How does general relativity solve the problem of extra precession of mercury that Newton can't smooth out?

For me, there is no higher honor in the world than scientific progress. Isaac? Newton's theory of gravity has dominated the world view of mankind for nearly two centuries, and there is nothing in the world that Newton can't solve. But he stumbled upon mercury.

Now we know that Einstein's general theory of relativity has surpassed Newton's theory, because if Newton's law is used, the precession of Mercury's orbit will have a small deviation that is hard to erase every century. So how does general relativity solve this problem? Many times we will skip this question, but today we will talk in detail about the advantages of general relativity over Newton's gravity.

From the above picture, we can see that every planet in the solar system revolves around the sun. More precisely, the orbit of the planet is not a perfect circle, but an ellipse, which Kepler discovered a century before Newton. In the inner solar system, the orbits of the earth and Venus are very close to a circle, but the orbits of Mercury and Mars look more like ellipses, and their distances from the sun are quite different.

In particular, Mercury's perihelion (the farthest point from the sun) is 46% larger than its perihelion (the closest point to the sun), while the difference between the earth is only 3.4%. This is enough to see what is a near circle and what is an ellipse.

As for why the orbits of planets are different, this gravity has nothing to do with it, that is, it has nothing to do with the distance from the sun, just because the conditions when the planets formed led to a specific orbit.

If Kepler's law is absolutely perfect in the solar system, then a planet orbiting the sun will return to a perfect closed ellipse, that is, the planet will orbit from one position and return to its original position once. That is to say, when the earth begins to revolve at perihelion, then the earth will return to perihelion accurately again one year later. The position of the earth in space relative to the sun is exactly the same as that of the previous year.

But we know that Kepler's law is only mathematically perfect, and its perfection only applies to particles without mass. But the solar system not only has mass, but also many celestial bodies in orbit interfere with the operation of a planet.

When a planet orbits the sun, there are other large celestial bodies around it, including planets, satellites, asteroids and so on. In addition, both the planet and the sun have mass, which means that the planet itself does not revolve around the center of the sun, but around the center of mass of the planet/sun system. Finally, our earth's rotation will precess around the axis, which means that our tropical year (season and calendar) and sidereal year (the earth revolves around the axis 360? ) there is a difference. In other words, the vernal equinox is constantly moving westward, and the tropic year is always 20 minutes and 24 seconds less than the star, which is called precession.

If we want to predict how much the orbit of another planet will change with time, we must consider all the above factors.

First of all, the difference between the sidereal year and the tropic year is small, but it is very important: the sidereal year is 20 minutes and 24 seconds larger than the tropic year. This means that when we talk about seasons, equinoxes and solstices, it happens on the basis of calendar years, but the perihelion of the earth changes slightly relative to these solar terms. A circle is 360 degrees, so from 65438+1 October 1 in one year to 65438+1 October1in the next year, the earth actually only turns 359.98604 degrees in orbit, that is to say (/kloc-0. (arc minutes), 1 arc minutes is 60 "(arc seconds)) Due to the precession of the earth, the perihelion of each planet will move at a speed of 5025" per century.

But at the same time, we should also consider the influence of planetary mass.

Each planet will have different effects on the motion of another planet, depending on its relative distance, mass, orbital proximity and whether it is inside or outside the planet. Mercury is the innermost planet, which can be said to be the easiest planet to calculate: all the planets are on the periphery of mercury, so the peripheral planets will advance the perihelion of mercury. The following are the impacts of these planets, in descending order of importance:

Venus is 277.9 per century? .

Jupiter: every century 153.6? .

Earth: 90.0 per century? .

Saturn: 7.3 per century? .

Mars: 2.5 per century? .

Uranus: 0. 14 per century? .

Neptune: 0.04 per century? .

There are other influences, such as the influence of asteroids and celestial bodies in the Kuiper Belt, and the oblateness (asphericity) of the sun and planets is 0.0 1 "or less per century, which can be ignored.

In short, these effects add up, the perihelion of Mercury advances by 532 inches every century, and if the precession of the earth is added, it advances by 5557 inches every century. But what we have observed is that the perihelion of Mercury is advancing at a speed of 5600 "per century.

The actual precession is larger than Newton predicted, so why?

The first thing to consider is that there is an unknown planet inside Mercury, and its revolution speed is very fast, which can generate extra thrust for Mercury through the influence of gravity, or the sun's corona is very huge; In both cases, the required additional gravitational effect may be generated. But the sun's corona is not big, and there is no so-called Vulcan!

The second idea comes from Simon? Newcomb and Asa? Hall, they think that if we change Newton's gravitational inverse square law into another law, that is, gravity is inversely proportional to the power of 2.005438+06 12 of the distance, we can explain the extra precession of Mercury. The implication is that Newton was wrong. We know today that if Newton's gravity equation is modified, the orbits of the moon, Venus and the earth will be disrupted, so it is impossible.

The third idea comes from Henry? Poincare, he pointed out that if we consider Einstein's special theory of relativity (Mercury orbits the sun at an average speed of 48 km/s, that is, 0.0 16% of the speed of light), we will get some (but not all) missing precession.

It is the combination of the second and third viewpoints that produces general relativity. The concept of time and space comes from Einstein's teacher Herman. Minkowski, when Poincare applied this concept to the orbit problem of Mercury, he took an important step towards solving this problem. Although newcomb and Hall's views are incorrect, it shows that if gravity is stronger than Newton's prediction of mercury's orbit, then the abnormal precession of mercury can be explained.

Of course, Einstein's great idea is that the existence of matter/energy will lead to the bending of space, and the closer an object is to a very massive object, the stronger its gravity will be. And the greater the deviation from Newton's gravity theory prediction.

That is to say, in the vicinity of a massive object, or in front of strong gravity, the gravity felt by the object is greater than that predicted by Newton's theory. This explains why Newton's theory can successfully explain the motion of other planets, but not on Mercury. Because mercury is closest to the sun. Einstein's gravity theory made up for the extra precession of Mercury and made an unusual prediction.

In other words, when light passes through a massive celestial body, such as the sun, it will bend. This prediction was finally used to test whether Newton's theory or Einstein's theory was correct.

Newton's theory predicts that starlight will never deflect when it passes through the sun, because light has no mass. But if we assign a mass to light according to Einstein's E = mc^2, then according to Newton's gravity theory, light will be deflected by 0.87 ". However, Einstein's theory gives twice the deflection: 1.75 ".

These numbers are very small, the difference is very small, but during the 19 19 solar eclipse, Arthur? Eddington and Andrew? Cromoline's joint investigation result is light deflection 1.438+0 "? 0.30 ",which is consistent with Einstein's prediction and inconsistent with Newton's prediction within the error range.

This is not only the story of Newton's gravity being replaced, but also the story of Newton's theory being flawed in some aspects. Since then, general relativity has won many predictions and has not failed so far.