Why is the time given by a sundial not necessarily the same as the time on your wristwatch?

Let's go back in time. Long before the existence of clocks, people used sundials to tell the time based on the position of the sun in the sky. A sundial displays time by casting a shadow on its surface, with markers indicating the hours.

Unlike modern wristwatches that show standard time, a sundial reveals 'solar time.' This is the time it takes for the sun to return to its highest point in the sky, which is considered solar noon. Here, we're focusing on the apparent motion of the sun, which is different from the standardized 24-hour cycle used by clocks and watches.

There’s something charming and inherently unique about each place on Earth having its time based on the local solar noon, but it can be impractical. Hence, your wristwatch is set to a standard time, agreed upon to simplify things in our interconnected world.

To understand why a wristwatch doesn't agree with a sundial, we should look at the concept of time zones. Time zones are a global compromise, a way to divide the world into longitudinal segments where all clocks are set to the same time within each zone.

Time zones were proposed to synchronize time for railways and communication across vast distances. They are based on Coordinated Universal Time (UTC) and are expressed as UTC offset hours. For example, if you live in New York, you're in the Eastern Time Zone, which could be UTC-5 or UTC-4, depending on daylight saving time.

Therefore, while a sundial gives you the solar time which changes as you move east or west, standard time zones keep time consistent within each zone, providing a predictable schedule for the complexities of modern life.

Now, let's deal with why solar time is not constant throughout the year - the tilt of Earth’s axis. Our planet is not upright in its orbit; it's tilted at an angle of approximately 23.5 degrees. This axial tilt is responsible for the seasons that we experience.

But it also means that the length of a solar day is not a constant 24 hours as we might expect. It fluctuates slightly over the year because the angle of the sun's trajectory in the sky changes as the Earth orbits.

This axial tilt has a direct impact on your sundial's accuracy. Around the solstices, when the sun's apparent path is most skewed, the discrepancy between solar time and the time on your wristwatch is most noticeable. This is where 'equation of time' comes into play—a method to calculate the difference between solar time and standard time throughout the year.

Lastly, we must discuss Earth's orbit to fully grasp the variances between sundial time and watch time. It's easy to imagine our planet's orbit as a perfect circle, but it's more of an ellipse. This means the distance between the Earth and the sun changes, affecting how fast the Earth travels.

When the Earth is closest to the sun (at perihelion), it travels slightly faster than average. Conversely, when it is at its farthest point (aphelion), it travels slower. This variation in orbital speed leads to changes in solar time—a solar day can be up to several seconds longer or shorter than the average 24-hour day.

This elliptical orbit, yet another reason for the discrepancy between the time told by a sundial and the time on your watch, adds an extra layer of complexity to the already intricate dance of timekeeping on our planet.