A Key Point in Physics
All bodies must follow certain basic rules which are variously described in Newton's Laws (especially his law of gravity) and Kepler's Laws of Planetary Motion. In particular, the first of Kepler's Law is loosely described as follows: Each planet moves around the sun in an elliptical orbit with the sun at a point called the focus.
All orbits in the solar system are elliptical; it's just that some are more than others. An ellipse is not an egg-shaped orbit, though it can be subscribed--in extreme cases--as cigar shaped. Take a circle and hold it at opposite ends and stretch it. Both ends have the exact same curvature but an egg is pointed on one end and round on the other.
Make an ellipse!
The classic way of making an ellipse is to place two tacks or nails into a board. Make a loop of string and place it around the two nails. The loop should be larger than the distance between the nails so that when you put a pencil in the loop of string and pull it tight, you get a triangle shape. Keeping the loop tight, move the pencil all around the nails. The figure you end up with is an ellipse.
Leave one nail in place and move the other closer or father by an inch or so. Repeat the above procedure. You will get an ellipse of a different degree of non-circularity. This is called eccentricity. The more eccentric the ellipse, the more cigar-shaped it is.
Most of the planets have nearly circular orbits. The Earth is only about 2% eccentric. Venus is almost as close to a circular orbit as we can get, a fraction of 1%. Mercury, on the other hand, is very eccentric, nearly 20%.
What does this mean? First, if you slice an ellipse any way all the way through its center, both halves are identical. But two slices are particularly important. The slice through the long axis or diameter of the cigar shape is called the major axis. The slice through the shortest diameter is the minor axis.
An ellipse can be fully described by the size of its major axis (or semi-major if you just measure from the center to the ellipse edge) and its eccentricity or degree of non-circularity.
Finally, the Sun is NOT in the center of the planetary orbit ellipse at all! It actually sits at one of the two "nail spots" which is called a focus. There is NOTHING at the other focus; it's empty space. But because the Sun is not central, the planet is not always the same distance away. Sometimes it is closer, sometimes farther. The closest point to the sun is called perihelion.
Mercury's orbit is rather cigar shaped. Now all the gravities of the Sun and planets pull on each other and in doing so they "perturb" each other's orbits. They can change the degree of eccentricity. They can also make the orbit "rotate," making it appear as if the "cigar" is slowly turning around, like a battleship gun on a turret. These can all be calculated by good ol' Isaac Newton's laws of motion and gravity though it is not an easy calculation.
When all this is added up, Mercury is still not quite predicted correctly. Its perihelion point, the sharp end of the ellipse closest to the Sun, differs from its predicted location by 43 seconds of arc each century. For comparison, the Moon and Sun are both around 1800 seconds of arc in angular size, on average. This is not a big amount and you might be tempted to dismiss it. But it was the ONLY planet whose motion did not follow the rules. That is a Big Deal.
The conclusion to be drawn was that some other planet that we didn't know about was pulling on Mercury. After all, when newly discovered Uranus was found not to be following its predicted orbit, the calculations indicated another planet beyond it was necessary and, some years later, Neptune was located. In Mercury's case, the planet had to be close to Mercury so it could only affect this planet and not any others. This planet was named Vulcan (no, not the planet of Star Trek's Mr. Spock) after the god of the forge who made Zeus' thunderbolts. After all, being close to the Sun, it had to be hot as a furnace!
For years, astronomers searched near the Sun for a planet. Sometimes, during solar eclipses, a bright star-like object might have been seen near the Sun--the planet Vulcan? Other times, a transit of a dark spot over the Sun's face (which Mercury and Venus do on rare occasions) was thought to be seen. No conclusive evidence was ever found to prove there was a planet pulling on Mercury's orbit, very close to the Sun.
This is a good analogy for Einstein's explanation of gravity. Each ball is a mass, an object, such as a planet or Sun or moon. The water surface represents only two dimensions, not three, but the analogy still works. When the ball (mass) is located someplace in space it bends space-time around it, like the water bed surface gets bent, only in three (or four) dimensions. The more mass, the deeper the hole. We feel this as gravity. The Earth bends space much more than we do. In order to not feel the gravity we have to climb out of the hole. Without a powerful rocket we're stuck here in this gravity well.
The Sun is very massive and makes a deep gravity well. You will need a great deal of speed and energy to get out of the well if you get too close. Take away the Sun for a moment but leave the gravity well in place. If you take a marble and roll it into the well, it will eventually fall in to the well's center. If you want it to go around the well and neither escape nor fall in, you have to make it go at JUST the right speed for your chosen distance. Else, the orbit isn't stable and the marble flies away or heads to center of the well. This is rather like those coin-wells seen in museums or for charities where you insert a coin and it rolls around the rim and then, faster and faster, as it gets near the hole in the center, before plunging into the hold and into someone's bank.
Mercury (especially) and all planets move at just the right speed for their distance. The closer they are, the faster they must move to prevent them from falling IN to the Sun and vanishing. (Kepler's Second Law, in fact.) They can't escape. They are all caught in the Sun's gravity well.
But Mercury has a very eccentric orbit and it is millions of miles closer at perihelion than it is at aphelion, its farthest distance from the Sun. So it really has to move FAST there to stay in orbit. When Mercury is that close, the Sun's gravity is even stronger. In Einstein's words, the curvature of space-time is greater here so Mercury "feels" like there is an extra mass here. That extra mass feels like it is trying to pull the planet inward. By giving Mercury this pull every three months, the orbit is kicked a bit, making it rotate very slowly in space. Remember our marble in the well? Suppose we give it a slight pull inwards every time it gets a little deeper in the well but not enough to pull it all the way in. The marble comes back out but not quite on the path it would have taken if we hadn't interfered. That's what the Sun's gravity is doing. Newton's gravity is much simpler than Einstein's gravity but Einstein's cleared up the mystery of the orbit turning the wrong amount!
The mystery planet is none other than the Sun's extra gravitational pull close in. If Mercury's orbit was more circular, or farther away, the effect would be too small to be seen.
You now know the basis of Einstein's Theory of General Relativity--mass warps space, creating the sensation of gravity!
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