The Wolfram|Alpha Blog is now part of the Wolfram Blog. Join us there for the latest on Wolfram|Alpha and other Wolfram offerings »
Todd Rowland

Following the Sun’s Unique Path

September 22, 2010 —
Comments Off

Every day the Sun crosses the sky, rising in the east and setting in the west, but in detail its path is different every time. If it is winter, or if you live in the north, the Sun is lower and stays closer to the southern horizon. While the time of year and the location have similar effects, they act independently on the overall path. The Sun’s path is unique for your place and time.

You can see the sunpath today at your location; the default is the perspective of looking toward the southern horizon.

The path of the Sun for Champaign, Illinois on September 22, 2010

The autumnal equinox is tonight (in North America), but in Pyramid Point (a place close to the equator in the Pacific), the equinox will occur Thursday, close to noon, when the Sun will be almost overhead.

Sunpath over Pyramid Point Kiribati on September 23, 2010

In other parts of the world, the Sun’s path is better viewed looking straight up to the zenith.

In the tropics, there will be a time of year when the Sun is directly overhead, making the horizon view difficult to visualize. Well, not precisely overhead. For a given position, the Sun is overhead if the Sun’s declination is the same as the latitude at the precise moment of solar noon. In other words, it basically never happens that the Sun is directly overhead. However, one notable near-exception is on the day of the vernal or autumnal equinox, when the Sun, as viewed from the equator, rises from almost exactly due east, passes over the zenith directly overhead, and sets at almost exactly due west.

Like Timbuktu on August 6, 2010:
The Sun's path over Timbuktu on August 6, 2010

An orthogonal path can be seen near a midnight Sun situation like in Reykjavik on June 21, 2010.
An orthogonal path in Reykjavik on June 21, 2010

Or near polar night:
The Sun's path in Reykjavik on December 20, 2010

Like other astronomy or calendar events, we can specify other times and locations, and we can get a sense of what it is like there and then. Just as an example, JFK’s assassination:
The Sun's path in Dallas, Texas on November 22, 1963

Each path is unique in detail, but not every geometry is possible because Earth’s rotation is very close to uniform, and because the obliquity also does not change very much. But from other places in our solar system, other sunpaths are possible; like from Uranus, one could see the Sun rotating close to the zenith because of its lopsided obliquity. Many bodies do not even rotate along a consistent axis, and from them anything is possible.

So check out the Sun’s path on Wolfram|Alpha, then go out and enjoy the day. There never will be another one quite like it.


How about moonpath?

Posted by Franco R Busetti September 24, 2010 at 4:46 am

It’s not working for me. When I enter “Sunpath,” as shown above, I get “Wolfram|Alpha doesn’t know how to interpret your input.”

When I enter “sunpath chicago, il september 24, 2010,” I get “Input interpretation: sun path, Friday, September 24, 2010, location: Chicago, Illinois,” but no graph!

I’m using Firefox 3.6.

Posted by Robert Teeter September 24, 2010 at 9:11 pm

This is one thing I tried on wolframalpha about 18months ago, or whenever it was
that wolframalpha started.
(I had my own code for it, in various languages, but the original source was
from an architect friend’s Java.)
I think the plot should display more numbers.
Those produced by
are more or less what people have got used to.

My guess is that people at wolfram look at what is requested and add the functionality
when they can/get time to do it/etc.. Good to see progress.

Posted by Grant Keady September 28, 2010 at 10:34 pm

I am a regular follower of your blog.

Is there a mathematical formula to calculate the two days in the year and exact times when the sun is exactly overhead in places within the tropics of Cancer and Capricorn?

Posted by Abu Ammar September 24, 2013 at 2:47 pm