Because today they don’t actually last 24 hours

In marking the passage of time, we have assigned 24 hours to every single day.

stock footage of the watch

Most of us are very used to 24-hour days, but aren’t used to the fact that that doesn’t equate to a 360-degree rotation of the Earth. Most days, however, are more or less 24 hours long; only 4 days a year do they have exactly 24 hours to themselves.

Credit: geralt/pixabay

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

astronomical analemma

This diagram shows an analemma, constructed by photographing the Sun at the same time throughout the year. The fact that the Sun is not in the same place is due to the combined effects of our axial tilt/obliquity and our orbital eccentricity and velocity changes as we rotate around the Sun. The Sun is not in the same position every day because every day is not exactly 24 hours.

Credit: Giuseppe Donatiello/Public domain

Counterintuitively, one day is not the time it takes for a 360° planetary rotation.

Earth's axis orbits the sun

The Earth, moving in its orbit around the Sun and rotating on its axis, always defines “noon” and “midnight” in the same way: where the altitude of the Sun above or below the horizon is maximized. This moment in time is not when the Earth rotated 360 degrees from the previous day, but rather closer to 360.9856 degrees, due to the added effects of the Earth’s motion around the Sun.

Credit: Larry McNish/RASC Calgary

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

rotating universe

These star trails appear in the sky due to long exposure photography of the north pole, combined with the physical phenomenon of the Earth’s rotation. While no one has ever successfully captured a full 360-degree star trail, it surprises people to learn that it wouldn’t take a 24-hour photograph to come full circle, just an exposure of 23 hours, 56 minutes, 4.09 seconds. as it is based on a sidereal day, rather than a solar one.

Credit: PxHere/Public Domain

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

sidereal day vs solar day

When the Earth rotates 360 degrees on its axis, it has not yet aged a full day, because it has also shifted its orbit around the Sun. It must therefore rotate about 1 degree more to “catch up”, which explains the difference between a sidereal day (360 degree rotation) and a solar/calendar day (where the Sun returns to the previous day’s position).

Credit: James O’Donoghue/CCA-3.0-unported

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

animated gif of terra analemma

Over the course of a 365-day year, the Sun appears to move not only up and down the sky, as determined by our axial tilt, but back and forth, as determined by both obliquity and our elliptical orbit around the Sun. When both the effects are combined, the resulting plucked figure 8 is known as an analemma. The images of the Sun shown here are a selection of 52 photographs from César Cantú’s observations of Mexico over the course of one calendar year.

Credit: César Cantú/AstroColors

This requires accounting for the movement of the Earth through space.

Earthmoving

This view of Earth comes to us courtesy of NASA’s MESSENGER spacecraft, which had to make flybys of Earth and Venus in order to lose enough energy to reach its final destination: Mercury. The round, rotating Earth and its characteristics are undeniable, as this rotation explains why the Earth swells in the center, is compressed at the poles, and has different equatorial and polar diameters. However, more than rotation is needed to explain the length of a day, since the Earth also moves through space relative to the Sun.

Credit: NASA/MESSENGER

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

sidereal day vs solar day

This unscaled diagram shows the difference between a sidereal day, in which the Earth rotates a full 360 degrees, and a solar day, which takes 3 minutes and 55.91 seconds longer for the Earth to rotate enough to return the Sun to its position on the previous day in the sky. The Earth not only rotates on its axis, but rotates around the Sun: both aspects must be taken into account when defining a calendar day.

Credit: Xaonon/Wikimedia Commons

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

The earth travels around the sun once

Traveling once around the Earth’s orbit on a course around the Sun is a journey of 940 million kilometres. The 3 million extra kilometers that the Earth travels through space, per day, ensures that the 360-degree rotation on our axis will not return the Sun to the same relative position in the sky from day to day. This is why our day is longer than 23 hours 56 minutes 4.09 seconds, which is the time it takes for the spheroidal Earth to rotate 360 ​​degrees.

Credit: Larry McNish at RASC Calgary Center

But Earth’s orbital speed also varies, moving fastest near perihelion in January and slowest around aphelion in July.

Kepler's second law

Kepler’s second law states that planets sweep out equal areas, using the Sun as focus, in equal times, regardless of other parameters. The same area (blue) is swept away in each fixed time period. The green arrow is speed. The purple arrow pointing towards the Sun is acceleration. The planets move in ellipses around the Sun (Kepler’s first law), sweep out equal areas in equal times (his second law), and have periods proportional to their semimajor axis raised to the 3/2 power (his third law). Earth’s orbit has a small eccentricity, causing its maximum orbital speed, at perihelion, to be about 3% greater than its minimum speed at aphelion.

(Credit: Gonfer/Wikimedia Commons, using Mathematica)

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

mercury mars venus earth orbit

The orbits of the planets in the inner Solar System are not exactly circular, but they are elliptical. Planets move faster at perihelion (closer to the Sun) than at aphelion (further from the Sun), conserving angular momentum and obeying Kepler’s laws of motion.

Credit: NASA/JPL

Considering our variable speed and our non-circular, oblique trajectory, the length of each day varies by several seconds throughout the year.

equation of time analemma

As the Earth orbits the Sun in an ellipse, it moves fastest at perihelion (closest to the Sun) and slowest at aphelion (farthest from the Sun), which leads to changes in the time when the sun rises and sets, as well as the length 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 each year and are latitude-specific, but generally lead to a “figure-8” pattern for Earth’s analemma: the shape our Sun makes in the sky at the same time each day throughout the year.

Credit: Rob Carr/Wikimedia Commons

These variations explain the “figure 8” shape of our analemma.

analemma on budapest

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

Credit: György Soponyai, CC BY NC 2.0

Only four times a year will your day last exactly 24 hours.

time equation

This graph shows the equation of time for a specific location on Earth. Where the slope of the graph is positive, the days become shorter; where the slope is negative, the days get longer; where the slope is zero (in the four marked locations), the day is precisely 24 hours. This happens four times a year in a latitude-dependent manner.

Credits: Drini & Zazou/Wikimedia Commons, annotations by E. Siegel

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

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Image Source : bigthink.com

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