South Jersey Skies: The instability of the solar system

Keith Johnson By Keith Johnson Gloucester County Times
on August 12, 2012 at 6:00 AM
Suth Jersey Skies.jpg

Once astronomers depicted the solar system as a stable place. The planets moved along in their stately orbits, dependably showing up where they should be at the predicted times. To the 3rd-grader I used to be, the solar system seemed like a giant clock with nine smoothly-turning gears.

We no longer believe in this simple system. Even Isaac Newton, who devised the law of gravity that governs the motions of the planets, realized that this law actually predicted that planetary orbits would slowly change. He postulated that God occasionally found it necessary to reach down from heaven to reset the planets into their proper positions.

The problem is that everything has gravity. The Earth's motion around the Sun is controlled almost completely by the force of gravity from the Sun that binds it into a permanent orbit. It's easy to come up with a stable orbit like that when you only need to worry about two celestial bodies.

But note the presence of the word “almost.” With more than two bodies, things get much more complicated mathematically, because each body exerts a force on every other body. The path of the Earth is continuously perturbed by the gravity of Jupiter, and the Moon, and even passing comets and asteroids; and each of them affects each of the others. It's no longer possible to solve the equations of motion and gravity and find a simple solution.

Those effects are minuscule, to be sure. The gravitational force of Jupiter on the Earth is 100,000 times weaker than that of the Sun. But that's enough to cause a slow change in our planet's orbit if you just let enough time go by.

It's also true that we don't know the details of the orbits perfectly precisely. We now list the positions of the planets in their orbits to an accuracy of a few inches, but no better.

Moreover, we now know that in certain kinds of systems, small uncertainties in starting conditions can build up to enormous differences in the end results. This is almost the scientific definition of the word “chaos.” The sense of this kind of chaos is often presented by saying that the flapping of a butterfly's wings in China today may change the path of a hurricane in the North Atlantic a year from now.

In the case of the solar system, scientist Scott Tremaine tells us that “shifting your pencil from one side of your desk to the other today could change the gravitational forces on Jupiter enough to shift its position from one side of the Sun to the other a billion years from now.”

In addition, there are many other quantities we don't know with perfect precision that could affect our analyses. How many asteroids are there? How is the gas within the Sun distributed, smoothly, or with symmetrical condensations? How much mass does the Sun lose each year to the solar wind? How strong is the tidal force of the Milky Way galaxy?

None of these factors are large, but we don't know how their effects could build up over the years. Therefore, we can't predict the positions of the planets with any accuracy for more than another 100 million years.

So what could happen? We can use powerful computers, and new mathematical techniques, to create computer models of the solar system.

We could start our study by slightly altering the positions of the planets, and let our computers crank out what the planets will be doing to each other in the future based on the various values. Some studies have changed only the initial positions of the planets by amounts no bigger than a millimeter-well within the precision of our measurements-and computed positions far into the future.

Most of the results were benign. Planets simply appeared ahead of or behind their expected positions in their orbits. Changes in orbit shapes and sizes were also seen, but usually not sizable ones. But in nearly 1% of the cases, Mercury's orbit became so eccentric that it would crash into Venus!

In general, the other orbits are also chaotic, and will change in size and shape, to a lesser degree but measurably. The future solar system may look quite different from what we see today.

Other possible changes may strike closer to home. Tidal forces from our own Moon may cause the Earth's tilt in its orbit to become chaotic and unpredictable. Since the severity of our seasons depends on how big that angle is, this is an important issue!

The critical question, then, is one of time. How fast will also this happen? Fortunately, the various studies all agree that very long times must elapse for anything significant to happen. Even the low-probability crash of Mercury and Venus would not happen until not long before the death of the Sun, five to seven billion years from now. On short time scales, we live in a very stable system.