A sundial is a time-telling instrument that uses the apparent position of the Sun to indicate the time of day. It consists of a flat plate, the dial, and a shadow-casting object called the gnomon. The gnomon’s edge, often a tilted blade, casts a shadow onto the dial’s hour lines, measuring Apparent Solar Time. This time is based on the Sun’s actual movement, with solar noon occurring when the Sun is at its highest point. The question of how much time 10 degrees represents on a sundial has a simple mathematical answer, which must be reconciled with celestial mechanics.
The Ideal Calculation Standard Astronomical Time
The Earth rotates on its axis once every 24 hours, completing 360 degrees. Based on this uniform rotation, the theoretical conversion from angular movement to time is straightforward: 360 degrees divided by 24 hours yields a rate of 15 degrees per hour.
This means that 1 degree of shadow movement corresponds to exactly four minutes of time (60 minutes divided by 15 degrees). Using this standard astronomical rate, 10 degrees of shadow movement ideally represents 40 minutes. This figure provides the baseline for understanding the sundial’s function, assuming the Earth’s rotation relative to the Sun is constant.
However, the time indicated by a sundial (Apparent Solar Time) consistently differs from the steady, uniform rate of a clock (Mean Solar Time). This discrepancy arises because the Sun’s apparent motion across the sky is not uniform throughout the year.
Astronomical Causes of Time Variation
The simple 40-minute figure for 10 degrees of movement is inaccurate because the Earth’s orbital dynamics cause the solar day length to vary. The primary cause is the elliptical shape of the Earth’s orbit. The Earth moves faster when nearer the Sun (perihelion) and slower when farther away (aphelion).
This varying orbital speed means the Sun’s apparent movement is not constant, causing the time between successive solar noons to fluctuate. The second major cause is the Earth’s axial tilt, approximately 23.5 degrees relative to its orbital plane. This tilt affects how the Sun’s motion is projected onto the celestial equator, contributing to the irregularity of the Sun’s apparent speed.
The combined effect of the elliptical orbit and the axial tilt means the Sun appears to run ahead of or fall behind clock time throughout the year. This non-uniformity prevents the time represented by 10 degrees of shadow movement from being fixed at 40 minutes.
Understanding the Equation of Time
The quantification of this celestial irregularity is known as the Equation of Time (EOT). The EOT is the difference between Apparent Solar Time (sundial time) and Mean Solar Time (clock time). Mean Solar Time is theoretical, based on a fictitious “mean Sun” moving uniformly along the celestial equator.
The EOT is constantly changing, causing sundial time to be significantly ahead or behind clock time. The difference can range from 14 minutes ahead (around early November) to 16 minutes behind (around mid-February). This daily shift means the “start time” for any 10-degree segment varies relative to a clock.
Due to this seasonal variation, the actual duration represented by 10 degrees of shadow movement fluctuates around the 40-minute average. To convert a sundial reading to accurate clock time, a user must consult a graph or table of EOT values for the specific date.
Local Adjustments Latitude and Longitude
Beyond the Equation of Time, two geographical factors translate a sundial’s Apparent Solar Time into standard clock time. These adjustments account for the observer’s specific location relative to the standardized time zone and the Earth’s axis.
Longitude Correction
The first is a correction for longitude, which accounts for a location’s east-west position within its time zone. Standard time zones are centered on meridians 15 degrees apart, and clock time is uniform across the zone. A sundial indicates local time, meaning its noon occurs when the Sun is directly over the observer’s specific meridian.
Since the Earth rotates 1 degree every four minutes, a location 5 degrees west of the central meridian will have a local solar time 20 minutes slower than the official clock time. This fixed correction aligns the sundial reading with the time zone.
Latitude Adjustment
The second geographical adjustment is the setting of the gnomon. The gnomon must be precisely aligned with the local latitude for the dial to function accurately. The angle of the gnomon’s shadow-casting edge must be tilted by an angle equal to the local latitude. This ensures the gnomon is parallel to the Earth’s axis of rotation, making the shadow’s movement proportional to the Sun’s motion throughout the day.