Geometry and Sunrise/Sunset.

The other day, I was rewatching NCIS and Jethro Gibbs made a comment about "Which sunrise?  There are three.".  I had to go check that out because I'd never learned that.

The three based on the position of the geometric center of the sun in reference to the horizon. Geometric center is the exact wording used by scientific writers.

There are two twilight times every day.  In the morning, we refer to it as dawn and in the evening it's called dusk.  If a location is far enough north or south, it may not experience all three twilights every day.  It just depends.

First is civil twilight which occurs between 6 degrees below the horizon and above.  Its the last one, the lightest one and only the strongest stars are still visible.  This is the time when Venus is still visible.  In the morning, it is from 6 degrees below and up while at night it lasts until the sun gets past the 6 degrees below the horizon.  Civil twilight is used by many countries for laws on aviation, hunting, etc.

Second is the nautical twilight, lasting between 12 and 6 degrees below the horizon.  It gets it name from history because sailors used this time to get bearings for their navigation.  During this period, there is enough light being produced to see the horizon, so it was light enough for sailors to use the horizon when determining their headings, etc. On a good day, it is possible to see ground based objects but not with great detail.  The United States military uses this definition when they are planning tactical operations

Finally is the astronomical twilight defined as going from 18 to 12 degrees below the horizon.  It is the darkest time and is most interesting to astronomers.  It is also the darkest of the three with no light in the sky.  Most people call this night because the lights have not yet begun to show

I found the equations used to calculate sunrise and sunset times locally in a paper on Solar Geometry  Notice the equations use trig to calculate dawn and dusk.  The times are based on a 24 hour clock with noon being 12:00

The first tangent term represents the latitude of the specific location where the local sunrise is being calculated while the second tangent is the Sun's declination angle for that day.

Tomorrow, I'll share more solar geometry with you.  Let me know what you think, I'd love to hear.  Have a great day.