And it’s not because of leap seconds; it’s a fundamental property of most days.
Human beings, in marking the passage of time, account for each day equally: with 24 hours.
One of the very first clocks ever produced by Christiaan Huygens, which operated on the principles of a fixed-period pendulum. The clock still survives today, and can be found in the Rijksmuseum in Amsterdam. Although it keeps time very accurately, it’s not quite correct to state that 24 hours marks a true solar day, nor is every day the same. (HANSMULLER / WIKIMEDIA COMMONS)
Although it takes Earth 23 hours and 56 minutes and 4.09 seconds to spin 360 degrees on its axis, the Earth is also in motion with respect to the Sun. If we demand that the Sun reach the same (longitudinal) point in the sky from one day to the next, we need to account for the Earth’s motion as well. (NASA / EXPEDITION 7)
A day isn’t the time it takes Earth to rotate 360°, which leaves us 3 minutes and 55.91 seconds short.
The Earth in orbit around the Sun, with its rotational axis shown. All worlds in our solar system have seasons determined by either their axial tilt, the ellipticity of their orbits, or a combination of both. These factors also determine the variations in the length of a day, as well as variations in sunrise/sunset times. Note that the Earth needs to rotate a little bit extra than 360 degrees in order to see the Sun reach the same apparent location from day to day. (WIKIMEDIA COMMONS USER TAUʻOLUNGA)
That’s what astronomers call a sidereal day, quite different from a common, solar day.
Earth’s and Mars’ orbits, to scale, as viewed from the Solar System’s north direction. Each planet sweeps out an equal amount of area in equal times, in accordance with Kepler’s second law, owing to the conservation of angular momentum. This means that there will be variations in how quickly the Sun appears to move through the sky throughout the year, as seen from any planet’s annual perspective. (WIKIMEDIA COMMONS USER AREONG)
To travel once around Earth’s orbit in a path around the Sun is a journey of 940 million kilometers. The extra 3 million kilometers that Earth travels through space, per day, ensures that rotating by 360 degrees on our axis won’t restore the Sun to the same relative position in the sky from day to day. This is why our day is longer than 23 hours and 56 minutes, which is the time required to spin a full 360 degrees. (LARRY MCNISH AT RASC CALGARY CENTRE)
Owing to its revolution around the Sun, the Earth must rotate approximately 361° to mark a solar day.
Over the course of a 365-day year, the Sun appears to move not only up-and-down in the sky, as determined by our axial tilt, but ahead-and-behind, as determined by our elliptical orbit around the Sun. When both effects are combined, the pinched figure-8 that results is known as an analemma. The Sun images shown here are a selected 52 photographs from César Cantú’s observations in Mexico over the course of a calendar year. (CÉSAR CANTÚ / ASTROCOLORS)
That extra rotation takes 235.91 seconds, which is why our solar day is 24 hours on average.
The effect of our orbit’s elliptical nature (left) and our axial tilt (middle) on the Sun’s position in the sky combine to create the analemma shape (right) that we observe from planet Earth.(AUTODESK GENERATED IMAGE VIA THE UK)
But Earth’s orbital speed isn’t uniform: it’s faster near perihelion (early January) and slower near aphelion (early July).
The theory of universal gravitation can explain the observed orbits of the planets, with Kepler’s 2nd law being derivable from that: that planets orbiting the Sun sweep out equal areas in equal times. Note that this means when Earth is at perihelion (closest to the Sun), it moves more quickly, while when it’s at aphelion (farthest from the Sun) it moves more slowly. (WIKIMEDIA COMMONS USERS RJHALL AND TALIFERO)
Earth’s actual motion around the Sun varies from a low of 29.3 km/s to a high of 30.3 km/s.
The planets move in the orbits that they do, stably, because of the conservation of angular momentum. With no way to gain or lose angular momentum, they remain in their elliptical orbits arbitrarily far into the future. The Earth makes its closest approach to the Sun every January 3rd or so, while it’s most distant in early July. (NASA / JPL)
Factoring this in, our day’s length varies by about ±4 seconds throughout the year.
The equation of time is determined by both the shape of a planet’s orbit and its axial tilt, as well as how they align. During the months nearest the June solstice (when the Earth nears aphelion, its farthest position from the Sun), it moves the most slowly, and that’s why this section of the analemma is pinched, while the December solstice, occurring near perihelion, is elongated.Note that where the equation of time has a derivative of zero, observers at that latitude will see a 24 hour day. (WIKIMEDIA COMMONS USER ROB COOK)
As the Earth rotates on its axis and orbits the Sun in an ellipse, the Sun’s apparent position appears to change from day-to-day in this particular shape: Earth’s analemma. The tilt of the analemma will correspond to the time of day at which the image is taken, while the height above the horizon will depend on your latitude. However, this shape is always reproduced from Earth if you take a photograph at the same time of every day. (GIUSEPPE DONATIELLO / FLICKR)
Only four times annually, latitude-dependent, are days actually exactly 24 hours.
Just 800 years ago, perihelion and the winter solstice aligned. Due to the precession of Earth’s orbit, they are slowly drifting apart, completing a full cycle every 21,000 years. 5,000 years from now, the spring equinox and the Earth’s closest approach to the Sun will coincide. This is a small, subtle effect that creates another minor departure from 24 hours being the exact length of a day, but it’s negligible when compared to Earth’s rotational motion on its axis and its orbital motion around the Sun. (GREG BENSON AT WIKIMEDIA COMMONS)
Mostly Mute Monday tells an astronomical story in images, visuals, and no more than 200 words. Talk less; smile more.
