Computing the equation of time
Bakersfield College and the William M. Thomas Planetarium are on winter break (evening shows resume again in mid-February). As I write this, though, I wonder if the weather is ever going to get the memo about winter temperatures!
Maybe that’ll happen when winter officially arrives on Dec. 21. Because the official beginnings of the seasons are tied to where the sun is with respect to the celestial equator (projection of Earth’s equator onto the sky), winter will begin at 7:27 p.m. Pacific Time on Dec. 21.
Although the winter solstice, Dec. 21, marks the longest night of the year, it is not the latest sunrise or the earliest sunset of the year. For Bakersfield, the earliest sunset was on Dec. 6 and the latest sunrise will be on Jan. 6 and 7. This mismatch between the longest night of the year and the latest sunrise/ earliest sunrise is described by the “equation of time” that is the difference between the variable motion of the true sun and the uniform motion of the “mean sun” that our timekeeping devices use.
Because our planet, Earth, moves around the sun once every 365 days, the sun appears to drift eastward with respect to the stars about one degree per day. That eastward drift of the sun is why the stars rise earlier and earlier each succeeding night according to our clocks. Earth’s rotation axis is tipped about 23.4 degrees with respect to its orbit around the sun (the “ecliptic plane”), so the sun’s motion among the stars will usually have part of its drift be in the northsouth direction (going northward after the winter solstice and going southward after the summer solstice).
If you plotted the sun’s distance from the celestial equator over the year, the resulting curve would be sort of like an up-anddown sine wave. The peak and troughs of that sine wave would be the solstice dates in June and December. On the solstice dates, all of the sun’s motion would be in the eastward direction (no north-south direction motion).
Another part of the equation of time is caused by Earth’s changing orbital speed as it goes around the sun. Earth moves faster when closer to the sun in July and slower when farther away in January (this also shows why the seasons are not due to the Earth-sun distance). This variable orbit speed is another reason why the eastward drift of the sun is not constant: a slower drift in July and a faster drift in January.
The maximum and minimum of the two effects (the sun’s north-south motion due to Earth’s tilt and the variable orbit speed) don’t coincide with each other, so the equation of time is a complicated curve when plotted over the year. I have pictures describing the Equation of Time on my Astronomy Notes website (the ninth page of the naked eye astronomy chapter or do a search for “Equation of Time” on the website’s homepage).
Astronomers got the motions all sorted out a long time ago to create the modern system of timekeeping. Our bodies’ circadian rhythms are still tied to the true sun’s position, so our “body clocks” can sometimes feel a bit off from the clock on the wall — I really hate the alarm clock that wakes me up before sunrise to get to work in the late fall/ early winter and I’m a bit more tolerant of the alarm clock in spring and early fall.
IN ASTRONOMY NEWS
Now for a couple of brief astronomy research notes. The first is about the discovery of 562 candidates for distant galaxies that have had their light strongly warped/distorted by the gravity of much nearer galaxies in an effect called “gravitationally lensing” due to the warping of the space-time around the closer galaxies. Light from a distant galaxy that would otherwise miss Earth is bent toward Earth, so the distant galaxy is brighter but the galaxy’s shape appears distorted. The strongly lensed galaxies can give us unique information about the evolution of the universe.
Finding the new strongly lensed galaxies required sifting through literally millions of images of galaxies, something only a specially programmed computer can do. However, the computer works only as well as its programming — the candidates found by the computer still have to be verified by a human and the search algorithm is biased by what we think a lensed galaxy should look like.
The second note is about a rare example of international collaboration between the U.S. and China that can happen in science. NASA has approved the use of its funds for U.S. scientists to study samples of the moon from China’s Chang’e 5 mission. It’s a very unusual event when China opens up its science research to international scientists, so this access to the Chang’e 5 samples is fantastic! Chang’e 5 brought back samples from a much younger part of the moon than we did with the Apollo missions and the Soviets did with the Luna missions in the 1960s and 1970s.
If you’d like to see my take on the Bethlehem Star, go to astronomynotes.com/history/bethlehem-star.html. Before you buy a telescope for that special person, take a look at the “Buying a Telescope” section of my website at astronomynotes.com/ telescop/s12.htm. I wish you many blessings this holiday season and a great 2024!