The total solar eclipse visible in parts of Mexico, the United States and Canada on Monday was a complete intersection of the sun and moon in the sky. But it's also the kind of event that has an expiration date. At some point in the distant future, Earth will experience its last total solar eclipse.
That's because the Moon is moving away from Earth, so much so that our nearest celestial neighbor will be unable to completely hide the Sun someday, millions or even billions of years into the future. It will appear small in the sky.
“There will never be an annular eclipse,” said Noah Petro, a planetary scientist at NASA's Goddard Space Flight Center, referring to an annular eclipse like the one that crossed the United States in October.
However, estimating the exact date of Earth's last total solar eclipse is a serious computational challenge involving various scientific disciplines.
Since the moon formed more than 4 billion years ago, it has been spiraling away from Earth. The moon's retreat occurs due to its gravitational interaction with our planet. Rising tides caused by gravity cause water in Earth's oceans to slide along the ocean floor and the edges of continents. This creates friction, which causes the Earth to spin more slowly, says Matthias Green, a marine scientist at Bangor University in Wales.
The moon moves outward in its orbit in response to Earth's slowing down. Dr. Green said to imagine a figure skater slowing down with his arms outstretched. “It's the same physical principle, but in reverse.”
One of the first to predict the expansion of the Moon's orbit was George Darwin, one of Charles Darwin's sons. However, his hypothesis, published in 1879, was not tested until American astronauts and Soviet robotic probes left devices known as retroreflectors on the moon's surface. The researchers were able to shine a laser pulse on a mirror in a suitcase-sized device and measure the time it took for the light to travel back and forth. This gave scientists a way to accurately measure the distance to the moon. By the early 1970s, researchers discovered that the moon was receding from Earth by about 1.5 inches each year.
This is about the same speed as human fingernails grow. “We're dealing with very small changes,” said Robert Tyler, a planetary scientist at NASA's Goddard Space Flight Center.
But over hundreds of millions of years, the moon becomes visibly smaller in the sky as it moves further away. At some point, it will appear too small to completely obscure the Sun, and total solar eclipses will be a thing of the past.
To calculate the date of the last total solar eclipse, it is important to remember that both the Moon's orbit around the Earth and the Earth's orbit around the Sun are ellipses. In other words, the distances between the Earth and the Moon, and between the Earth and the Sun are not constant. The apparent sizes of the moon and sun as seen from Earth change accordingly. The sizes of the largest and smallest visible satellites differ by about 14 percent, while the corresponding difference for the Sun is about 3 percent.
The final total solar eclipse occurs when the moon, which appears the largest, barely covers the sun, which appears the smallest. A little calculation, taking into account the moon's diameter and the apparent sizes of the moon and sun, gives us an estimate of about 620 million years.
But researchers caution that there is uncertainty in that number. First, assume that the Moon is moving away from the Earth at its current speed. And that almost certainly won't happen, Dr. Green says.
The moon's regression rate is affected by many parameters, including the length of the day on Earth, the depth of ocean basins and the placement of continents, he said. These things change over time, so it would be naive to assume that the moon will always recede at the same pace, Dr. Green said.
Most researchers agree that the recession rate will likely decrease in March. “If I had to guess, the currents would probably weaken in the future,” said Brian Urbick, a physical oceanographer at the University of Michigan. Weakening the tidal forces would slow the moon's retreat and increase the chance that Earth would be exposed to the moon's umbra.
There is also ample evidence that the Moon retreated more slowly in the past. Geologist Marguerite Lantinck of the University of Wisconsin-Madison analyzed Australian sedimentary rocks that record climate change caused by changes in the distance between Earth and the moon. “I read the fingerprints of those astronomical changes,” Dr. Lantink said.
Her team's findings and those of other researchers have been used in simulations that suggest the moon has been receding about 0.4 to 1.2 inches per year for most of its history. These simulations also revealed that during periods lasting tens of millions of years, the moon was moving away from Earth at a rate of more than 4 inches per year.
Dr. Tyler's model tackles the difficult task of predicting recession rates for future months. They suggest that the moon will move away from us at an average rate of about 0.3 inches per year over the next billion years. And future moon recessions will be less variable than they were in ancient times, he said. “Most of the interesting stuff has already happened.”
If Dr. Tyler's simulation is correct, total solar eclipses will continue to be observed for about 3 billion years. He cautioned that there were significant uncertainties in that estimate.
And while there will still be a long time to experience a total solar eclipse, Dr. Petro said that's no excuse not to explore its splendor. After all, they are celestial phenomena specific to our terrestrial existence.
“No other planet in our solar system experiences a total solar eclipse,” Petro says. “We have this amazing opportunity.”