Home Site Map Search

GeoAstro Applets

Astronomy

Chaos Game

Java

Miscel- laneous

The Day and Night Terminator Across the Earth

How to compute the day/night terminator on a world map

Map (c) Apple Computers, Inc.

The applet source

More details:
Lines of simultaneous sunrise and sunset, lines of equal solar altitude

The elevation angle h of a celestial body at a given latitude is determined by it's declination and hour angle (tau) 

sin h = sin(latitude)*sin(declination) + cos(latitude)*cos(declination)*cos(tau)

for rise and set: h=0

0 = sin(latitude)*sin(declination) + cos(latitude)*cos(declination)*cos(tau)

0 = tan(latitude)*tan(declination) + cos(tau)

The terminator can be calculated from:

tan(latitude) = - cos(tau)/tan(declination)

The coordinates (longitude,latitude) are

latitude = arctan(- cos(longitude)/tan(declination)),
longitude = x+ tau, -180°<= x<= 180°

details

(c) 2006-2023 J. Giesen

Last update: 2023, Oct 06