Veritasium – The SAT Question Everyone Got Wrong
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That was great! Thank you, Chris McLaughlin.
I would have said 3, too, so, glad I took the SAT prior to 1982.
When I first saw this problem (I saw this video a few months back), my intuitive answer was “4,” because it is the same problem as the number of times the Earth rotates on its axis in the year that it goes around the Sun. The answer was obvious by inspection.
It is an old concept, and it is a tricky one. As our presenter said, it is a concept that is vitally important for astronomers to understand when figuring out where to point their telescopes each night. There are 365¼ days in a year, but the Earth rotates 366¼ times in that year. This is why the Zodiac constellations change positions relative to midnight. The Moon rotates once a month (actually, a little more), but from our point of view it does not rotate at all, and if we do think of it as rotating, we would usually think it rotates 12 times a year, but it rotates once more than that (actually, closer to 13½ times).
It just goes to show that the people who put together the SAT tests (and similar tests) are not rocket scientists, brain surgeons, nuclear engineers, or astronomers.
The SAT people also have not played much with Spirograph sets, because that is another experience that can show the same results.
It is also a concept that is important for orbital mechanics, so I will add them to the list of people not writing these tests. Orbital mechanics (the engineers doing the calculations) need to understand this concept in order to calculate where their spacecraft is over the planet. If they don’t understand this one, they don’t take pictures of Mars in the right place, and Robert would be giving us the wrong locations for some of the Cool Image Time! pictures.
The concept appears in a few unexpected areas of life. There are gears called “orbital gears,” or “planetary gears,” that do this same thing, and their shafts turn more than the number of times they go around the center (or less, if they are on the inside).
The presenter gave us examples from different reference frames, showing how important frame of reference can be. From our frame of reference on the Earth, the Sun rises in the east, but from a reference frame fixed to the Sun, it doesn’t rise at all; the Earth rotates as it revolves around the Sun. It is a completely different experience, giving completely different realities. Frame of reference is one reason why Lagrange Points are so difficult to understand, because they are presented in a rotating frame of reference, but they only work because of the revolutions of the secondary body. For instance, the L1 point is not a balance of gravity, as the usual presentation of Lagrange points suggests, but is the balance of gravity and the momentum of a body at the revolving L1 point.