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August Sky

August Sky


Do you ever take a moment to gaze at the night sky? During late August and early September of 2003, who could miss the sharply focused bright red spot in the sky? Other celestial bodies may have seemed faint and far away, obscured perhaps by light pollution, but that bright body claimed our whole attention anyway. It was Mars, the red planet, which burnt into our memories. The interesting thing is that this scene was just as remarkable and unique as it appeared. Astronomers tell us that Mars has not been this close to Earth in 60,000 years. They base such conclusions on computer models of planetary motion. However, in a young universe, it may be that Mars has never approached us this closely before. We live in special times.

We take the motions of the planets for granted. What could be more reliable than the appearances of the planets in the night sky? The topic seems so humdrum that text books hardly discuss the solar system any more. But things are far from boring and far from being clearly understood. It was French mathematician Jules Henri Poincare (1854-1912) who first argued that the long term motions of the planets are not as predictable as had been supposed. Indeed Poincare is famous for his demonstration that there is no single and obvious solution to equations involving the motion of three or more moving objects. While it is perfectly possible to solve equations predicting the motion of two bodies about each other, once there are more moving objects, the calculations are swamped with unknowns which block clear answers. Thus n-body (where n is more than two) equations involving orbiting bodies are formally unsolvable. (This is not the case for equations in your math text books. They may seem unsolvable, but usually an answer can be found if you work long and hard enough at it!) We therefore have no theoretical explanation for planetary motions in the solar system. Why they stay in place, undisturbed by nearby moving bodies, we can’t really say.

So, one might ask, how is it that modern astronomers have computer models of planetary motion?

While the astronomers cannot make predictions of planetary motion based on theoretical considerations, they can base their models on actual past performance. Thus present-day observations are used to build models which are run backwards to see what possibly happened in the past, and forwards to see what may happen in the future. From this, astronomers draw conclusions about Mars’ past positions relative to Earth.

The scene is not simply one of the planets moving in simple orbits about the sun. German astronomer Johannes Kepler (1571-1630) first proposed that the planets follow elliptical orbits. This complicates the situation since each planet moves most rapidly when it is closest to the sun and more slowly when it is farthest from the sun. Kepler apparently was fascinated by the beautiful mathematics of the motion of the planets. In addition, he found that the length of time a planet requires to proceed once around the sun (its year), varies with that object’s distance from the sun. In other words, the distance from the sun (in astronomical units where the earth to sun distance equals one astronomical unit), once cubed, yields a value which when the square root is found, equals the number of earth years which that planet takes to orbit the sun. This may sound too much like math for your taste, but the result is that the inner planets move much faster around the sun and thus they regularly whiz past the more remote planets. The situation is like racers on a oval track. One runner may appear to be behind another, but is in reality almost a whole lap ahead.

Further complicating factors do arise however, like the shape and tilt of the elliptical orbits. While most of the planets’ orbits are nearly circular, the orbits of others are considerably longer and thinner. There is actually a fair amount of variety in orbit shape. Scientists call this value eccentricity. While the eccentricity of a circle is zero, the orbit of the planet Earth has an eccentricity of 0.017. In addition, the orbits of two planets are more nearly circular than Earth’s: namely Venus at 0.007 and Neptune at 0.010. Mars however has a considerably longer ellipse with a value of 0.093. The most extreme eccentricities are found with innermost Mercury at 0.206 and outermost Pluto at 0.248. Apparently Mercury’s elliptical orbit is particularly interesting. The ellipse rotates about the sun so that a diagram of the ellipse positions looks like daisy petals (with the sun as the daisy centre). Moreover it is Mercury and Pluto which also have the most extremely inclined (tilted) orbits while the tilt of the other orbits are all much like Earth’s.

It is the difference in orbit shape which has led to this unusual close approach of Mars to Earth. Astronomers tell us that on August 27, 2003, Mars was a mere 55 million kilometres from Earth. Depending upon the computer model used, this is said to have last happened 50,000 to 100,000 years ago. The unusual proximity came about because Mars was at its closest approach to the Earth on August 27 and also at its shortest distance from the sun on August 30. The rendezvous began on August 10, 2002.

At that time Mars was on the opposite side of the sun, about 400 million kilometres from Earth. The result of the much decreased distance in late August 2003, was that Mars appeared 85 times brighter than it did the year before. However, like ships passing in the night, the two planets are now, in their continuing ballet, moving away from each other again.

Questions arise as to why the orbits of the planets are so different. Secular explanations for the origin of the solar system would probably favour more circular orbits of similar shape for all planets. In addition, Poincare’s n-body problem suggests to mathematicians that the solar system may be chaotic. This means that the system could suddenly fall apart into random tumbling motions. Some of the computer models have suggested that if the system continued over millions of years, this would happen. In similar vein, a recent study suggests that the Earth/Moon system plays an important dynamic role in maintaining the stability of the orbits of Venus and Mercury. Without the Earth and her moon, suggests this study, gravitational push and pull from the large planets would cause the orbits of the two inner planets to immediately lose their position. (L. Innanen, S. Mikkola and P. Wiegert. 1998. Astron. J. 116: 2055). The result could potentially be a terrible crash! Our nice regular solar system would be utterly devastated. Isn’t it wonderful that the Earth and Moon are so precisely positioned?

Our image of the clockwork regularity of the solar system thus disintegrates on closer inspection. The fact that the system holds together is not automatic nor can science explain why it does so. The final lesson for us from this topic is that when things seem simple or uncomplicated, it is often merely our ignorance that makes them appear that way. What we most need to appreciate is with what finesse and how precisely our solar system is designed. The events of this past August certainly reinforce this realization.

Margaret Helder
October 2003

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