19 September 2011

Autumnal Equinox: what do you see?

Friday September 23rd is the start of Fall here in the Northern Hemisphere, an event that has a specific moment, in this case 2:05 am on the West Coast. What happens at this moment? Can you 'see' an Equinox?

The two Solstices of the year, in December and June, get much more fanfare because they mark more dramatic transitions, both in the weather and in the slow change of the seasons. The longest day and shortest day of each year are much easier to understand. But the balance points in the equation of Earth's orbit, the Equinoxes, get much less attention because there is much less drama. But for me, there is a lot going on. From an observational point of view, there are three things to look for.

1. Sunrise is precisely due East and Sunset precisely due West, the two days of the year this happens.

2. The Sun is above the horizon 12 hours and below the horizon 12 hours (give or take a few minutes owing to the bending of light around the horizon as experienced at Sunrises and Sunsets).

3. The Sun's height in the sky at local noon, as measured in degrees above the southern horizon, is 90 degrees minus your latitude on Earth. For example, in San Francisco, we are about 38 degrees north of the equator, so the Sun's height at local noon is 90 - 38, or 52 degrees above the horizon.

There is a fourth, more subtle effect that happens around the time of the Equinox. The length of the day is changing most rapidly around this time. From the Summer Solstice to the Winter Solstice, the length of the day is continually reducing. On the Equinox, it is 12 hours, but from one day to the next the length changes about 2 1/2 minutes, around 16 minutes during the full week. That is noticeable, and if you get up at the same time each day, you are certainly aware of the changing light of the morning (or lack of light at this point in time).

The combination of the Earth's annual circuit around the Sun, the tilt of the Earth's axis, and the slightly eccentric orbit of the Earth around the Sun all contribute to very interesting effects that are most pronounced around the interesting transition points of Equinoxes and Solstices. Take a moment this Friday to appreciate what you are observing in the sky around you.


Linda said...

Hi Urban Astronomer!
Thanks for a great site! I posted the link to my current Astronomy 101 students and added this note:

We'll be talking about the equinoxes and solstices today and tomorrow so if you have time before class today, do read this blog post. I would add 2 more aspects to the equinoxes that are not included here, but that help define the term, equinox (think about the prefix equ; it always connotes equality):

1. The sun is directly (at a 90 degree angle) above earth's equator. This is related to the sun's rising due east and due west, as mentioned in the blog, and can be seen with spectacular clarity if you live ON the equator. At that time and location the sun will be directly overhead or at your zenith, twice each year. Also, if you could see the earth from space, the sun will be reflected off the surface of the bright oceans at the equator.
2. Both of earth's north and south hemispheres will have equal amounts of day and night hours. This is an additional feature of the 12 hours of day and 12 hours of night, meaning that the north hemisphere is equal to the south hemisphere in this respect.

Cool, huh?

The Urban Astronomer said...

Thanks for the comments, Linda. I have always found it fascinating that locations on or near the equator experience the strongest sunlight on the Equinox dates rather than the first day of Summer, as we do in latitudes north or south of the equator.

And yes, I really like the fact that from pole to pole across the entire globe, the two Equinoxes are the dates when the entire planet experiences the same amount of time with the Sun above and below the horizon.

If you want to have fun, check out the change in the length of the day from far north latitudes such as Alaska or Iceland. From one day to the next, this time of year, the length of a day changes by 8-9 minutes. Truly astonishing.

I hope your class likes the blog post!

Linda said...

I was trying to figure something out recently and maybe you can help: here in Seattle we can see sunset with respect to the mostly N/S orientation of the Olympic Mts to the west. The Solstices mark the ends of the range, and the Equinoxes occur over a particular mountain in the middle. I wanted to calculate the angular change of sunset position along that bumpy horizon by mileage and circumference (like Eratosthenes!) but then compare that to other latitudes. As you say, the change in time of sunset is 8-9 minutes at those far northern latitudes, but what is the angular change along the horizon? Off to class now!

The Urban Astronomer said...

Outstanding question, Linda. Here's how I see it: At the equator, the point of sunset (or sunrise) moves plus or minus 23.5 degrees from the point at the equinox to solstice. The movement is based on a sinusoidal curve representing the number of days + or - from the date of the equinox, something like this:

Angle = +/- 23.5 * sin(days_since_equinox/91)

So for the equator, on the Spring Equinox the delta is 0 degrees, and 91 days later at the Summer Solstice, it is +23.5 degrees.

As you move north of the equator, this delta from equinox to solstice becomes greater because of the angle of the celestial equator to the horizon (which represents your latitude). There must be some way to relate this mathematically, and I need to think about that. More tomorrow. Or perhaps you can ask your students to think about this one!

-- Paul

The Urban Astronomer said...

Correction to the above comment:

An approximate equation is actually this:

Angle = +/- 23.5 * sin(days_since_equinox)

Since there are approximately 90 days per season, and 90 degrees along the sine curve from the equinox to the solstice.