einstein and the orbit of mercury--1/21/26

21 Jan 2026

einstein and the orbit of mercury--1/21/26

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Today's selection-- from Space Oddities by Harry Cliff. The puzzle of the orbit of Mercury helped establish Albert Einstein’s new theory of relativity:

“On December 31, 1859, the country physician Edmond Lescarbault was at his home in the small French village of Orgeres-en-Beauce, about sixty-five miles southwest of Paris, when there was an unexpected knock at the door. Perhaps he had been sitting by the fire writing cards to give to his friends and neighbors the next morning, or simply looking forward to a quiet New Year's Eve meal with his family. He almost certainly wasn't expecting to find himself confronted by the commanding figure of Urbain Le Verrier, director of the Imperial Observatory in Paris and France's foremost astronomer, famed for his role in the discovery of the planet Neptune.

“When his duties as a rural doctor allowed, Edmond Lescarbault was an enthusiastic amateur astronomer and had even built his own small observatory next to his house. Just over a week before Le Verrier's unannounced visit, Lescarbault had been leafing through a popular astronomical journal when his eyes alighted on an article describing a recent piece of work by Le Verrier on Mercury, the closest planet to the Sun. Mercury's orbit around the Sun had been puzzling astronomers for decades; the planet seemed to stubbornly refuse to follow the path laid out for it by Newton's law of gravity. For more than a century, astronomers had been embarrassed by the little planet while attempting to observe its transits, rare astronomical events when Mercury passes directly between the Earth and the Sun, appearing as a small black dot against the Sun's brilliant surface. Mercury repeatedly failed to appear when predicted, sometimes causing astronomers to miss transits by hours, or in one extreme case, by more than a day. In Newton's predictable clockwork universe, a planet with such poor timekeeping was extremely disturbing.

“Le Verrier had made his name by solving a similar problem with the orbit of the outermost planet, Uranus. Like Mercury, Uranus's orbit didn't conform to the predictions of Newton's theory, an anomaly that Le Verrier had claimed could be explained if its orbit was being perturbed by the gravitational tug of an unseen eighth planet. In a virtuoso calculation, Le Verrier was able to predict precisely where this eighth planet ought to appear in the night sky, and when astronomers looked through their telescopes, they discovered a brand-new planet—Neptune—less than one degree from the point where Le Verrier had said it should be.

“Emboldened by his previous triumph, Le Verrier was now hoping to pull off the same feat with the planet Mercury. Earlier in December, he had published a paper suggesting that Mercury's orbit could be accounted for if there existed a hitherto undiscovered planet between Mercury and the Sun. A small world, or perhaps a collection of asteroids, hiding in the dazzling glare of our local star could well have escaped notice, he argued.

“On reading the article, Lescarbault's heart began to race. Nine months earlier, on March 26, he had been observing the Sun using his handmade telescope when he had noticed a small dark object on its surface. He had quickly convinced himself that it wasn't a sunspot and tracked the object until it disappeared over the edge of the Sun's disk. While a curious observation, Lescarbault was unsure of exactly what he had seen, and hoping to catch sight of it again, he kept his discovery to himself, that is until he read of Le Verrier's prediction. Thrilled by the prospect of having discovered a ninth planet, Lescarbault,fired off a letter to Le Verrier in Paris, telling him that he might have sighted his hypothesized world. What he hadn't anticipated was that his letter would elicit such a strong response that Le Verrier would immediately jump on a train from Paris and would, just a few hours later, be hammering on Lescarbault's front door.

“With barely a ‘how do you do,’ Le Verrier forced his way into Lescarbault's hallway demanding to inspect his observatory and records while berating the startled doctor for sitting on what could be a momentous discovery for almost nine months. After submitting Lescarbault to a fearsome interrogation (which one account compared to the meeting of a lion and a lamb), he proceeded to examine his homemade equipment and, finding it relatively satisfactory, made some minor corrections to Lescarbault's observations of the mysterious object. Apparently not content with this, he then proceeded to demand character witnesses from Lescarbault's neighbors, presumably to make sure he wasn't being taken for a ride by a confidence trickster. By the end of what appears to have been a rather grueling day for Lescarbault, Le Verrier returned to Paris, assured that his predicted planet had been found. Given its nearness to the furious heat of the Sun, he named it after the Roman god of fire, Vulcan.

“Announced to the astronomical community by Le Verrier, Lescarbault's discovery caused a nationwide sensation, with newspapers across France reporting on the remarkable new planet. Lescarbault found himself catapulted from unknown country physician to astronomical superstar and was made chevalier de la Legion d'honneur (knight of the Legion of Honor) just a month later. Meanwhile, Le Verrier basked in the glory of a second audacious prediction proved true. By February, news had spread to France's imperial rival Britain, and while there was no shortage of dismay that the French had beaten Old Blighty to yet another planet, the story proved irresistible, with newspapers and public lectures spreading word of the tiny, scorched planet Vulcan.

“Le Verrier soon found himself inundated with reports of further observations of the new planet as it crossed the Sun's disk. With each one, he adjusted his calculations of Vulcan's orbit and issued new predictions for when the next transit might be seen. When the predicted transits failed to materialize, he was forced to adjust his orbital model and issue new predictions. Sporadic sightings of Vulcan continued to come in over the next few decades; however, it proved impossible to make accurate predictions of when the planet would show up. As the years rolled by, skepticism began to grow about whether Vulcan really existed at all, although Le Verrier clung to belief in his new world until he died in 1877.

“Astronomers would continue to scour the skies for Vulcan into the early years of the twentieth century. It was hoped that the planet might become visible during total eclipses, when the Sun's glare was blocked by the Moon, allowing a small pinprick of reflected light to stand out against the temporarily darkened sky. However, despite attempts to spy Vulcan during the eclipses of 1883, 1887, 1889, 1900, 1901, 1905, and 1908, the planet failed to make an appearance. Particularly conclusive were thorough photographic searches made by the American astronomer Charles Dillon Perrine during the solar eclipses of 1901, 1905, and 1908. By 1908, William Wallace Campbell, director of California's Lick Observatory, was ready to declare that the search for Vulcan had finally been brought ‘to a close.'

Orbit of Mercury (2006)

“But despite Vulcan's demise, the problem of Mercury's anomalous orbit remained. Vulcan or no, there was still something seriously fishy about its motion around the Sun, and if it wasn't caused by a new planet, then what? The solution, when it was eventually found, turned out to be far more profound than anyone could have imagined.

“To understand the specific issue with Mercury's orbit, the first thing to know is that planets don't orbit the Sun in perfect circles as Nicolaus Copernicus had argued when he published his Sun-centered model of the universe in 1543. Instead, they orbit in ellipses. That means that at some times of their years they are closer to the Sun than at others. In fact, of all the planets, Mercury's orbit shows the biggest difference between its closest (forty-six million kilometers) and its most distant (seventy million kilometers) points from the Sun. Astronomers call the closest point to the Sun on a planet's orbit the perihelion, which is just a fancy ancient Greek way of saying ‘closest to the Sun.’

“The second thing to know about Mercury's orbit is that the elliptical path it follows around the Sun doesn't stay fixed in space; the ellipse itself slowly rotates around the Sun over time, changing its orientation. You can imagine Mercury's orbit as a squashed hula hoop, with the Sun acting like the person swinging the hoop around their waist. The reason that Mercury's orbit gradually changes its alignment is thanks to the gravitational tugs of the other planets in the solar system, particularly from its nearest neighbor, Venus.

“The rotation of Mercury's orbit causes the perihelion to gradually move around the Sun over the course of many Mercurian years. It was this phenomenon that astronomers were failing to accurately account for. The perihelion appeared to be advancing faster than predicted by Newton's law of gravity, meaning that Mercury completed an extra orbit once every twelve million Mercurian years — a tiny effect, but enough to explain why astronomers kept missing its transits.

“At the very time that the search for Vulcan was reaching its disappointing conclusion, a young Albert Einstein was embarking on a journey that would ultimately lead to his greatest contribution to science: the general theory of relativity. This journey would take Einstein through a labyrinth of abstract mathematics, so mind-meltingly hard that few mathematicians at the time, let alone physicists, were able to understand it. Einstein's objective was nothing less than a revolution in our understanding of gravity, space, and time, and it would take him a full eight years to complete his magnum opus.

“Einstein's general theory of relativity promised to overturn Newton's law of gravity, which had ruled the heavens for 250 years. Instead of describing gravity as a force exerted between two massive bodies—say the Sun and Mercury—Einstein's theory said that gravity was an illusion created by the way massive bodies warp the fabric of space and time. The difference was more than just conceptual; it had real-world effects. The Sun has a huge mass, meaning that space-time close to the Sun-that is, around the orbit of Mercury-is highly curved, much more so than it is for the other planets. This means that Mercury would be especially sensitive to the differences between general relativity and Newton's law.

“By 1915, Einstein had almost completed work on his theory. He had long been aware of the problem with Mercury, and although it hadn't been his motivation for embarking on general relativity, he realized that if he could account for its weird orbit, it would give a huge boost to the chances of his radical new theory being accepted. By the early twentieth century, painstaking observations by astronomers had resulted in a precise measurement of how much faster Mercury's perihelion was moving around the Sun than predicted by Newton's theory, resulting in a figure of 45 ± 5 seconds of arc per century. ‘What's a second of arc?’ I hear you cry. It's a measure of how far apart two points appear on the sky, but the key thing is to note that it has a value ( 45) and an uncertainty (5).

“In 1913, Einstein had tried, unsuccessfully, to calculate the advance of Mercury's perihelion, getting a figure of 18 seconds of arc per century—disappointingly far from the measured value of 45. However, two years on, Einstein had carried out a major overhaul of his theory, and when he tried the calculation again in November 1915, to his delight he got an answer in almost eerie agreement with the measured value: 43 seconds of arc. Einstein was so overcome with excitement that he suffered heart palpitations and had to lie down to recover. On November 15 he wrote enthusiastically to his friend Heinrich Zangger,

“‘I have now derived the up to this point unexplained anomalies in the motion of the planets from the theory. Imagine my good fortune!’

“Just three days later, on November 18, Einstein stood up at the prestigious Prussian Academy of Sciences to give a lecture that would change science forever. In it, he outlined, for the first time, his general theory of relativity and, what's more, showed how it had solved the centuries-old puzzle of the planet Mercury. The scientific world was stunned. Einstein's rival David Hilbert was astonished, writing generously to Einstein, ‘Congratulations on conquering the perihelion motion.’

“Einstein had solved the Mercury anomaly. In doing so, he ensured that his theory got the attention it deserved.

“A revolution in our understanding of the cosmos began that day. Not only had the planet Vulcan been destroyed once and for all, but Einstein's theory would ultimately overturn Newton's theory of gravity, accepted for centuries as the law that governed the universe. The advent of general relativity would lead to the modern discipline of cosmology, the big bang theory, black holes, and much more besides. Today, it is one of the two great pillars of modern physics, arguably the most profound and beautiful theory ever discovered.

“What can we learn from the story of Vulcan? Well, perhaps the most obvious lesson is that paying careful attention to small anomalies can lead to major breakthroughs in how we understand the world around us. Of course, we have to be a bit careful here; Einstein didn't start work on general relativity because of the Mercury anomaly. But it did provide the crucial supporting evidence at the moment he felt ready to let his new theory out into the wild. Without its early success in explaining Mercury's orbit, general relativity might have taken far longer to be accepted as the new theory of the cosmos.”