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. The round, rotating Earth and its features are undeniable, as this rotation explains why Earth bulges at the center, is compressed at the poles, and has different equatorial and polar diameters. However, more than rotation is needed to explain the duration of a day, as Earth also moves through space relative to the 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.

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 and 4.09 seconds, which is the time required for the spheroidal Earth to spin a full 360 degrees. Similarly, a “year” is not the time it takes for Earth to make a full 360 degree revolution around the Sun, but is determined by the return of its axis to the same position relative to the Sun to the year before.

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

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. For extremely elliptical orbits, such as comets, the velocity near perihelion is enormous, while the velocity near aphelion is relatively tiny.

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

The orbits of the planets in the inner Solar System aren’t exactly circular, but are elliptical, as are the orbits of all bodies gravitationally bound to the Sun. Planets move more quickly at perihelion (closest to the Sun) than at aphelion (farthest from the Sun), conserving angular momentum and obeying Kepler’s laws of motion, which were put on a more solid, generalized mathematical footing by Newton. Once the quantitative relationships between orbital period and distance were uncovered, it became possible to know the distance from the Earth to the Sun.

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.