Jan 22 2021 If you remember my column from last week, it tried to explain a phenomenon I've known of for a long time: the sun rising later every day after the winter solstice for about three weeks. The explanation involves our idea of noon. (You know, as in "twelve-" and "after-" and "go-have-lunch-at-").
This week's column delves into what noon means, and why the time when it happens (typically, not 12) varies from day to day. Here you go: https://www.livemint.com/opinion/online-views/opinion-what-is-it-about-noon-anyway-11611302099871.html Let me know your thoughts, please! cheers, dilip --- What is it about noon, anyway? What is it about noon, anyway? In my last column here, I wrote that despite our familiarity with the phrase "12 noon", strictly it is not that moment in the day when the clock strikes 12. Instead, it is the moment in the day when the sun is directly overhead. Though even that is inaccurate, because if you live north of 23.5 degrees North or south of 23.5 degrees South, you will never see the sun directly overhead. Why so? On any day in the year - at any point in the Earth's orbit around the Sun - imagine a line connecting the centre of the Sun and the centre of the Earth. The point where that line pierces our planet's surface is - visualize it for yourself - where the Sun will be overhead that day. Now imagine the Earth's axis is not tilted; that it is instead perpendicular to the plane of the orbit. A little more visualizing will show you that throughout the year, the line will pierce the Earth's surface somewhere on the Equator. Nowhere on this hypothetical untilted planet, except for along the Equator, will we see the Sun directly overhead. But of course the Earth's axis is tilted. On the two equinoxes - March and September - that pierced point is on the Equator. But as the tilted Earth revolves around the Sun, that pierced point moves across the surface of the Earth. From March till June, it moves North of the Equator, reaching a latitude of 23.5 degrees North - the angle of the tilt. Then it swings South, crossing the Equator in September, touching 23.5 degrees South in December and then turning North again. The point stays firmly within the belt between 23.5 degrees N (the Tropic of Cancer) and 23.5 degrees S (Tropic of Capricorn). Thus it is that people outside this belt - in Punjab and Kashmir and Iceland, New Zealand and Tierra del Fuego and the Kerguelen Islands - will never see the sun directly overhead. So noon is really that moment in the day when the sun is at its highest in the sky. When it is exactly halfway in its path across the sky between sunrise and sunset. That might happen at 12 where you are; but much more likely, it won't. It might be when the Sun is directly overhead where you are today; but much more likely, it won't. If that's clear, let's try to figure out why this solar noon's clock time, at any given latitude, varies from day to day. For example, here in Mumbai it occured at 12:36 on the winter solstice a month ago, 21 December. Today, it comes at 12:50. Call the time between today's solar noon and tomorrow's, wherever you are, a solar day. That's 24 hours, we all know. (Actually a few minutes short of 24 hours, but never mind that.) The thing to note is, the length of a solar day varies through the year. How so? First of all, think what defines a day on Earth: the rotation of the planet on its axis. Let's say you're at a latitude where the sun is directly overhead at solar noon today; that is, that pierced point is precisely where you sit reading this. Because of the rotation of the Earth, that point travels westward around the Earth. (Westward, because the Earth rotates west-to-east). When it has gone all the way around and returned to where you are, that's one solar day, defined as 24 hours. If the Earth only rotated and did not orbit the Sun, each day would be exactly this long. Noon would come at the same clock time every day. But the Earth does orbit the Sun; so in those same 24 hours, it has also moved about a degree forward in its orbit. That orbital motion has an effect on the length of the solar day. Imagine for a moment that the Earth only orbits the Sun and does not rotate on its axis. Again, visualize this with an untilted Earth. You'll realize that that pierced point, moing along the Equator as we noted, makes one rotation around the planet in a year. This motion is eastward, because as seen from above our North Pole, the Earth's orbit is anti-clockwise around the Sun. In other words, rotation around the axis moves that point westward; revolution around the Sun moves it eastward (though much more slowly). Taken together, this makes each solar day - solar noon to solar noon - slightly longer than it would be from just rotating. This is why the clock time of solar noon changes from day to day. But that's not all. Again, we must now account for the Earth's tilt. Again, think for a moment only about the orbital motion, not the rotation. Because of the tilt, the pierced point does not traipse along the Equator through the year, but along a path tilted at 23.5 degrees from the equator. It still moves broadly eastward, but now there's a northward (December to June) and southward (June to December) component to its motion as well. And it moves eastward fastest at the June and December solstices, when the sun is "turning around" at one of the Tropics; it moves eastward slowest at the March and September equinoxes, when the sun crosses the Equator. Remember that it's only the eastward component of this motion that counts, against the westward motion of the point due to the Earth's rotation. At the solstices, when the eastward motion is at its highest, the solar day is lengthened by more than it is at the equinoxes, when the eastward motion is at its lowest. All of which means that the daily change in the clock time of solar noon is greater around the equinoxes than around the solstices. Naturally, you want to check that. As I mentioned above, solar noon moved from 12:36 on 21 December to 12:50 today, 22 January - in 32 days after the winter solstice, a difference of 14 minutes. On 22 September, it was at 12:31; on 24 October, it was at 12:22 - in 32 days again after the autumn equinox, a difference of 9 minutes. All of which is part of the explanation for steadily-later clock sunrises from winter solstice to January 14 (in Mumbai), even as the length of the day increased. This phenomenon has intrigued me for years and prompted my previous column and this one. That column ended by asking: "what, if anything, happens to sunrises and sunsets around the summer solstice, 21 June?" Well: after the summer solstice, as you might expect, the length of the day starts decreasing. But counter-intuitively, the sunsets get later for about three weeks afterward. It's because the sunrises get later at a faster pace than the sunsets do that the days get shorter. Check: On 21 June 2020, the sun rose at 6:02am and set at 7:18pm - 13 hours and 16 minutes of daylight. On 10 July 2020, it was 6:09am and 7:19pm respectively, for 13 hours and 10 minutes of daylight. But that's after the summer solstice. I'll leave you to find out and explain what happens in the weeks leading up to the summer solstice. Is there a parallel to the winter phenomenon? As you can tell, the questions are endless. That's because there's endless fascination in such examinations of planetary and other cosmic motion. Never enough hours in the day to get to them all. --- (I owe what's in these two columns to several sources; most of all to an essay by Larry Denenberg, a mathematician in Boston). -- My book with Joy Ma: "The Deoliwallahs" Twitter: @DeathEndsFun Death Ends Fun: http://dcubed.blogspot.com -- You received this message because you are subscribed to the Google Groups "Dilip's essays" group. 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