How's this for a long-range forecast?
NASA knows that on January 27, in the year 2837, a total solar eclipse will pass over southern Mexico. If the onlookers (our descendants or our conquering alien overlords) are lucky, and it's a clear day, they'll see something like this — a show that's captivated people on this planet for as long as we've been on Earth.
They even know the exact time, down to the fraction of a second, that the eclipses will occur. Here are the stats for that 2837 eclipse over Mexico.
NASA is able to make eclipse predictions because it has all of the variables: the orbit of the Earth around the sun, the orbit of the moon around the Earth, and the daily rotation of the Earth.
But these calculations aren't all that simple. For one, the moon's orbit around the Earth is constantly changing (there are actually several ways to measure the length of a lunar month, which complicates matters). Still, it boils down to this: Any given eclipse will repeat on an "eight years, 11 days, eight hours" cycle, or what's known as the Saros cycle. And though the eclipses repeat, they don't repeat in the exact same locations.
"Because the Saros period is not equal to a whole number of days, its biggest drawback is that subsequent eclipses are visible from different parts of the globe," NASA explains. (For a more thorough explanation of how eclipses are predicted, check out this video.)
On this website, which draws from NASA's data, you can explore all the solar eclipses (total, partial, annular, or hybrid) and map them. I wanted to know if there would ever be a total solar eclipse on my birthday, August 27. There will be! Unfortunately it will be in 2212, and it will occur over the southern Atlantic Ocean. (You can similarly explore lunar eclipses here).
There's some comfort in knowing that people 1,000 years from now can look up in wonderment at the same natural phenomenon we see today. Life on Earth may change, but the cosmic properties of the Earth itself will not.
For the near term, know that there will be a few total solar eclipses over North America during our lifetimes. NASA has them mapped, too.
The next chance to check out a total solar eclipse on this continent will, of course, be on August 21.