Skip to content

Instantly share code, notes, and snippets.

@mbostock
Last active November 14, 2023 01:06
  • Star 7 You must be signed in to star a gist
  • Fork 10 You must be signed in to fork a gist
Star You must be signed in to star a gist
Save mbostock/4597134 to your computer and use it in GitHub Desktop.
Solar Terminator
license: gpl-3.0
redirect: https://observablehq.com/@mbostock/solar-terminator

The current solar terminator is shown in blue.

Thanks to Ben Elsen and NOAA for help implementing the correct equations for the position of the sun, which turned out to be quite a bit more complicated than I expected.

<!DOCTYPE html>
<meta charset="utf-8">
<style>
.night {
stroke: steelblue;
fill: steelblue;
fill-opacity: .3;
}
</style>
<body>
<script src="//d3js.org/d3.v3.min.js"></script>
<script src="//d3js.org/topojson.v1.min.js"></script>
<script>
var width = 960,
height = 480;
var π = Math.PI,
radians = π / 180,
degrees = 180 / π;
var projection = d3.geo.equirectangular()
.translate([width / 2, height / 2])
.scale(153)
.precision(.1);
var circle = d3.geo.circle()
.angle(90);
var path = d3.geo.path()
.projection(projection);
var svg = d3.select("body").append("svg")
.attr("width", width)
.attr("height", height);
d3.json("/mbostock/raw/4090846/world-50m.json", function(error, world) {
if (error) throw error;
svg.append("path")
.datum(topojson.feature(world, world.objects.land))
.attr("class", "land")
.attr("d", path);
var night = svg.append("path")
.attr("class", "night")
.attr("d", path);
redraw();
setInterval(redraw, 1000);
function redraw() {
night.datum(circle.origin(antipode(solarPosition(new Date)))).attr("d", path);
}
});
d3.select(self.frameElement).style("height", height + "px");
function antipode(position) {
return [position[0] + 180, -position[1]];
}
function solarPosition(time) {
var centuries = (time - Date.UTC(2000, 0, 1, 12)) / 864e5 / 36525, // since J2000
longitude = (d3.time.day.utc.floor(time) - time) / 864e5 * 360 - 180;
return [
longitude - equationOfTime(centuries) * degrees,
solarDeclination(centuries) * degrees
];
}
// Equations based on NOAA’s Solar Calculator; all angles in radians.
// http://www.esrl.noaa.gov/gmd/grad/solcalc/
function equationOfTime(centuries) {
var e = eccentricityEarthOrbit(centuries),
m = solarGeometricMeanAnomaly(centuries),
l = solarGeometricMeanLongitude(centuries),
y = Math.tan(obliquityCorrection(centuries) / 2);
y *= y;
return y * Math.sin(2 * l)
- 2 * e * Math.sin(m)
+ 4 * e * y * Math.sin(m) * Math.cos(2 * l)
- 0.5 * y * y * Math.sin(4 * l)
- 1.25 * e * e * Math.sin(2 * m);
}
function solarDeclination(centuries) {
return Math.asin(Math.sin(obliquityCorrection(centuries)) * Math.sin(solarApparentLongitude(centuries)));
}
function solarApparentLongitude(centuries) {
return solarTrueLongitude(centuries) - (0.00569 + 0.00478 * Math.sin((125.04 - 1934.136 * centuries) * radians)) * radians;
}
function solarTrueLongitude(centuries) {
return solarGeometricMeanLongitude(centuries) + solarEquationOfCenter(centuries);
}
function solarGeometricMeanAnomaly(centuries) {
return (357.52911 + centuries * (35999.05029 - 0.0001537 * centuries)) * radians;
}
function solarGeometricMeanLongitude(centuries) {
var l = (280.46646 + centuries * (36000.76983 + centuries * 0.0003032)) % 360;
return (l < 0 ? l + 360 : l) / 180 * π;
}
function solarEquationOfCenter(centuries) {
var m = solarGeometricMeanAnomaly(centuries);
return (Math.sin(m) * (1.914602 - centuries * (0.004817 + 0.000014 * centuries))
+ Math.sin(m + m) * (0.019993 - 0.000101 * centuries)
+ Math.sin(m + m + m) * 0.000289) * radians;
}
function obliquityCorrection(centuries) {
return meanObliquityOfEcliptic(centuries) + 0.00256 * Math.cos((125.04 - 1934.136 * centuries) * radians) * radians;
}
function meanObliquityOfEcliptic(centuries) {
return (23 + (26 + (21.448 - centuries * (46.8150 + centuries * (0.00059 - centuries * 0.001813))) / 60) / 60) * radians;
}
function eccentricityEarthOrbit(centuries) {
return 0.016708634 - centuries * (0.000042037 + 0.0000001267 * centuries);
}
</script>
Sign up for free to join this conversation on GitHub. Already have an account? Sign in to comment