Time: Sidereal vs Solar Days and the Equation of Time

Two Types of Day

Most people take for granted that a day is exactly 24 hours. But 24 hours is actually a carefully defined average, and there are two quite different ways to measure a ‘day’, each with a different duration. Understanding the distinction is one of the most common areas where students lose marks.

A sidereal day is the time for Earth to rotate once relative to the distant stars. Because the stars are so far away that they can be treated as fixed reference points, the sidereal day measures Earth’s true rotation period: approximately 23 hours 56 minutes. If you note the exact position of a star in the sky tonight, it will return to the same position about 4 minutes earlier tomorrow night — and 4 minutes earlier still the night after. Over a year, these 4 minutes accumulate to account for why the night sky shifts through a full cycle of constellations.

A solar day (also called the synodic day) is the time from one local noon to the next — the interval between successive passages of the Sun across the meridian. This takes 24 hours on average. The extra ~4 minutes compared with the sidereal day arise because Earth is simultaneously orbiting the Sun. During one sidereal day, Earth has moved about 1° along its orbit. To ‘catch up’ with the Sun’s position in the sky, Earth must rotate a little further — taking that extra ~4 minutes. This is why we use the solar day for everyday life: it keeps noon at midday, regardless of where Earth is in its orbit.

Apparent Solar Time and Mean Solar Time

Even within a single solar day, the Sun does not behave with perfect regularity. The time read directly from the Sun’s position — when the Sun crosses your local meridian (highest point in the sky) — is called Apparent Solar Time (AST). In an ideal world, successive solar noons would be exactly 24 hours apart. In reality they are not, for two reasons:

• Earth’s elliptical orbit: Earth moves faster near perihelion (closest to the Sun, around early January) and slower near aphelion (furthest, around early July). When Earth moves faster, the Sun appears to move more quickly along the ecliptic, shortening the apparent solar day. When Earth moves slower, the solar day is longer.
• Earth’s axial tilt: Even if Earth’s orbit were perfectly circular, the axial tilt of 23.5° means the Sun’s motion along the sky is not uniform throughout the year. Near the solstices the Sun moves primarily north or south rather than east or west along the ecliptic, so it takes slightly longer to return to the meridian. Near the equinoxes the eastward motion is fastest, shortening the apparent solar day.

To avoid clocks that run at slightly different speeds throughout the year, astronomers and civil timekeepers define Mean Solar Time (MST) using the concept of the Mean Sun — an imaginary Sun that moves at a perfectly uniform rate along the celestial equator. Local Mean Time (LMT) is the time at a specific longitude based on the Mean Sun. This is the time your clock shows (adjusted for time zones and daylight saving).

The Equation of Time

The difference between Apparent Solar Time (what the Sun actually does) and Mean Solar Time (what an ideal clock says) is called the Equation of Time. This difference varies throughout the year between about −14 minutes in mid-February and +16 minutes in early November. The Equation of Time can be read from a figure-of-eight graph called an analemma. On four dates each year, the apparent and mean times coincide (Equation of Time = 0). The rest of the year, apparent solar noon is either early or late relative to clock noon by up to 16 minutes.

The practical consequence is that the latest sunrise and earliest sunset around the December solstice do not occur on exactly the same date. At that time the Equation of Time is falling quickly, so apparent solar noon slips about half a minute later each day. That drift moves the earliest sunset to about 12 December and the latest sunrise to about 30 December.

Shadow Sticks and Sundials

A shadow stick (or gnomon) is the simplest possible solar instrument: a vertical rod that casts a shadow. As the Sun moves across the sky, the shadow sweeps around the stick. The shortest shadow of the day occurs at local noon — the moment when the Sun reaches its highest point (crosses the meridian). At local noon the shadow points directly toward true north (in the Northern Hemisphere).

A sundial uses a gnomon set parallel to Earth’s rotational axis (pointing toward the celestial pole) to cast a shadow across a calibrated dial. The shadow sweeps around the gnomon at 15° per hour, since Earth rotates 360° in 24 hours. On an equatorial dial the hour lines are equally spaced at 15°; on a horizontal dial they are not evenly spaced. A sundial reads Apparent Solar Time — the time dictated by the actual position of the Sun. To convert a sundial reading to clock time, you need to:

1. Apply the Equation of Time correction (add or subtract up to 16 minutes depending on the date).
2. Apply a longitude correction: for every degree of longitude your sundial is west of the standard meridian for your time zone, add 4 minutes (since Earth rotates 1° per 4 minutes). For degrees east, subtract 4 minutes.
3. If applicable, add 1 hour for Daylight Saving Time.