Earth & Sun
Terminator
MapPlanet can show the boundary between the illuminated and dark sides of Earth. This line is called the terminator. It moves with Earth's rotation during the day and changes shape through the year because Earth's axis is tilted.
Interactive day-night terminator on a world map and globe
Interactive day-night map of Earth: move the date and time sliders or switch to the globe to see how the terminator changes through the day and the seasons.
The sideways motion over the year is not a programming error, but part of the analemma. It is caused by Earth’s axial tilt and its elliptical orbit.
The terminator is a great circle
On a spherical Earth, the terminator is geometrically a great circle. Its plane passes through Earth's center and is perpendicular to the direction of the Sun. Every point on this great circle has one thing in common: the Sun is exactly on the horizon there.
On a world map, however, this circle does not look like a circle. MapPlanet's equirectangular projection distorts it, sometimes strongly depending on the season and its orientation relative to Earth's axis. The unusual shape in the map view therefore does not come from a complicated boundary on Earth, but from projecting a simple great circle onto a plane.
Three angles determine the Sun's position
Three angles are enough to describe the Sun's position at a given place and time: geographic latitude φ, solar declination δ and hour angle H.
φ - geographic latitude
It tells how far a place lies north or south of the equator: 0° at the equator, +90° at the North Pole and −90° at the South Pole.
δ - solar declination
It tells which latitude has the Sun directly overhead. Over the year, δ moves between roughly −23.44° and +23.44°.
H - hour angle
It describes the rotation of a place relative to local solar noon. The diagram is a view down onto the North Pole: meridians spread out radially, and H is the angle between the local meridian and the solar-noon meridian.
From three angles to the day-night boundary
The Sun's altitude h above the horizon is:
- φ is the latitude of the place.
- δ is the Sun's north-south position over the year.
- H is the angular time difference from local solar noon.
On the terminator, the Sun is on the horizon. Therefore h = 0° and sin h = 0.
Solving for φ:
For example, at the June solstice with δ = +23.44° and H = 60°:
One point of the terminator is therefore at about 49.1° south. Repeating the calculation for many hour angles traces the line on the map.
Why does the line change through the year?
The key quantity is solar declination δ. At the equinoxes in March and September it is close to 0°. At local noon the Sun is then directly above the equator, and the terminator passes through both poles.
At the June solstice, δ reaches about +23.44°. The Sun is directly overhead at the northern tropic. At the December solstice, δ is about −23.44°, placing the subsolar point over the southern tropic.
A simple approximation for day N of the year is δ ≈ −23.44° · cos(360° / 365 · (N + 10)). It reproduces the annual cycle well; MapPlanet uses a more accurate astronomical approximation for the actual calculation.
Wikipedia: Position of the Sun
Declination through the year
Move the slider. Earth travels around the Sun while its rotation axis keeps nearly the same direction in space. Below, δ is shown as the angle between the equatorial plane and the direction to the Sun.
Schematic drawing; sizes and distances are not to scale.