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@mbostock /.block
Last active Aug 17, 2018

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Solar Terminator
license: gpl-3.0

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>
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