Or, the lilt of the tilt.
The “equation of time” – which means the difference between where the Sun would appear if it moved around the sky at absolutely consequent speed and where it actually appears – continues to be a tricky little subject, about which people ask, and which I ask myself to explain over again to myself. So it’s all in our page about it, part of the “astronomical miscellany.”
A graph there shows a curve that ripples through the year, like a tune on a musical staff, returning to its keynote (the zero line). I’ve made an improvement, at which you might like to look: at Anthony Barreiro’s suggestion, I’ve added a version of the graph with two curves in other colors, to show the components of the main curve. It’s now a tune with harmonies!
Love your 3 color graph. Thank you Guy and Anthony. I made a crude one myself last year when you had a similar post.
Unlike Eric, I have trouble picturing the difference in ecliptic placement and R.A.
If it’s not too much to ask, perhaps you can add a Sky Chart at 11 hour sidereal time. Then place the sun on the 10th, 20th, and 30th of each month on the ecliptic, with a line along the corresponding RA line from the ecliptic to the celestial equator. This would demonstrate how the gaps on the ecliptic are constant while the gaps on the celestial equator are variable.
I have trouble picturing it myself, and am copying your suggestion to my list of things to do If. (You know what If means.)
I still have a very maddening mental block with this phenomenon. You state that at the time around the solstices “the Sun travels across the lines of right ascension on the map of the sky faster than it is traveling in longitude” ~ I get that. It also makes sense that around the time of the equinoxes, “at those times the Sun’s right ascension changes more slowly than its longitude.” I can visualize both of those. What I can’t reconcile is that during both times surrounding the March and September equinoxes, the Sun goes from being “behind at Noon” to being “ahead at Noon” which implies that it is traveling *faster* than its average speed from the standpoint of right ascension, which you state “is the measure of when it is on the meridian at noon.” I must be missing something here.
Ha! Mercy indeed!
This was so informative! Seeing the equation of time as the sum of two sinusoidal curves makes the oddly-shaped ET curve so much easier to understand. Thank you both, Guy and Anthony B, for the very helpful explanation!
Thank you Guy! It is so helpful to see all three curves on the same graph. And even so, when I try to hold everything in my mind — the Earth’s varying speed around the Sun, the swinging tilt of the Earth’s axis of rotation relative to the plane of her orbit, how each of these movements affects the Sun’s path across the sky from one day to the next, and how those two different effects combine to give us one apparent result, I almost always get muddled somewhere along the way. Those moments when I understand it all are blissful, and bliss is always short-lived. Fortunately the Nautical Almanac gives me the Sun’s Greenwich Hour Angle for every hour of the year, so I can easily calculate the equation of time when needed!
I like thinking of the different curves as harmonizing musical tones.
Somewhere I read that when accurate pendulum clocks were first manufactured, each clock came with a table of the dates when the equation of time changes by one minute, so that people could reset their clocks to stay close to local apparent time. This was before they tyranny of standard time zones and the unimaginable idiocy of daylight saving time.
It would be quite interesting to see the ET, and its components, of other planets with more or less eccentricity and obliquely. Perhaps “someone” might write a Java model with sliders for those parameters…
Have mercy!