipse trips, with 99 fellow chasers. The least expensive berth, Arnott recalls, was $18,000.

Next year, many chasers like Arnott will charter jets to chase the moon’s shadow. The umbra of an eclipse passes across the earth’s surface traveling about one kilometer per second, but at airplane speeds it’s possible to stay within the eclipse longer and extend its length. In 1974 a Concorde followed the darkest part of the shadow and remained in the eclipse for 74 minutes.

In 2010, Brown, the commodities trader, organized a small group of fellow eclipse hunters on a trip aboard an Airbus A319 normally used to shuttle gear and workers to Antarctica. At 39,000 feet they followed an eclipse across the South Pacific for 9½ minutes, a record for a commercial (nonexperimental, nonmilitary) aircraft. As the plane first began banking into the lunar shadow, Brown watched a line of darkness march across the earth. “It looked like the end of the world, this black shadow coming at us,” he recalls. Next March, some 30 to 40 airplanes will be chasing the eclipse through the sky over the Arctic.

Not all eclipse chasers, of course, can afford to hire a plane. Patrick Poitevin (first eclipse: Kenya, 1980), a chemist at a confectionery company by day (“I innovate packaging,” he says) based in Tissington, England, has never seen an eclipse in midair, yet he organizes and runs the annual Solar Eclipse Conference, a two-day summit that brings together some 150 professional astronomers and amateurs.

At this year’s event — Oct. 24-26 at the Sacramento Peak Observatory in New Mexico’s Museum of Space History — there will be a session on eclipse photography through the ages, from Thomas Jefferson using a pinhole camera to capture an eclipse to shooting eclipse-induced waves as they ripple through the ozone layer. In another session, Iranian businessman Hamid Khodashenas — he bills himself as the “Mr. Eclipse” of Iran — will describe his plans to travel into space to watch an eclipse (“I’m sure he will succeed in that one — he has the money,” Poitevin says).

The larger, more significant trend is that it’s quite normal now to travel the globe for the opportunity to glimpse an eclipse. And while chasers never get to pick their destination, sometimes the tourism and astronomy stars align. On March 9, 2016, the moon’s shadow during a total eclipse will travel across part of Indonesia and then drift north across the Pacific, a favorable spot for cruises out of Hawaii and Japan — and ideal for the eclipse-tourism industry, since Americans and Japanese are the most fervent chasers. “The Japanese are absolute fanatics,” says Arnott, who recalls a trip to the Sahara when a contingent of about 10,000 Japanese had huge sets of tents, fields of sand marked out with precise rectangles for undisturbed viewing, and even organizers to shoo away dumbstruck Americans wandering into their encampment.

How does Arnott know if someone is likely to become obsessed with eclipses? There’s a predilection to astronomy, sure. But he views it more simply. Some see their first eclipse and say, “Well, I can check that off the list — been there, done that”; others realize they must see another. It’s hard to know who will fall into which category. Best to simply go and experience it. Besides, he adds, how else will you decide to take a vacation to central Mongolia?

Eclipses, explained

Go outside on a sunny day, hold up a basketball, and watch where its shadow falls. Someone standing in the shadow would see all of the ball and none of the sun. Imagine the basketball is the moon. That’s an eclipse.

A total eclipse occurs when the moon passes directly in front of the sun. The event is completely visible only in the darkest part of the moon’s shadow, what’s known as the umbra. Outside the umbra is the penumbra — the “partial shadow.” The umbra is about 100 miles in diameter; the penumbra can get to be much larger. You want to be in the umbra during a total eclipse, not simply because it’s more spectacular (it is) but because during totality it’s the only area in which it is safe to stare at the sun without protective eyewear.

Other eclipses are annular or partial. Annular eclipses occur when the moon is farther from the earth and does not block the sun entirely: The moon covers the center, and the rest of the sun looks like a ring (annulus), what some solar chasers describe as “the ring of fire.” A partial eclipse is what you’d expect — the moon covers a part of the sun, leaving a crescent shape that can look like a waxing moon ablaze in the midday sky.

Planning your trip

Want to see an eclipse? Here’s how.

Travelquest: This pro outfitter operated by enthusiast Aram Kaprielian offers two trips for next year’s subarctic eclipse: one to Svalbard (starts at $5,880) and another to the Faroe Islands (starting at $3,660). See travelquesttours.com.

Gear: Bring image-stabilized binoculars to stare at the sun’s corona during totality — when the moon blocks out all of the sun. A tour will provide eclipse glasses, which you’ll need before and after the eclipse. If you’re traveling solo, buy a pair from Rainbow Symphony (see rainbowsymphony.com).

Mr. Eclipse’s Pro Tips on Eclipse Chasing

We asked Fred Espenak, a retired NASA astrophysicist known as “Mr. Eclipse,” for his tips for first-time chasers. (For more, visit mreclipse.com.)

Travel: The oldest, most established tour companies often advertise in Sky and Telescope and Astronomy magazines, says Espenak. If you find a company you aren’t sure about, ask the right questions: Do they scout the location one year ahead of the eclipse? All the pros do. And how long have they been around? “Before a big eclipse, a number of agencies just pop up out of nowhere,” says Espenak. “They are not to be trusted.”

Photography: If it’s your first eclipse, don’t try to take pictures of it: “Cameras make people befuddled, especially if you’re new to the experience. Just take it in.” Mostly, Mr. Eclipse says, “don’t let technology get in the way of the experience. It just happens so fast.”

2017: If you’re interested in eclipse watching but not ready to travel halfway across the globe to do it, 2017 is your year. A total eclipse will cross “right smack-dab through the middle of the U.S., from coast to coast, central Oregon to South Carolina, on Aug. 21. It will be an eclipse you can drive to,” says Espenak. If you plan to go: “Watch the weather, reposition yourself to improve your odds, decide on the area that’s best for you — and book hotels immediately.”

This story is from the May 19, 2014 issue of Fortune.

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