Selamat datang ke blog bagi kursus kami SME 3023: Trends and Issues in Educational for Mathematical Sciences, bagi Sem 1 2011/2012. Kursus ini adalah di bawah seliaan Prof. Dr. Marzita binti Puteh. Diharapkan semua yang mengikuti blog ini akan mendapat manfaatnya.

Wednesday, 14 December 2011

Just a Coincidence?

Even educated people can be surprisingly reluctant to accept simultaneous events as coincidence. Say lightning strikes the church steeple just as old Aunt Mildred dies. Many will see a mystical connection between the events rather than view them as a weird but statistically plausible chance occurrence. 

Coincidences are fun and fascinating, but they make scientists nervous. Case in point: the Andromeda galaxy. This nearest of all spiral galaxies could have had any size at all. In fact, Andromeda is the biggest and brightest within 50 million light-years of Earth. Astronomers, suspicious of what later turned out to be mere coincidence, initially doubted their distance measurements to the galaxy. We want our neighborhood to represent the universe, not be populated by oddballs. 

Space, empty as it is, is crammed with coincidences. We gaze into a sky that displays only two disks, sun and moon, that just happen to appear the same size. The sun’s rotation and the moon’s revolution have nearly the same period of just under a month--coincidentally, of course. In the nineteenth century astronomers were thrown into a tizzy when they found that the planets’ distances from the sun (in astronomical units) seemed to follow a numerical sequence generated by taking the progression 0, 3, 6, 12, 24, 48, 96, 192, and 384, adding 4 to each, and then dividing by 10. The law, however, turned out to have no physical basis; it’s just a numerological quirk. 

More instructive are the apparent coincidences, where chance is not involved. Novice astronomers are often amazed that the moon spins on its axis in the same period in which it revolves around Earth, keeping its far side forever hidden from our view. A closer look, however, reveals the noncoincidental explanation: our planet’s greater pull on the near side of the moon brakes the moon’s rotation and holds it in place like an invisible finger. 

Similarly, planetary observers often saw particular dusky markings on Mercury when that planet completed its orbit; it seemed certain that Mercury had an 88-day rotation, in sync with its 88-day revolution around the sun. But radar imaging in the mid-1960s showed a rotation of 59 days, two-thirds of Mercury’s 88-day year. How, then, to explain the seemingly annually recurring features? 

Mercury Planet

Again, gravitational tugs--only this time from the sun--are to blame. Mercury, like Earth, is not quite round. Instead, it has a slight egg shape, with bulges at either end of the planet. The bulges have a bit more mass than the rest of the planet, and so the sun tugs on them extra hard--harder still when Mercury is at perihelion, the point in its orbit closest to the sun. The tugs slow Mercury’s rotation so that one or the other bulge always faces the sun at perihelion. The result is not a synchronous orbit but a stable variation: in every revolution, Mercury rotates one and a half times. To observers, then, markings on the planet reappear every two revolutions--enough to falsely convince them of the features’ permanence and of a synchronous rotation that does not exist. 

Had enough? Did you know that the number of astronomical units in a light-year (63,240) is virtually the same as the number of inches in a mile (63,360)? Or that the number of seconds in a day (86,400), times 10, is the same as the approximate diameter of the sun (864,000 miles)? 


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