Great Astronomers: Adams
Great Astronomers in Modern English
by Sir Robert S. Ball, 1895 (paraphrased by Leslie Noelani Laurio)
To view the table of contents for the rest of this book, click here.
John Couch Adams, 1819-1892
Mathematical prodigy who accounted for lunar acceleration and discovered the path of the Leonid meteor showers.
Our next [and last] astronomer is an Englishman second only to Isaac Newton in his theoretical discoveries. John Couch Adams was born June 5, 1819 in the Lidcot farm, Laneast, where his father was a tenant farmer, seven miles from Launceston in Cornwall. His first school lessons came from Rev. John Couch Grylls, his mother's cousin. His education was pretty ordinary -- classics and mathematics -- but he spent his free time studying whatever astronomy books he could find in the library of the Mechanics' Institute at Devonport. When he was twenty years old, he was enrolled at St. John's College, Cambridge. He did extremely well and graduated at the top of his class in 1834, getting more than double the points for the Wranglership exam that the second-place student got.
After his death, among his papers was the following note from July 1841: 'I formed a plan this week to research, as soon as I get my degree, the irregularities in the orbit of Uranus. Nobody knows what causes them, and I want to know whether they're caused by some unknown planet beyond it. And then, if possible, I want to determine enough of its orbit to actually locate that planet.'
He got his degree and took some time off to relax after his hard studies. Then he set to work to study the perturbations of Uranus as he had resolved to do while he was still an undergraduate. First, he imagined that there was a planet outside of Uranus, at double the distance from the sun as Uranus's distance from the sun. He calculated the effect that this hypothetical planet would have on the orbit of Uranus. He saw that this kind of method would help to narrow down a mystery planet outside of Uranus, as long as the planet was big enough and its orbit was correctly guessed at. But his equation would have to be more precise [it would have to be based on more accurate data from Uranus]. So he asked Professor James Challis, the Director of the Cambridge Observatory, to write to the Astronomer Royal [George Biddell Airy] and get him more accurate measurements for the irregularities of Uranus's orbit. Once he had better data, John Couch Adams started new calculations. Once he had completed his results, he visited the Greenwich Observatory in October 1845 and left a paper for the Astronomer Royal that included his results. He had calculated the mass of the mystery planet and its distance from the sun, as well as other figures that would help calculate its exact position.
As we saw in the last chapter, Le Verrier was working on the same problem. In 1847, Le Verrier had calculated a position for this mystery planet that was one degree different [and more accurate] than the calculations that Adams had sent to the Astronomer Royal seven months earlier. In July 1846, Professor Challis began scanning the sky for the mystery planet with the Northumberland telescope in the Cambridge Observatory. He confined his search to the area around the location that John Couch Adams had specified. He had all of the star-like objects within this area carefully measured and their positions recorded. He repeated this a week or two later. The objects that were in the same place were confirmed as stars, but if any of the objects had moved, then it might be the planet. This method of searching was tedious, but would have to work eventually. There was no other method available to try to find the mystery planet. So Challis searched for the planet for two months before Johann Gottfried Galle looked from his telescope Berlin -- but Galle had an accurate star map that enabled him to locate the planet on the very first night.
Claims were brought forward by friends of both astronomers -- neither Le Verrier nor Adams condescended to enter into the personal aspect of the question. The issue was settled long ago, as this letter of Sir John Herschel to the Royal Astronomical Society in 1848 attests:
'Genius and destiny have joined the names of Le Verrier and Adams, so I will not attempt to separate them. As long as science celebrates its most sublime triumphs, their names will be joined. The great discovery of Neptune has intelligently and legitimately surpassed the wildest guesses of intuition, but there's no need for me to say any more about that. The glorious discovery and the steps that led up to it are already familiar to those who follow science. There is not the slightest rivalry between these two illustrious men. They have met as brothers, and I am sure they will always feel like brothers to each other. So neither will we make any distinction between them now, on this occasion. May both of them beautify and enhance our science for a long time to come, and add to their already bright fame with fresh new achievements.'
John Couch Adams was made a Fellow of St. John's College, Cambridge in 1843. But he didn't take orders [to become a priest] so, according to the rules of the time, he had to step down in 1852. But the year after that, he was made a Fellow of Pembroke College, and he kept that position for the rest of his life. In 1858 he was appointed Professor of Mathematics at the University of St. Andrews [a British University in Fife, in eastern Scotland]. But he didn't stay there for long -- later in the year he was called back to Cambridge to succeed George Peacock as Lowndean Professor of Astronomy and Geometry. In 1861 James Challis retired, and Adams succeeded him as Director of the Cambridge Observatory.
Discovering Neptune was a brilliant way for Adams to begin his career in astronomy. But that's not all he did. He also researched the theory of the movements of Biela's comet [a periodic comet seen about every six years until the time Adams started researching it; in 1846, it split in two and was no longer seen after 1852]. He made a correction about Saturn, investigated the mass of Uranus because it was related to the discovery of Neptune, and improved the system used to calculate the orbits of double stars. But these were minor accomplishments. Besides his discovery of Neptune, he is mostly famous for researching lunar movements and the November meteors [Leonid meteor showers].
The time it takes for the moon to complete one full orbit is called its periodic time. Today we know exactly what that time is [27.3 or 29.5 days, depending on whether you use "sidereal" or "synodic" measurements], and we can use records of ancient eclipses to determine the moon's periodic time from 2000 years ago. Halley discovered that the moon's periodic time has been slowly but steadily diminishing [this is called secular -- or "agonizingly slow" -- lunar acceleration: the moon is speeding up over eons]. It's happening so slowly that it's not significant over one lifetime, but it's noticeable over thousands of years. If we compare ancient lunar orbits with current lunar orbits, we can estimate how much the moon is accelerating. If we calculate as if the moon was maintaining the same speed, and we calculate backwards, we can figure out when some of the ancient lunar eclipses should have occurred. But that estimated time is different than the actual time: it's about a degree off, or the measurement of an arc on the heavens, which is twice the moon's diameter. [An arc refers to an arcsecond or arcminute describing a small angle; read more on Wikipedia.]
If nothing else existed in the universe except the earth and the moon, it's pretty certain that the moon would not be accelerating. If the universe were simply two celestial bodies, the moon's orbit would have stayed the same forever. But there's the sun, and it exerts an attraction force on the moon's orbit [and the earth's too!]. Every time the moon makes its orbit, the sun pulls it a tiny bit off its regular orbit. The irregularity this causes is called perturbations of the lunar orbit. These perturbations have been studied for a long time, and most of them have been sufficiently accounted for. But the first men who researched lunar acceleration realized that it couldn't be explained by solar perturbation. There was no other celestial body to account for it. So what was causing the moon to speed up? It was an unsolved mystery.
In the 1780's, Pierre-Simon Laplace began working on this mystery. He found a solution that seemed to work. Imagine if the moon was lying right in between the earth and the sun. The sun's attraction force would be pulling on both the moon and the earth. But since the moon is closer to the sun, the sun would draw it more strongly, making it pull away from the earth and closer to the sun. The distance between the moon and the earth would thus be greater. In the same way, when the moon is on the other side of the earth, so that the earth is in between the sun and the moon, the sun's attraction force will pull more strongly on the earth than on the moon. As the earth is pulled closer to the sun, the earth and the moon will be pulled further apart. Thus, one of the results of the sun's gravity on the earth and its moon is that the moon is slowly being pulled a tiny bit farther away from the earth -- and its orbit around the earth is slowly growing a tiny bit larger. That means it takes it a little more time to make an orbit, so its periodic time is increasing, as compared to what it would have been if the sun wasn't exerting its gravity on it.
This was known before the time of Laplace, but it didn't explain lunar acceleration. It confirmed that the moon's periodic time was affected by the disturbance, but didn't give any implications that there was a continuous change taking place. But it was clear that the solar disturbance was somehow related to the change in periodic time. If there was any change in how much the sun affected the orbit, there must be a correlating change in the moon's periodic time. Laplace realized that if he could find any continuous change in the sun's disturbance of the moon's orbit, then he could explain the change in the moon's periodic time. Thus, he'd be able to explain why the moon was speeding up.
The sun's ability to affect the earth/moon system is, of course, connected with the distance of the earth from the sun. If the earth's orbit never changed at all, then the sun's ability to disturb it wouldn't account for the change. But if there were any change in the shape or size of the earth's orbit, then that would put the earth closer to the sun or farther away, which would change how much the sun's gravity affected the earth, and might cause the effects on lunar periodic times. It had already been known that earth's orbit, though it looks like a perfect circle, is actually a slight ellipse. If the earth was the only planet revolving around the sun, its ellipse would stay the same forever. But the earth isn't the only planet. Other planets are also orbiting around the sun, guided and controlled by the sun's attraction force. All of these planets also exert their own attraction force on each other and cause slight disturbances in each other's elliptical orbits. That makes the earth's orbit not quite elliptical, but we can consider it an ellipse if we recognize that the ellipse is in slow motion.
An interesting thing about the disturbance caused by the various planets is that earth's ellipse always retains the same length. In other words, its longest diameter never changes. But in every other respect, the ellipse is always changing. It changes its position, it changes its plane, and, most importantly, it becomes more and then less eccentric. From age to age, the earth's ellipse may be evolving into more of a circle, and then in another age, it might be growing more elliptical. The changes are very small and they happen slowly, over thousands of years, but they are continually in flux and their change can be accurately calculated. Currently, and for thousands of years in the past and thousands of years to come, the earth's ellipse has been becoming more circular and less elliptical. Yet the widest part of the ellipse doesn't change. That means that the earth's orbit is gradually increasing in distance. The average distance between the earth and the sun is growing greater because of the perturbations from the other planets. We already discussed how the ability of the sun to influence the moon's movement depends on the distance between the earth and the sun. Since that distance is slowly increasing, that means that the sun is slightly less able to influence the moon's orbit and cause disturbances.
Because of the sun's disturbance, the moon's orbit is slightly increasing. The sun's influence on the moon's orbit is growing slightly weaker, so the moon's orbit, when adjusted to correspond with the average amount of disturbance from the sun, must also be gradually declining. The moon's orbit must be a little closer to the earth because of how the earth's orbit is becoming more circular as the other planets affect it. Admittedly, these are very small changes, and the acceleration they cause in the moon is insignificant unless you measure it over great periods of time. Laplace tried to calculate this change. He knew how much the planets disturbed the earth's orbit, and he was able to use this figure to determine how much change there would be in the moon's orbit. His calculations using observations of ancient eclipses identified that the acceleration of the moon's orbit could be completely accounted for as a result of planetary perturbation. This was quite a scientific triumph. It confirmed that the universal principles of gravity were consistent -- that the inconsistencies weren't a flaw in the law of gravity, but were caused by perturbation.
No one questioned Laplace's calculations for fifty years. He was an amazingly brilliant mathematician, so it's no surprise that no one would doubt his results. But when John Couch Adams started a new calculation of the same data, he realized that Laplace had not worked his approximation far enough, so there was a significant error in his conclusion. Adams didn't challenge Halley's deduction that the moon was accelerating, but he showed that Laplace's calculations to explain this acceleration was off. In fact, Laplace's figure only accounted for half of the planetary influence. Many respected mathematicians came forward to defend Laplace's calculations. They did the math themselves and presented the same figures he had. But some mathematicians also did the math and came up the same figures as Adams. Why such a discrepancy? It was a math problem; there can only be one correct solution. Gradually, it was found that those whose results had agreed with Laplace had actually arrived at various answers, different from Adams, and usually different from each other. Adams was able to point out the error in each of the other calculations until it became obvious that Adams, the Cambridge Professor, had corrected Laplace in a very basic point of astronomical theory.
It was good to have gotten to the truth, but it meant that the mystery Laplace thought he had solved now became unsolved again. If Laplace's figures had been correct, it would have accounted for the phenomenon that had been observed. But now it seemed that the lunar acceleration that had been observed from ancient eclipses could only be partially caused by solar perturbation. The perturbation couldn't be accounted for by gravitational laws alone if the celestial bodies that orbit the sun are rigid particles. But what if there was another explanation?
We haven't explained yet why the lunar period is shorter than it used to be. If we measure how long the moon takes to make its orbit in days, then that means we're counting by how many times the earth turns on its axis [the earth rotates on its axis once per day]. The discrepancy is that it takes fewer days for the moon to get around the earth than it did thousands of years ago. Is that because the moon is moving faster, or is there something else going on? What if the moon is moving at the same speed it always did, but the days themselves are getting longer? If days were getting longer, then it would take the moon fewer days to get all the way around the earth. Apparently lunar acceleration has two causes. The first is the planetary-induced perturbations of the moon influencing the earth, which was discovered and calculated by Laplace, although he overestimated their effects. The other cause is not that the moon is slowly picking up speed, but that the earth is gradually slowing down its spin and revolving a little more slowly, so we're losing time. This has an interesting physical effect that we can measure on the earth itself: the ebb and flow of the tides help to slow down the earth, a little like brakes, and we can see for ourselves that tides are gradually lengthening out and slowing the earth down, making our days longer. Perhaps the action of the tides helps to explain the phenomenon of lunar acceleration. It's too soon to tell for sure. [One theory says that earth days used to be 18 hours long.]
The third of Adams' discoveries related to the shower of November meteors that astonished the world in 1866. [These meteors appear to rain down from the constellation Leo -- which is why they're called "Leonid" -- around Nov 14-19. About every 33 years, they peak and present an unusually spectacular display. The next peak is expected in 2031.] Astronomers became fascinated with the movements of the little objects that produced the bright display. It was John Couch Adams who calculated the exact path that these little objects revolve in, working with some base figures that had been laid out by Hubert Anson Newton of Yale and other astronomers.
Meteors move around the sun in a huge swarm. Every particle of the swarm stays in an orbit according to the well-known laws of Kepler. Scientists who wanted to understand their movement and predict when they would return on their periodic recurrence needed to figure out the size and shape of the path they followed, and the position of that path. There were some facts they already knew. The meteor shower happens every November 13 [back in the 1800's], which identifies one of the points the orbit has to pass through. The spot in the sky where the meteors appear to separate identified another point of their orbit. The sun, of course, is the focal point that the meteors revolve around. The only missing bit of information was the periodic time. Hubert Anson Newton of Yale had shown that the meteor swarm was limited to one of five possible orbits. One is the great elliptical orbit that revolves once every 33.25 years, and that actually is the path the meteors take. Another was a circular orbit that revolves in a little more than a year. Another was a similar track that takes almost a year, and there were two other possible smaller orbits. Hubert Newton had suggested a test to identify one of the five possibilities as the true orbit. The mathematical equations to figure this out were intimidating, but not daunting enough to perplex John Couch Adams.
The date that these meteor showers are visible is continuously advancing -- currently, they cross our track on November 13, but that date is gradually changing. The only influence we're aware of that could be slowly changing the plane of the meteor's orbit is the attraction force of the various planets. Calculating how much change that causes can be done like this: A specific amount of change in the meteor's plane of orbit is known to happen, and calculations for all five potential orbits needed to be computed. John Couch Adams took on the challenge. The difficult part is trying to calculate for the wide variance of the largest of the orbits. Ordinary methods of calculating don't apply. It took him months of work [months working on the same complicated math problem], but in April 1867, Adams had his solution. He showed that, with the largest of the five orbits, the one that took 33.25 years, the perturbations of Jupiter would account for twenty minutes of an arc at the point where the orbit crosses the earth's track. Saturn's gravity would add seven minutes to this, and Uranus would add one more minute. The influence of Earth and the other planets were too imperceptible to count. All total, that makes twenty-eight minutes of an arc, which matches Hubert Anson Newton's estimate as speculated from ancient observation records. Once Adams had shown that the largest of the five possible orbits was the most likely path, he demonstrated mathematically that the other four wouldn't match the observations. The only orbit that would work was the long one. Thus, the orbit of the Leonid meteor shower was finally determined.
But John Couch Adams didn't only research astronomy. Sometimes he worked on astonishingly long numerical calculations to relax[!] He calculated some important mathematical constants to the 200th decimal place[!] He read books about history, geology, and botany. Like many other great men, he liked to read novels. He also enjoyed collecting books -- he had about eight hundred copies of early printed books, many rare and valuable. As far as his personality, his biographer James Whitbread Lee Glaisher wrote, 'People who met him for the first time were always struck by his simple, natural mannerisms. He was a pleasant companion, always cheerful and friendly, showing only a trace of his extremely shy, reserved disposition. He had an affectionate and generous nature, and perfectly balanced moral and intellectual qualities.'
In 1863 (at age 44) he married Eliza Bruce, the daughter of Haliday Bruce of Dublin. He lived at the Cambridge Observatory until his death, working at his mathematics and enjoying time with his friends.
[Roger Hutchins wrote in a 2004 article, "Adams was happily married, profoundly devout, and enjoyed social visits, house guests, entertaining, music, dancing, parties, long daily walks, croquet, bowls, and whist. . . A bibliophile, when not socializing in the evenings, he read."]
In 1889 he became ill with a stomach hemorrhage, and battled that on and off until he died in January 1892. He was buried in St. Giles's Cemetery at Cambridge.
[William Sheehan and Steven Thurber wrote a fascinating article published at the Royal Society in which they speculated that Adams may have been on the autism spectrum. "Adams emerges as a rather complex and even paradoxical individual, whose intellectual astuteness was offset by equal measures of social-skills deficiencies, a tendency to procrastinate and tinker even when the situation called for action, and an almost pathological difficulty in writing prose narrative. . . Apart from his ability to juggle figures in his head, Adams seems to have been a notoriously faint and forgettable personality . . . This difficulty with prose--especially narrative, which is almost entirely lacking in Adams's writings--may also reflect his inability to imagine things from another's perspective." Alternate link]
by Sir Robert S. Ball, 1895 (paraphrased by Leslie Noelani Laurio)
To view the table of contents for the rest of this book, click here.
John Couch Adams, 1819-1892
Mathematical prodigy who accounted for lunar acceleration and discovered the path of the Leonid meteor showers.
Our next [and last] astronomer is an Englishman second only to Isaac Newton in his theoretical discoveries. John Couch Adams was born June 5, 1819 in the Lidcot farm, Laneast, where his father was a tenant farmer, seven miles from Launceston in Cornwall. His first school lessons came from Rev. John Couch Grylls, his mother's cousin. His education was pretty ordinary -- classics and mathematics -- but he spent his free time studying whatever astronomy books he could find in the library of the Mechanics' Institute at Devonport. When he was twenty years old, he was enrolled at St. John's College, Cambridge. He did extremely well and graduated at the top of his class in 1834, getting more than double the points for the Wranglership exam that the second-place student got.
After his death, among his papers was the following note from July 1841: 'I formed a plan this week to research, as soon as I get my degree, the irregularities in the orbit of Uranus. Nobody knows what causes them, and I want to know whether they're caused by some unknown planet beyond it. And then, if possible, I want to determine enough of its orbit to actually locate that planet.'
He got his degree and took some time off to relax after his hard studies. Then he set to work to study the perturbations of Uranus as he had resolved to do while he was still an undergraduate. First, he imagined that there was a planet outside of Uranus, at double the distance from the sun as Uranus's distance from the sun. He calculated the effect that this hypothetical planet would have on the orbit of Uranus. He saw that this kind of method would help to narrow down a mystery planet outside of Uranus, as long as the planet was big enough and its orbit was correctly guessed at. But his equation would have to be more precise [it would have to be based on more accurate data from Uranus]. So he asked Professor James Challis, the Director of the Cambridge Observatory, to write to the Astronomer Royal [George Biddell Airy] and get him more accurate measurements for the irregularities of Uranus's orbit. Once he had better data, John Couch Adams started new calculations. Once he had completed his results, he visited the Greenwich Observatory in October 1845 and left a paper for the Astronomer Royal that included his results. He had calculated the mass of the mystery planet and its distance from the sun, as well as other figures that would help calculate its exact position.
As we saw in the last chapter, Le Verrier was working on the same problem. In 1847, Le Verrier had calculated a position for this mystery planet that was one degree different [and more accurate] than the calculations that Adams had sent to the Astronomer Royal seven months earlier. In July 1846, Professor Challis began scanning the sky for the mystery planet with the Northumberland telescope in the Cambridge Observatory. He confined his search to the area around the location that John Couch Adams had specified. He had all of the star-like objects within this area carefully measured and their positions recorded. He repeated this a week or two later. The objects that were in the same place were confirmed as stars, but if any of the objects had moved, then it might be the planet. This method of searching was tedious, but would have to work eventually. There was no other method available to try to find the mystery planet. So Challis searched for the planet for two months before Johann Gottfried Galle looked from his telescope Berlin -- but Galle had an accurate star map that enabled him to locate the planet on the very first night.
Claims were brought forward by friends of both astronomers -- neither Le Verrier nor Adams condescended to enter into the personal aspect of the question. The issue was settled long ago, as this letter of Sir John Herschel to the Royal Astronomical Society in 1848 attests:
'Genius and destiny have joined the names of Le Verrier and Adams, so I will not attempt to separate them. As long as science celebrates its most sublime triumphs, their names will be joined. The great discovery of Neptune has intelligently and legitimately surpassed the wildest guesses of intuition, but there's no need for me to say any more about that. The glorious discovery and the steps that led up to it are already familiar to those who follow science. There is not the slightest rivalry between these two illustrious men. They have met as brothers, and I am sure they will always feel like brothers to each other. So neither will we make any distinction between them now, on this occasion. May both of them beautify and enhance our science for a long time to come, and add to their already bright fame with fresh new achievements.'
John Couch Adams was made a Fellow of St. John's College, Cambridge in 1843. But he didn't take orders [to become a priest] so, according to the rules of the time, he had to step down in 1852. But the year after that, he was made a Fellow of Pembroke College, and he kept that position for the rest of his life. In 1858 he was appointed Professor of Mathematics at the University of St. Andrews [a British University in Fife, in eastern Scotland]. But he didn't stay there for long -- later in the year he was called back to Cambridge to succeed George Peacock as Lowndean Professor of Astronomy and Geometry. In 1861 James Challis retired, and Adams succeeded him as Director of the Cambridge Observatory.
Discovering Neptune was a brilliant way for Adams to begin his career in astronomy. But that's not all he did. He also researched the theory of the movements of Biela's comet [a periodic comet seen about every six years until the time Adams started researching it; in 1846, it split in two and was no longer seen after 1852]. He made a correction about Saturn, investigated the mass of Uranus because it was related to the discovery of Neptune, and improved the system used to calculate the orbits of double stars. But these were minor accomplishments. Besides his discovery of Neptune, he is mostly famous for researching lunar movements and the November meteors [Leonid meteor showers].
The time it takes for the moon to complete one full orbit is called its periodic time. Today we know exactly what that time is [27.3 or 29.5 days, depending on whether you use "sidereal" or "synodic" measurements], and we can use records of ancient eclipses to determine the moon's periodic time from 2000 years ago. Halley discovered that the moon's periodic time has been slowly but steadily diminishing [this is called secular -- or "agonizingly slow" -- lunar acceleration: the moon is speeding up over eons]. It's happening so slowly that it's not significant over one lifetime, but it's noticeable over thousands of years. If we compare ancient lunar orbits with current lunar orbits, we can estimate how much the moon is accelerating. If we calculate as if the moon was maintaining the same speed, and we calculate backwards, we can figure out when some of the ancient lunar eclipses should have occurred. But that estimated time is different than the actual time: it's about a degree off, or the measurement of an arc on the heavens, which is twice the moon's diameter. [An arc refers to an arcsecond or arcminute describing a small angle; read more on Wikipedia.]
If nothing else existed in the universe except the earth and the moon, it's pretty certain that the moon would not be accelerating. If the universe were simply two celestial bodies, the moon's orbit would have stayed the same forever. But there's the sun, and it exerts an attraction force on the moon's orbit [and the earth's too!]. Every time the moon makes its orbit, the sun pulls it a tiny bit off its regular orbit. The irregularity this causes is called perturbations of the lunar orbit. These perturbations have been studied for a long time, and most of them have been sufficiently accounted for. But the first men who researched lunar acceleration realized that it couldn't be explained by solar perturbation. There was no other celestial body to account for it. So what was causing the moon to speed up? It was an unsolved mystery.
In the 1780's, Pierre-Simon Laplace began working on this mystery. He found a solution that seemed to work. Imagine if the moon was lying right in between the earth and the sun. The sun's attraction force would be pulling on both the moon and the earth. But since the moon is closer to the sun, the sun would draw it more strongly, making it pull away from the earth and closer to the sun. The distance between the moon and the earth would thus be greater. In the same way, when the moon is on the other side of the earth, so that the earth is in between the sun and the moon, the sun's attraction force will pull more strongly on the earth than on the moon. As the earth is pulled closer to the sun, the earth and the moon will be pulled further apart. Thus, one of the results of the sun's gravity on the earth and its moon is that the moon is slowly being pulled a tiny bit farther away from the earth -- and its orbit around the earth is slowly growing a tiny bit larger. That means it takes it a little more time to make an orbit, so its periodic time is increasing, as compared to what it would have been if the sun wasn't exerting its gravity on it.
This was known before the time of Laplace, but it didn't explain lunar acceleration. It confirmed that the moon's periodic time was affected by the disturbance, but didn't give any implications that there was a continuous change taking place. But it was clear that the solar disturbance was somehow related to the change in periodic time. If there was any change in how much the sun affected the orbit, there must be a correlating change in the moon's periodic time. Laplace realized that if he could find any continuous change in the sun's disturbance of the moon's orbit, then he could explain the change in the moon's periodic time. Thus, he'd be able to explain why the moon was speeding up.
The sun's ability to affect the earth/moon system is, of course, connected with the distance of the earth from the sun. If the earth's orbit never changed at all, then the sun's ability to disturb it wouldn't account for the change. But if there were any change in the shape or size of the earth's orbit, then that would put the earth closer to the sun or farther away, which would change how much the sun's gravity affected the earth, and might cause the effects on lunar periodic times. It had already been known that earth's orbit, though it looks like a perfect circle, is actually a slight ellipse. If the earth was the only planet revolving around the sun, its ellipse would stay the same forever. But the earth isn't the only planet. Other planets are also orbiting around the sun, guided and controlled by the sun's attraction force. All of these planets also exert their own attraction force on each other and cause slight disturbances in each other's elliptical orbits. That makes the earth's orbit not quite elliptical, but we can consider it an ellipse if we recognize that the ellipse is in slow motion.
An interesting thing about the disturbance caused by the various planets is that earth's ellipse always retains the same length. In other words, its longest diameter never changes. But in every other respect, the ellipse is always changing. It changes its position, it changes its plane, and, most importantly, it becomes more and then less eccentric. From age to age, the earth's ellipse may be evolving into more of a circle, and then in another age, it might be growing more elliptical. The changes are very small and they happen slowly, over thousands of years, but they are continually in flux and their change can be accurately calculated. Currently, and for thousands of years in the past and thousands of years to come, the earth's ellipse has been becoming more circular and less elliptical. Yet the widest part of the ellipse doesn't change. That means that the earth's orbit is gradually increasing in distance. The average distance between the earth and the sun is growing greater because of the perturbations from the other planets. We already discussed how the ability of the sun to influence the moon's movement depends on the distance between the earth and the sun. Since that distance is slowly increasing, that means that the sun is slightly less able to influence the moon's orbit and cause disturbances.
Because of the sun's disturbance, the moon's orbit is slightly increasing. The sun's influence on the moon's orbit is growing slightly weaker, so the moon's orbit, when adjusted to correspond with the average amount of disturbance from the sun, must also be gradually declining. The moon's orbit must be a little closer to the earth because of how the earth's orbit is becoming more circular as the other planets affect it. Admittedly, these are very small changes, and the acceleration they cause in the moon is insignificant unless you measure it over great periods of time. Laplace tried to calculate this change. He knew how much the planets disturbed the earth's orbit, and he was able to use this figure to determine how much change there would be in the moon's orbit. His calculations using observations of ancient eclipses identified that the acceleration of the moon's orbit could be completely accounted for as a result of planetary perturbation. This was quite a scientific triumph. It confirmed that the universal principles of gravity were consistent -- that the inconsistencies weren't a flaw in the law of gravity, but were caused by perturbation.
No one questioned Laplace's calculations for fifty years. He was an amazingly brilliant mathematician, so it's no surprise that no one would doubt his results. But when John Couch Adams started a new calculation of the same data, he realized that Laplace had not worked his approximation far enough, so there was a significant error in his conclusion. Adams didn't challenge Halley's deduction that the moon was accelerating, but he showed that Laplace's calculations to explain this acceleration was off. In fact, Laplace's figure only accounted for half of the planetary influence. Many respected mathematicians came forward to defend Laplace's calculations. They did the math themselves and presented the same figures he had. But some mathematicians also did the math and came up the same figures as Adams. Why such a discrepancy? It was a math problem; there can only be one correct solution. Gradually, it was found that those whose results had agreed with Laplace had actually arrived at various answers, different from Adams, and usually different from each other. Adams was able to point out the error in each of the other calculations until it became obvious that Adams, the Cambridge Professor, had corrected Laplace in a very basic point of astronomical theory.
It was good to have gotten to the truth, but it meant that the mystery Laplace thought he had solved now became unsolved again. If Laplace's figures had been correct, it would have accounted for the phenomenon that had been observed. But now it seemed that the lunar acceleration that had been observed from ancient eclipses could only be partially caused by solar perturbation. The perturbation couldn't be accounted for by gravitational laws alone if the celestial bodies that orbit the sun are rigid particles. But what if there was another explanation?
We haven't explained yet why the lunar period is shorter than it used to be. If we measure how long the moon takes to make its orbit in days, then that means we're counting by how many times the earth turns on its axis [the earth rotates on its axis once per day]. The discrepancy is that it takes fewer days for the moon to get around the earth than it did thousands of years ago. Is that because the moon is moving faster, or is there something else going on? What if the moon is moving at the same speed it always did, but the days themselves are getting longer? If days were getting longer, then it would take the moon fewer days to get all the way around the earth. Apparently lunar acceleration has two causes. The first is the planetary-induced perturbations of the moon influencing the earth, which was discovered and calculated by Laplace, although he overestimated their effects. The other cause is not that the moon is slowly picking up speed, but that the earth is gradually slowing down its spin and revolving a little more slowly, so we're losing time. This has an interesting physical effect that we can measure on the earth itself: the ebb and flow of the tides help to slow down the earth, a little like brakes, and we can see for ourselves that tides are gradually lengthening out and slowing the earth down, making our days longer. Perhaps the action of the tides helps to explain the phenomenon of lunar acceleration. It's too soon to tell for sure. [One theory says that earth days used to be 18 hours long.]
The third of Adams' discoveries related to the shower of November meteors that astonished the world in 1866. [These meteors appear to rain down from the constellation Leo -- which is why they're called "Leonid" -- around Nov 14-19. About every 33 years, they peak and present an unusually spectacular display. The next peak is expected in 2031.] Astronomers became fascinated with the movements of the little objects that produced the bright display. It was John Couch Adams who calculated the exact path that these little objects revolve in, working with some base figures that had been laid out by Hubert Anson Newton of Yale and other astronomers.
Meteors move around the sun in a huge swarm. Every particle of the swarm stays in an orbit according to the well-known laws of Kepler. Scientists who wanted to understand their movement and predict when they would return on their periodic recurrence needed to figure out the size and shape of the path they followed, and the position of that path. There were some facts they already knew. The meteor shower happens every November 13 [back in the 1800's], which identifies one of the points the orbit has to pass through. The spot in the sky where the meteors appear to separate identified another point of their orbit. The sun, of course, is the focal point that the meteors revolve around. The only missing bit of information was the periodic time. Hubert Anson Newton of Yale had shown that the meteor swarm was limited to one of five possible orbits. One is the great elliptical orbit that revolves once every 33.25 years, and that actually is the path the meteors take. Another was a circular orbit that revolves in a little more than a year. Another was a similar track that takes almost a year, and there were two other possible smaller orbits. Hubert Newton had suggested a test to identify one of the five possibilities as the true orbit. The mathematical equations to figure this out were intimidating, but not daunting enough to perplex John Couch Adams.
The date that these meteor showers are visible is continuously advancing -- currently, they cross our track on November 13, but that date is gradually changing. The only influence we're aware of that could be slowly changing the plane of the meteor's orbit is the attraction force of the various planets. Calculating how much change that causes can be done like this: A specific amount of change in the meteor's plane of orbit is known to happen, and calculations for all five potential orbits needed to be computed. John Couch Adams took on the challenge. The difficult part is trying to calculate for the wide variance of the largest of the orbits. Ordinary methods of calculating don't apply. It took him months of work [months working on the same complicated math problem], but in April 1867, Adams had his solution. He showed that, with the largest of the five orbits, the one that took 33.25 years, the perturbations of Jupiter would account for twenty minutes of an arc at the point where the orbit crosses the earth's track. Saturn's gravity would add seven minutes to this, and Uranus would add one more minute. The influence of Earth and the other planets were too imperceptible to count. All total, that makes twenty-eight minutes of an arc, which matches Hubert Anson Newton's estimate as speculated from ancient observation records. Once Adams had shown that the largest of the five possible orbits was the most likely path, he demonstrated mathematically that the other four wouldn't match the observations. The only orbit that would work was the long one. Thus, the orbit of the Leonid meteor shower was finally determined.
But John Couch Adams didn't only research astronomy. Sometimes he worked on astonishingly long numerical calculations to relax[!] He calculated some important mathematical constants to the 200th decimal place[!] He read books about history, geology, and botany. Like many other great men, he liked to read novels. He also enjoyed collecting books -- he had about eight hundred copies of early printed books, many rare and valuable. As far as his personality, his biographer James Whitbread Lee Glaisher wrote, 'People who met him for the first time were always struck by his simple, natural mannerisms. He was a pleasant companion, always cheerful and friendly, showing only a trace of his extremely shy, reserved disposition. He had an affectionate and generous nature, and perfectly balanced moral and intellectual qualities.'
In 1863 (at age 44) he married Eliza Bruce, the daughter of Haliday Bruce of Dublin. He lived at the Cambridge Observatory until his death, working at his mathematics and enjoying time with his friends.
[Roger Hutchins wrote in a 2004 article, "Adams was happily married, profoundly devout, and enjoyed social visits, house guests, entertaining, music, dancing, parties, long daily walks, croquet, bowls, and whist. . . A bibliophile, when not socializing in the evenings, he read."]
In 1889 he became ill with a stomach hemorrhage, and battled that on and off until he died in January 1892. He was buried in St. Giles's Cemetery at Cambridge.
[William Sheehan and Steven Thurber wrote a fascinating article published at the Royal Society in which they speculated that Adams may have been on the autism spectrum. "Adams emerges as a rather complex and even paradoxical individual, whose intellectual astuteness was offset by equal measures of social-skills deficiencies, a tendency to procrastinate and tinker even when the situation called for action, and an almost pathological difficulty in writing prose narrative. . . Apart from his ability to juggle figures in his head, Adams seems to have been a notoriously faint and forgettable personality . . . This difficulty with prose--especially narrative, which is almost entirely lacking in Adams's writings--may also reflect his inability to imagine things from another's perspective." Alternate link]
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