Twice-yearly solstice marks sun’s switch in direction

The December solstice occurs at 12:44 a.m. Hawaii time Wednesday. At this instant the sun will reach its southernmost point on the ecliptic and start northward again.

The ecliptic is the apparent path of the sun as viewed from Earth’s perspective due to the combined effect of the tilt of its axis to the plane of its revolution around the sun.

It is reportedly the shortest day of the year in the Northern Hemisphere but the longest day in the Southern Hemisphere. In reality the day length is the same within one minute from Dec. 17 to 24, about 10 hours and 50 minutes in Honolulu.

The multiple “longest” days can be traced to the meaning of “solstice,” which derives from Latin words meaning “sun stands still.” The apparent motion of the sun along the horizon at sunrise and sunset is like a pendulum that slows down and stops instantaneously at the two end points as it swings.

From day to day the sun’s motion along the horizon is faster near the center of the swing of the pendulum, which happens at the two equinoxes in March and September as the sun crosses the equator to begin slowing down in the opposite hemisphere until the two solstices in December and June, when it stops momentarily.

The actual day length from sunrise to sunset does change, but only by a matter of seconds. On Dec. 20 the day will be 10 hours, 48 minutes, 51 seconds long. That is 31 seconds longer than Dec. 19 and 29 seconds shorter than Dec. 22.

Orbit’s influence

One might expect that the December solstice would mark the latest sunrise and earliest sunset. This would be true if Earth’s orbit were perfectly circular, but there are no perfectly circular orbits anywhere in the solar system.

Earth’s orbit is elongated elliptically, but only slightly. If the orbit were circular, then Earth would rotate exactly 360/365.25 degrees per day, slightly less than 1 degree per day — specifically, about 0.9856 degrees. As Earth moves slower in its orbit near aphelion (when it is farthest from the sun), it still rotates on its axis at the same rate, so it must turn less to complete a solar day near aphelion than at perihelion (when Earth is closest to the sun).

Eccentricity is the measure of the ellipse, where zero is circular and one is a straight line.

Jupiter’s gravity causes Earth’s orbit to vary from nearly circular with an eccentricity of 0.005 to quite elliptical with an eccentricity of 0.06. Currently we enjoy an eccentricity of 0.0174, nearly its minimum. At present there is only a 3 percent difference in the distance to the sun at perihelion and aphelion.

Because Earth is closest to the sun in January, the time at sunrise migrates later in the morning to 7:11 a.m. from Jan. 7 to 25 as Earth passes through perihelion. The earliest sunset, meanwhile, occurs at 5:48 p.m. from Dec. 20 to Jan. 1, differing by seconds every day just like this year.

The date and time of the solstice, and all of the seasons, drift over a four-year period as Earth’s clock gets out of sync with the calendar until leap year brings it back in sync. In 2017 the solstice will be about six hours later at 6:28 a.m. Dec. 20. This is about one-fourth of a day.

Richard Brill is a professor of science at Honolulu Community College. His column runs of the first and third Fridays of the month. Email questions and comments to brill@hawaii.edu.