# Equinox Sunset

April 21, 2014The Vernal Equinox was close to a month ago. On that date (March 20, 2014) I captured a nice time-lapse of the sunset to demonstrate an effect you might not be aware of. I present it here for your edification. It shows the final 20 minutes before the Vernal Equinox sunset as seen from mid-Arizona. The speed-up factor is 48X.

The Equinox Sun rises exactly in the east, at azimuth 90°, and sets exactly in the west, at azimuth 270°. That much is commonly known. What you might not know is: The Equinox Sun’s path through the sky on its way up from sunrise, or on its way down to sunset, is inclined at an angle *equal to your latitude*. Of course, between sunset and sunrise, the Sun moves in various directions as it arcs across the sky. But during the first 30 minutes after sunrise, or the last 30 minutes before sunset, this rule holds quite nicely.

Here in Arizona, at latitude 34° North, we see that sunset path inclined at an angle of 34° to the vertical. That’s the yellow line in the animation above. Run the animation now, and watch the Sun follow that line until it disappears behind those mountains. Even though you lose sight of the Sun, you can see it heading straight for the West point on the horizon.

Note: The actual horizon, at elevation 0°, is hidden behind that mountain range. So I added it as the white line labeled “Geometric Horizon.” Likewise the actual sunset point labeled “West.”

At the Equator, latitude 0°, the sunset path would be *perpendicular* to the horizon. At both Poles, latitude ± 90°, the Sun’s path would be *parallel* to the horizon. At the Poles, you’d see the top half of the Sun skimming along the horizon, circling 360° around you in 24 hours, and never fully rising or setting.

Now since *sunset* begins when the Sun first touches the horizon, and ends when the upper part of the Sun drops below the horizon, how long sunset lasts is a function of date and latitude. The Sun’s angular diameter is very close to 0.5°, and it moves across the sky at about 15°/hour (0.25°/minute). So with a little geometry and simple kinematics, it’s easy to calculate how long an Equinox sunset will last. I’ll spare you the geometry. The calculation is simply:

Δt = 2 minutes/cosΘ [where Δt is the length of sunset, and Θ is your latitude in degrees]

The angle the Sun’s path makes with the horizon (near sunrise or sunset) is steepest on an Equinox, so you get the shortest sunrise and sunset on those dates: a mere 2 minutes at the Equator, but about 2.4 minutes in Arizona. At higher latitudes, say around 88°, the Sun sets along an almost-grazing path tilted just 2° from the horizon, and Δt can stretch to an hour. At the poles, as described above, things get a bit more complicated.

Next Week in Sky Lights ⇒ GMT vs. UTC