I read that Einstein’s general relativity theory solved the case of Mercury’s perihelion. What is this thing about Mercury’s perihelion all about?
It is a fascinating story, both historically and technically, but here I can just give you a brief synopsis.
Newton’s gravitational law, first presented to the world in 1687, was a monumental achievement. Newton had reduced the motions of the observable cosmos to a simple formula involving mass, distance, and a gravitational constant. It was not until the 1850s, through the work of astronomer Urbain Jean Joseph Le Verrier, that observation of the planet Mercury began to call doubt on the general validity of Newton’s formulation. Le Verrier had discovered an anomalous advance in the perihelion of the planet Mercury. A planet’s perihelion is the point of its elliptical orbit that is closest to the Sun. Because of gravitational interaction with the other planets in the solar system this perihelion point is not in a fixed location. Le Verrier’s observations showed that the perihelion of Mercury was off by a very slight amount from the predictions given by Newton’s gravitational formula.
Many attempts were made to explain this anomalous observation of Mercury. Adjustments were made as to planetary masses but no consistent set of changes could account for the discrepancy without also changing predictions for other well-known phenomena. Assumptions were made about the oblateness of the Sun but this was not consistent with obervations that were made. Another planet was hypothesized, one whose mass could account for the anomaly. This hypothetical planet, Vulcan, had to be in orbit between the Sun and Mercury. Although claims were made of observation of such a planet, the existence of Vulcan remained a myth. Various theories were formulated that modified Newton’s inverse square law (Netwon’s gravitational force was inversely proportional to the square of the distance separating the masses), but these were all ad hoc modifications that only led to other problems, such as disagreement with the motion of the Moon’s perigee.
Einstein was well-aware of this outstanding anomaly in the perihelion advance of Mercury, and in 1907, two years after his publication of special relativity, he started his work on a more general theory that also included gravitation. His early attempt tried to account for this discrepancy in Mercury, but it did not succeed. In 1911 Einstein realized that he needed a radically new theory, not simply a modification of special relativity. He put concern about Mercury aside and spent the next four years developing a most general theory, one based on principles not conceived of before. It took Einstein four more years to finalize that theory.
On November 18, 1915, Einstein wrote to the great mathematician David Hilbert telling Hilbert about how he had succeeded in his work. Einstein ended the letter with:
“Today I am presenting to the Academy a paper in which I derive quantitatively out of general relativity, without any guiding hypothesis, the perihelion motion of Mercury discovered by Le Verrier. No gravitation theory had achieved this until now.” [The Collected Papers of Albert Einstein, Volume 8, Ann M. Hentschel, Translator, p. 148, Princeton University Press, 1998.]
Einstein had solved the general problem of gravitation with a theory that "is beautiful beyond comaparison [ibid. p. 151], and the anomalous advancement in the perihelion of Mercury was solved, a simple consequence of the theory of general relativity. There are three “classical” predictions of the early theory of general relativity: The deflection of light grazing the Sun, gravitational redshift, and the advance in the perihelion of the planet Mercury. The former prediction is what catapulted Einstein to world-wide fame, but the latter, the solution to the perihelion problem of Mercury, remains as one of the first great accomplishments of modern physics.
Also I have a question about gravity. Let’s take body1 and body2. When they start moving towards each other, the distance between them decreases and consequently the attraction force increases according to Newton’s law of gravitation. However, when they move towards each other, the frequency of the waves/particles, which actually cause gravity, hitting the two bodies should increase. Shouldn’t this also contribute towards the increased force too?
Newton’s law of gravitation is silent on the means by which gravity works. It is simply a mathematical construct that accurately predicts the gravitational behavior of masses within a certain context. When you start talking about the particles that “cause gravity,” you are now talking about particle physics and asking how gravity works on a quantum level. There is no standard theory of quantum gravity that explains gravitation on a quantum level, though there are many theories in development by different groups. They have not yet given consistent results.