In honor of the vernal equinox, this animation shows the progression of the solar terminator at approximately 5.2 million times its normal rate. Each frame of the animation advances twenty-four hours ahead of real-time so that the seasonal changes of the solar terminator are visible. The blue region is night; the white region is day. Best accompanied with the theme song from Buck Rogers.
<!DOCTYPE html>
<meta charset="utf-8">
<style>
body {
background: #fcfcfa;
}
.stroke {
fill: none;
stroke: #000;
stroke-width: 3px;
}
.fill {
fill: #fff;
}
.graticule {
fill: none;
stroke: #777;
stroke-width: .5px;
stroke-opacity: .5;
}
.land {
fill: #222;
}
.boundary {
fill: none;
stroke: #fff;
stroke-width: .5px;
}
.night {
stroke: steelblue;
fill: steelblue;
fill-opacity: .3;
}
text {
font-family: Menlo, monospace;
}
</style>
<body>
<script src="//d3js.org/d3.v3.min.js"></script>
<script src="//d3js.org/d3.geo.projection.v0.min.js"></script>
<script src="//d3js.org/topojson.v1.min.js"></script>
<script>
var width = 960,
height = 570;
var π = Math.PI,
radians = π / 180,
degrees = 180 / π;
var formatDate = d3.time.format.utc("%b. %d, %Y"),
formatTime = d3.time.format.utc("%X UTC");
var circle = d3.geo.circle()
.angle(90);
var projection = d3.geo.kavrayskiy7()
.scale(170)
.translate([width / 2, height / 2])
.precision(.1);
var path = d3.geo.path()
.projection(projection);
var graticule = d3.geo.graticule();
var svg = d3.select("body").append("svg")
.attr("width", width)
.attr("height", height);
svg.append("defs").append("path")
.datum({type: "Sphere"})
.attr("id", "sphere")
.attr("d", path);
svg.append("use")
.attr("class", "stroke")
.attr("xlink:href", "#sphere");
svg.append("use")
.attr("class", "fill")
.attr("xlink:href", "#sphere");
var g = svg.append("g");
g.append("path")
.datum(graticule)
.attr("class", "graticule")
.attr("d", path);
d3.json("/mbostock/raw/4090846/world-50m.json", function(error, world) {
if (error) throw error;
var dayOffset = 0;
var date = svg.append("text")
.attr("dy", "-1.35em");
var time = svg.append("text");
svg.selectAll("text")
.attr("x", 16)
.attr("y", height - 16);
g.insert("path", ".graticule")
.datum(topojson.feature(world, world.objects.land))
.attr("class", "land")
.attr("d", path);
g.insert("path", ".graticule")
.datum(topojson.mesh(world, world.objects.countries, function(a, b) { return a !== b; }))
.attr("class", "boundary")
.attr("d", path);
var night = svg.append("path")
.attr("class", "night");
d3.timer(function() {
var now = new Date(Date.now() + dayOffset);
date.text(formatDate(now));
time.text(formatTime(now));
night.datum(circle.origin(antipode(solarPosition(now)))).attr("d", path);
dayOffset += 864e5;
});
});
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.
// //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>