Something about the timing of sunrises and sunsets seems oddly complicated. During summer, the earliest sunrise typically occurs up to two weeks before the summer solstice (the longest day of the year), while the latest sunset happens up to two weeks after it.
This surprising pattern isn't just due to time zones or daylight saving time. A key factor in this solar "unpredictability" is a phenomenon called the equation of time—one of several elements that make our relationship with the sun more complex than our neat, orderly clocks suggest.
What is the equation of time?
Most of us imagine the Earth rotating steadily around the sun like a perfect clockwork mechanism. If this were true, the sun would cross the sky at exactly the same pace every day, and our watches would match the sun's position perfectly.
But reality is more complex. The equation of time captures this complexity—it's a formula that measures how the actual motion of the Earth around the sun deviates from the simplified, idealized motion we use for our clocks.
Equation of time visualised
Find the difference between apparent solar time and mean solar time throughout the year.
In practical terms, the equation of time tells us the difference between "mean solar time" (the steady, averaged time our clocks use) and "apparent solar time" (the actual, variable position of the sun in the sky). This difference reflects the true, slightly irregular relationship between Earth and sun.
If you were to mark the position of the sun in the sky at the exact same clock time (say, noon) every day for a year, you wouldn't get a simple straight line or circle. Instead, you'd trace an elongated figure-8 pattern in the sky known as an "analemma." This distinctive pattern is the visual representation of the equation of time combined with seasonal changes in the sun's height.
What causes the changes in time?
The mismatch between clock time and solar time comes down to two main natural phenomena. Each of them can be clearly seen when you look back at the analemma after reading:
1. Earth's tilted axis
Our planet is tilted at about 23.5 degrees, which gives the majority of the world our seasons. Because as you know, the sun follow a path much higher through the sky in summer than during winter. The Earth's tilted axis is mostly responsible for the vertical variation in the analemma shown above.
2. Earth's elliptical orbit
Our path around the sun is slightly elliptical, which means sometimes we're closer to the sun (moving faster in our orbit) and sometimes we're farther away (moving slower). This changing orbital speed affects when the sun reaches its highest point in the sky, and is mostly repsonsible for the horizonal deviation—and thus the eight-shape of the analemma.
When the equation of time matters
For most daily activities, this discrepancy doesn't matter much—after all, that's why we invented standardized time in the first place. But understanding the equation of time helps explain several curious phenomena.
Religious traditions often require precise solar positioning—Jewish Sabbath observance begins at sunset, while Islamic prayer times depend on the sun's position. Culturally, ancient structures like Stonehenge and Mayan temples were built to align with specific solar events, accounting for these variations. Professionally, solar engineers use these calculations to optimize energy collection, astronomers need them for accurate observations, and navigators historically relied on them for celestial positioning. Even today's GPS satellites must account for these solar time variations to maintain accuracy.
Nature's reminder: It's complicated
The equation of time serves as a humbling reminder that nature doesn't always follow our human desire for neat, regular patterns. While we've created remarkably precise timepieces, the Earth and Sun dance to their own rhythm—one that's beautiful in its natural complexity.
Next time you glance at your watch, remember that it represents a convenient human compromise. Apparent solar time follows its own slightly irregular beat, one that has guided human existence for thousands of years before the invention of mechanical clocks.