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Plotting the analemma on your window

March 24, 2009 @ 16:01 By: gordon Category: Astronomy, Photography

Near the end of January, I posted some pictures I took of sunrise one morning. Last week, on the first day of Spring, I took some more pictures at sunrise. Here’s a photo from each day, side by side for your viewing convenience:

IMG_9000
January 21, 2009
First sunrise of Spring 2009 002
March 20, 2009

The astute observer will have noticed that the sun is rising 10 to 20 degrees to the left of where it did on January 21st. This got me to thinking that there’s an experiment you can try at home based on this difference.

The difference is due to the fact that the Earth’s axis of rotation is tilted 23.5 degrees compared to the plane of the Earth’s orbit around the Sun. When the Sun is directly over the equator, as it is at the equinoxes, it will right at an azimuth of exact east. When the sun is north of the equator, as it is in the summer, it will rise to the north of exact east. Similarly, when it’s south of the equator, such as in the winter, sunrise occurs south of exact east.

In fact, if you have a window that you can see the sun from at the same time of the day, you can see the effect of the tilt of the Earth’s axis during a year. All you need it a bit of tape and a grease pencil or marker.

First, pick a spot where you can stand and reach the window without bending. Put a couple of pieces of tape on the floor so that you can return to the exact same spot every day.

At the same time every second or third day, stand on the spot and put a small X on the window with the grease pencil. The X should be aligned with the centre of the sun as you stand on your tape marks.  (Note: if the clocks change because of daylight saving time, you need to adjust when you make the marks to compensate. The easiest way is to make the marks at the same time in UTC (sometimes known as Greenwich Mean Time)).

Over the course of a year, you’ll find an elongated figure-of-eight called an analemma appearing on your window that looks something like this:

image

If you look carefully, you’ll notice that it’s not symmetrical along its axis. This is because there’s a slight misalignment between the points when the Earth is at apogee (furthest distance from the Sun) and perigee (closest to the Sun) and the solstices.

Wikipedia has some excellent pages about analemma and some of the other terms I used in this entry.

Disclaimer: Of course, you should wear proper eye protection when staring at the Sun and ideally not stare at it any longer than necessary. I will not be held responsible if you burn your retinas out.


A tip o’ the hat to Wikipedia member jailbird who put together the picture showing the analemma and released it under a Creative Commons license.

One Response to “Plotting the analemma on your window”


  1. If you have a south-facing window you can do this… It’s a project that takes time, but is great for a play room.

    On the sill, place a small mirror, maybe an inch or less in diameter. Glue it to the flat sill so the sun will reflect off it and make a spot on the wall/ceiling.

    As often as you think about it, take a permanent marker of some sort, trace the reflected circle/oval and put the date and time.

    Eventually (years), you’ll have a pretty accurate sundial that tells the time and date, and a science lesson for your kids.



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