Why today really isn’t 24 hours long

In marking the passage of time, we’ve assigned 24 hours to each and every day.

Most of us are very used to 24 hours being in a day but aren’t used to the fact that this doesn’t correspond to a 360 degree rotation of the Earth. Most days, however, are either longer or shorter than 24 hours; only 4 days a year have precisely 24 hours to them.

While that’s a day’s length on average, most days aren’t actually 24 hours.

This diagram shows an analemma, constructed by photographing the Sun at the same time throughout the year. The fact that the Sun isn’t in the same place is the combined effects of our axial tilt/obliquity and our orbital eccentricity and speed variations as we revolve around the Sun. The Sun is not in the same position every day because each day is not exactly 24 hours.

Counterintuitively, a day isn’t the time required for a planet-wide 360° rotation.

The Earth, moving in its orbit around the Sun and spinning on its axis, always defines “noon” and “midnight” in the same fashion: where the Sun’s height above or below the horizon is maximized. This moment in time doesn’t correspond to when Earth has rotated 360 degrees from the prior day, but rather closer to 360.9856 degrees, owing to the added effects of Earth’s motion around the Sun.

We rotate 360° each 23 hours, 56 minutes and 4.09 seconds, leaving us 00:03:55.91 short.

These star trails appear in the sky due to long-exposure photography of the north pole, combined with the physical phenomenon of the rotating Earth. Although no one has ever successfully captured a full 360 degree star trail, it surprises people to learn that you wouldn’t need a 24 hour photograph to complete the circle, merely a 23 hour, 56 minute and 4.09 second exposure, as it relies on a sidereal, rather than a solar day.

A full rotation, astronomically, is a sidereal day: different from a solar (calendar) day.

When the Earth spins a full 360 degrees about its axis, it hasn’t yet aged by one full day, because it has also shifted in its orbit around the Sun. It must therefore rotate nearly an extra 1 full degree to “catch up,” which explains the difference between a sidereal day (360 degree rotation) and a solar/calendar day (where the Sun returns to its prior day’s position).

Conventional days are defined by the Sun returning to its prior position the day before.

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 both obliquity and 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.

This requires accounting for Earth’s motion through space.

This view of the Earth comes to us courtesy of NASA’s MESSENGER spacecraft, which had to perform flybys of Earth and Venus in order to lose enough energy to reach its ultimate destination: Mercury. Several hundred images, taken with the wide-angle camera in MESSENGER’s Mercury Dual Imaging System (MDIS), were sequenced into a movie documenting the view from MESSENGER as it departed Earth. Earth rotates roughly once every 24 hours on its axis and moves through space in an elliptical orbit around our Sun.

Earth requires ~1° of additional rotation to account for its daily motion around the Sun.

This not-to-scale diagram shows the difference between a sidereal day, where Earth spins a full 360 degrees, and a solar day, which requires an extra 3 minutes and 55.91 seconds, in order for Earth to rotate by enough to return the Sun to its prior day’s position in the sky. Earth not only spins on its axis, but revolves around the Sun: both aspects must be taken into account in defining a calendar day.

That “extra” 0.9856° of rotation equates to an additional 235.91 seconds, lengthening the solar day to 24 hours.

From one day to the next doesn’t correspond to just a 360 degree rotation of the Earth, but enough extra rotation to correspond to the Sun returning to the same position in Earth’s sky. Similarly, the duration of a lunar month isn’t simply the time it takes the Moon to revolve 360 degrees around Earth, but to return to the same position relative to the Sun as seen from Earth.

But Earth’s orbital speed also varies, moving faster near January’s perihelion and slower around July’s aphelion.

Even before we understood how the law of gravity worked, we were able to establish that any object in orbit around another obeyed Kepler’s second law: it traced out equal areas in equal amounts of time, indicating that it must move more slowly when it’s farther away and more quickly when it’s closer. At every point in a planet’s orbit, Kepler’s laws dictate at what speed that planet must move.

Nearest the Sun, Earth orbits at 30.3 km/s, while at its farthest, it moves at 29.3 km/s.

While all of the planets in the Solar System orbit the Sun in the same direction, Venus, uniquely, rotates in the opposite direction. For each orbit completed by Venus, although it is the slowest-rotating planet, it experiences roughly two “days” of sunrises and sunsets.

Factoring in our varying speed and our non-circular, oblique trajectory, each day’s length varies by several seconds throughout the year.

As the Earth orbits the Sun in an ellipse, it moves more quickly at perihelion (closest-to-the-Sun) and more slowly at aphelion (farthest-from-the-Sun), which leads to changes in the time at which the Sun rises and sets, as well as the duration of the actual day, over the course of a year. The obliquity of Earth’s orbit also affects the equation of time. These patterns repeat annually and are latitude-specific, but generally lead to a “figure 8” pattern for Earth’s analemma: the shape our Sun traces throughout the sky at the same time every day throughout the year.

Those variations explain our analemma’s “figure 8” shape.

This composite image shows the path that the Sun traces through the sky at the same time every day throughout the year 2014 from Budapest, Hungary. This shape is known as an analemma, and its tilt and height above the horizon corresponds to the time-of-day at which each photo was taken as well as the observer’s latitude.

Only four times each year will your day actually be precisely 24 hours long.

This graph shows the equation of time for a specific location on Earth. Where the slope of the graph is positive, days are shortening; where the slope is negative, days are lengthening; where the slope is zero (at the four locations marked), the day is precisely 24 hours. This happens four times per year in a latitude-dependent fashion.

Mostly Mute Monday tells an astronomical story in images, visuals, and no more than 200 words.