What is wrong with Mercury's orbit? | Mercury Planet Exploration | Deep Science Documentary Tapes
What is wrong with Mercury's orbit? | Mercury Planet Exploration
The 200-year-old mystery of Mercury's orbit — solved!
It wasn't too long after Newton published his laws of motion that people noticed something was off about them. To be specific, they were off by the orbit of an entire planet. And they remained off until Einstein, and general relativity explained why Mercury moves the way it does.
The laws of motion were, and remain powerful tools for understanding the world. When they debuted, Newton used them to explain the motions of pendulums and the motions of planets. Both the earthly and the celestial fell into the realm of the explainable, and people settled back, comfortable with their conception of the universe. That is until something about Mercury's orbit seemed just a tad off.
The Precession of Mercury
The orbits of the planets are slight ovals, with the sun located toward one end of the oval. The point at which the planet comes closest to the sun is the perihelion, and the farthest point of the oval is the aphelion. The oval orbits themselves move. As if the sun were a pin stuck into them, the orbits slowly rotate around it, in a motion called precession.
The precession of the orbits is accounted for by Newton's laws of motion. As astronomers charted the progress of the planets, they conformed agreeably to predictions based on those laws of motion. All except one. Mercury's orbit made it's round faster than predicted. It didn't race ahead. The precession was 93 percent accounted for, but no one could adequately explain that last seven percent.
Phantom Planets and Invisible Dust
After Vulcan failed to show up, other astronomers assumed there was an asteroid field or a massive field of dust near Mercury. This would add a little extra mass to the equations and explain why Mercury precessed so quickly. Still the years went by, and no field of dust showed up.Something strange was going on. Astronomers assumed that they had missed something. It wasn't an unreasonable assumption. Urbain Le Verrier, after all, had noticed that something was going on with Uranus' orbit, and by studying the variation deduced the existence of Neptune. It was easy to lose a little planet in such a big sky. For a while, people assumed that a mysterious planet called Vulcan was throwing off the precession of Mercury.
Einstein and Relativity
Where people went wrong was looking for objects. Einstein eventually revealed that they should have been looking at space itself. In his theory of general relativity, Einstein showed that mass warps space. This warping didn't noticeably affect planets far from the sun, but Mercury was so close that its strange precession was visible as soon as people started paying close attention.
For two hundred years, we were the observers of that inexplicable penny. We saw Mercury makings its rounds around the sun, quickly and sharply, without knowing the reason why. And although we still can't see the curve of the universe, we do now know that it's there.One way to understand the warp in space, and how it affects Mercury's orbit is to draw a quick, exaggerated oval on a piece of paper. Put the sun at one end. Draw a line from the aphelion (the farthest point from the sun) to the sun itself. Then cut along that line, and slightly overlap the two resulting flaps of paper. The paper itself will be drawn into a slight cone shape. If you look at the orbit, it will literally be bent out of shape. Instead of the orbit gently curving one its way back towards the aphelion, it will curve much more tightly. Another way to think about it would be to imagine rolling a penny along a surface that suddenly curves. As the penny goes around the curve, it changes speed and course, but if you can't see the curve, it would look like it inexplicably turned on its own.
Top Image: NASA/Johns Hopkins University Applied Physics Laboratory/Carnegie Institution of Washington
Via Cornell, UCR, Relativity.
Precession of the perihelion of Mercury
A long-standing problem in the study of the Solar System was that the orbit of Mercury did not behave as required by Newton's equations.
To understand what the problem is let me describe the way Mercury's orbit looks. As it orbits the Sun, this planet follows an ellipse...but only approximately: it is found that the point of closest approach of Mercury to the sun does not always occur at the same place but that it slowly moves around the sun (see Fig. 7.20). This rotation of the orbit is called precession.
The precession of the orbit is not peculiar to Mercury, all the planetary orbits precess. In fact, Newton's theory predicts these effects, as being produced by the pull of the planets on one another. The question is whether Newton's predictions agree with the amount an orbit precesses; it is not enough to understand qualitatively what is the origin of an effect, such arguments must be backed by hard numbers to give them credence. The precession of the orbits of all planets except for Mercury's can, in fact, be understood using Newton;s equations. But Mercury seemed to be an exception.![\begin{figure} \centerline{ \vbox to 3.8 truein{\epsfysize=8 truein\epsfbox[0 -180 612 612]{7.gtr/prec_mercury.ps}} }\end{figure}](https://aether.lbl.gov/www/classes/p10/gr/img249.gif)
As seen from Earth the precession of Mercury's orbit is measured to be 5600 seconds of arc per century (one second of arc=1/3600 degrees). Newton's equations, taking into account all the effects from the other planets (as well as a very slight deformation of the sun due to its rotation) and the fact that the Earth is not an inertial frame of reference, predicts a precession of 5557 seconds of arc per century. There is a discrepancy of 43 seconds of arc per century.
This discrepancy cannot be accounted for using Newton's formalism. Many ad-hoc fixes were devised (such as assuming there was a certain amount of dust between the Sun and Mercury) but none were consistent with other observations (for example, no evidence of dust was found when the region between Mercury and the Sun was carefully scrutinized). In contrast, Einstein was able to predict, without any adjustments whatsoever, that the orbit of Mercury should precess by an extra 43 seconds of arc per century should the General Theory of Relativity be correct.
An early success of Einstein's theory was an explanation for the 43'' per century precession of the perihelion of Mercury. In a curved spacetime, a planet does not orbit the Sun in a static elliptical orbit, as in Newton's theory. Rather, the orbit is obliged to precess because of the curvature of spacetime. When Einstein calculated the magnitude of this effect for Mercury he got precisely the previously unexplained 43''. He correctly took the view that this was an important confirmation of his theory.
Einstein's theory also correctly accounts for a smaller discrepancy of 8.6'' per century in the precession of the perihelion of Venus. The value is smaller than that of Mercury because Venus is further from the Sun and the curvature of spacetime is less.
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