Here are a few simple formulas to determine Sunrise or Sunset time.
"Cos-1" means use the arc cosine key.
"Integral hour" means the single hour figure without minutes. Example- "12" not 12:14.
To make things easier first get the GHA of Sunrise using the following formula. You can also simplify the process of getting the GHA by using HO-249, (with your AP. Latitude and the Sun's declination) finding the LHA for when Hc is closest to 0° and add your Ap. Longitude to it.
For the declination figure just use the average declination for the day you want to calculate Sunrise.
360º – Cos-1( -Tan(Declination) x Tan(AP Latitude)) + Ap. Longitude = GHA of Sunrise
Look up the GHA in The Nautical Almanac and find the GHA integral hour figure lower than the calculated GHA figure found above. Also obtain the GHA (in degrees) of the integral hour and the declination for the integral hour.
Use the figures in the following formula to get the time of sunrise-
GHA Integral Hour + (360 – Cos-1( -Tan(Declination) x Tan(Ap. Latitude)) + Ap. Longitude – GHA of Integral Hour) / 15
Now, to calculate Sunset do the following;
First get the GHA of Sunset using this formula. You can also simplify the process of getting the GHA by using HO-249, (with your AP. Latitude and the Sun's declination) finding the LHA for when Hc is closest to 0° and add your Ap. Longitude to it.
Cos-1( -Tan(Declination) x Tan(AP Latitude)) + Ap. Longitude = GHA of Sunset
Look up the GHA in The Nautical Almanac and find the GHA integral hour figure lower than the calculated GHA figure found above. Also obtain the GHA (in degrees) of the integral hour and the declination for the integral hour.. Use the figures in the following formula to get the time of Sunset-
GHA Integral Hour + Cos-1( -Tan(Declination) x Tan(Ap. Latitude)) + Ap. Longitude – GHA of Integral Hour) / 15
Pretty simple.
You can use The Nautical Almanac and find the date you'd like to know the approximate sunrise and sunset times for using the latitude figure which is closest to you.
Here's an example;
"Cos-1" means use the arc cosine key.
"Integral hour" means the single hour figure without minutes. Example- "12" not 12:14.
To make things easier first get the GHA of Sunrise using the following formula. You can also simplify the process of getting the GHA by using HO-249, (with your AP. Latitude and the Sun's declination) finding the LHA for when Hc is closest to 0° and add your Ap. Longitude to it.
For the declination figure just use the average declination for the day you want to calculate Sunrise.
360º – Cos-1( -Tan(Declination) x Tan(AP Latitude)) + Ap. Longitude = GHA of Sunrise
Look up the GHA in The Nautical Almanac and find the GHA integral hour figure lower than the calculated GHA figure found above. Also obtain the GHA (in degrees) of the integral hour and the declination for the integral hour.
Use the figures in the following formula to get the time of sunrise-
GHA Integral Hour + (360 – Cos-1( -Tan(Declination) x Tan(Ap. Latitude)) + Ap. Longitude – GHA of Integral Hour) / 15
Now, to calculate Sunset do the following;
First get the GHA of Sunset using this formula. You can also simplify the process of getting the GHA by using HO-249, (with your AP. Latitude and the Sun's declination) finding the LHA for when Hc is closest to 0° and add your Ap. Longitude to it.
Cos-1( -Tan(Declination) x Tan(AP Latitude)) + Ap. Longitude = GHA of Sunset
Look up the GHA in The Nautical Almanac and find the GHA integral hour figure lower than the calculated GHA figure found above. Also obtain the GHA (in degrees) of the integral hour and the declination for the integral hour.. Use the figures in the following formula to get the time of Sunset-
GHA Integral Hour + Cos-1( -Tan(Declination) x Tan(Ap. Latitude)) + Ap. Longitude – GHA of Integral Hour) / 15
Pretty simple.
You can use The Nautical Almanac and find the date you'd like to know the approximate sunrise and sunset times for using the latitude figure which is closest to you.
Here's an example;