math - Calculate whether it is close to dawn/dusk based on sunrise/sunset?

Question

Is it possible to calculate when dawn/dusk will be if I have the time for sunrise, sunset and the longitude and latitude of a particular location?

Answer 1

there are some simplified equations for that but the real thing is this:

• solving Kepler's equation
• btw your question is very similar to this: time when the sun is X degrees below/above Horizon

if you want easy solution then obtain sunrise calendar for your location

it should look something like this:

Just pick the closest latitude or generate the right diagram for your location. The picture was taken from here so there should be also the generation applet somewhere. Can't find any image of the astronomy sun calendar on the WEB so here is scan from really old book of mine:

Booth are the same thing but the scan is just for single long/lat geo-location.

• x axis is the date

• y axis is the time sun reach (sun rise/set or dusk/dawn,...)

• Noc means night and Den means day

• all the marks are unimportant for you

• dash dash line is sun rise/set (leading visual edge at mathematical horizont)

• dash dot line is the civil twilight (visual center of sun is 6 deg below horizont)

• filled line is astronomical twilight (visual center of sun is 18 deg below horizont)

  Diagram is for latitudes 48,49,50 deg, nautical twilight (visual center of sun is 12 deg below horizon) is not on the image. When you approximate this curve by polynomial or piecewise polyline then you can easily compute what you need per any date unless you want to use this for thousands of years then you can take this as periodic function so you need just one year table and all the other years are the same.

[Notes]

visual

• means geometric position + atmospheric refraction + aberation + precession/nutation + speed of light
• near horizon is the difference little more then 0.5 degree !!! (one Sun disc)
• and the time difference is around 8 minutes