17 March 2012

Equilux

Though it's a seldom used term, I thought I'd write something about it since today happens to be the equilux. No, I hadn't heard of it either, but I was reading wikipedia and was perhaps a little too interested by it.

A similar, more commonly used term would be the equinox, which comes from the latin "aequus nox", meaning equal night. It's a little bit of a misnomer, since the it doesn't necessarily fall on the day which is the same length as the night. The equinox isn't really a day at all- it's simply the moment at which the sun crosses the equator. This Spring, that happens to be at 5:12am on Tuesday (20/3/12). That day where I am in Fife, Scotland happens to last 12 hours and 13 minutes.

The equilux is simply the day which lasts closest to 12 hours, which would make it today, as it lasts 11 hours 59 minutes.

This necessarily true of everywhere, however. It's certainly not true of anywhere in the southern hemisphere. I can only say with certainty that it's true for Scotland, and probably the rest of the UK. Sydney, Australia for example will have an Equilux on the 24th March, with the sunrise at 7:02am and sunset at 7:02pm.

Since the moment of equinox is the when the sun crosses the equator, it is not dependant on the observers location so it will be the same time worldwide. The only possible difference in this will be down to time zones, or the fact that my 2 sources stste different times! Wolfram states 5:12am, but Wikipedia and it's source state 5:14am. Go figure.

The reason that equilux and equinox are different is mainly because the sun is so big and so close. If all that light were to come from something that appeared in our sky as small as any other star, it would rise and set in an instant. It's the time that it takes such an apparently large disc of light to set that adds these extra few minutes onto the day closest to the equinox.

Had I simply read, understood and moved on, I guess that'd be the end of my blog post, but no. I went on thinking about it and for some reason or other I decided to challenge myself to figure out the subsolar point at equinox. That's where exactly on earth would see the sun as directly overhead at the time of equinox.

Possible places are immediately rounded down of course, since I'm giving myself the latitude for free. Since equinox is the moment the sun crosses the equator, the latitude of the subsolar point would have to be 0. 

Since the sun will be overhead this point at midday (by conventional solar time), it shouldn't be too difficult to make this calculation. The time given for equinox is 5:12am, so this place is 6 hours and 48 minutes ahead in time from 0 longitude (Greenwich meridian, therefore GMT). For calculation, put into the decimal 6.8 hours. (48/60 = 0.8)

Another known fact is that it takes 24 hours for the earth to rotate 360 degrees. So I can use this to work out the longitude, which will be the angle the earth will rotate in 6.8 hours.

Rotation (r) / Time taken (t) = constant
r1/t1 = r2/t2
r2 = r1/t1 * t2
( 360 / 24 ) x 6.8 = 102 degrees.

Going with the 

So the subsolar point at equinox is 102 degrees different longitude than Greenwich. This makes some countryside in Pangkalan Kuras, Indonesia the exact point I was looking for. I'm just amazed I hit land!

If you were thinking that the 2 minute difference between sources might have made a difference, I've checked that out too. The 2 minutes equate to 0.5 degrees of rotation, which in turn equates to about 35 miles west of the last link.

6 comments:

  1. Oh dear! oh dear!! oh dear!!! Are you retired from gainful employ that you are able to spend so much time working this all out.

    What other things do you in your spare time???

    ReplyDelete
  2. It probably looks a little worse than it is- most of the working is done on the internet- wolfram alpha mostly, but you're right I do have a little much time on my hands

    ReplyDelete
    Replies
    1. You lost me on the maths but I travelled down the same path after noticing that our Autumnal Equinox was earlier in the week but the days were still longer than the nights. I believe today is our Equilux in Melbourne (Kilmore) Australia?

      Delete
    2. Btw, it's Saturday 24th March here. I do have a full time job, commute etc. but am a self-confessed word nerd so love adding to my vocab.!

      Delete
    3. hard to say without a more accurate source- when I look it up, 23rd is 12:01, 24th is 11:59 so it could be either or!

      Glad to hear there's interest out there, thanks!

      Delete
    4. Estimado, gusto en saludarle: Sabia ud. que el equilux esta estipulado en la Biblia y en el libro de Enoc, como el primer dia del año del verdadero calendario, instaurado por Dios en la creacion?...saludos y bendiciones.

      Delete