The current solar terminator is shown in blue, assuming a spherical Earth and an axial tilt of 23.4°. Hmm, on second thought, I think I didn’t account for the orbit of the Earth around the sun, so this is not entirely accurate. Please fork this example and fix it!
<!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/d3.geo.projection.v0.min.js"></script>
<script src="//d3js.org/topojson.v0.min.js"></script>
<script>
var width = 960,
height = 500;
var projection = d3.geo.cylindricalEqualArea()
.parallel(38.5)
.scale(196)
.precision(.1);
var circle = d3.geo.circle()
.angle(89.9975572);
var path = d3.geo.path()
.projection(projection);
var svg = d3.select("body").append("svg")
.attr("width", width)
.attr("height", height);
d3.json("/d/4090846/world-50m.json", function(error, world) {
svg.append("path")
.datum(topojson.object(world, world.objects.land))
.attr("class", "land")
.attr("d", path);
var night = svg.append("path")
.attr("class", "night")
.attr("d", path);
redraw();
setInterval(redraw, 250);
function redraw() {
var sunPos = getSolarWGSPosition( Date.now() );
var darknessAngle = 90 - Math.asin( (constants.meanRsun - constants.meanRearth) / sunPos.range ) * constants.rad2deg;
night.datum(circle.origin([ -180+sunPos.lon, -sunPos.lat ]).angle(darknessAngle)).attr("d", path);
}
});
var getSolarWGSPosition = function getSolarWGSPosition(time) {
var eci_pos = getSolarECI(time);
var wgs_pos = ECItoWGS84(eci_pos, time);
return {lat: wgs_pos.latitude, lon: wgs_pos.longitude, range: eci_pos.w};
};
var getSolarECI = function getSolarECI(time) {
var mjd, year, T, M, L, e, C, O, Lsa, nu, R, eps;
var jd_utc = unix2jd( time / 1000 );
mjd = jd_utc - 2415020.0;
year = 1900 + mjd / 365.25;
T = (mjd + constants.deltaUTCTT / 86400) / 36525.0;
M = (( 358.47583 + ((35999.04975 * T) % 360) - (0.000150 + 0.0000033 * T) * (T*T) ) % 360) * constants.deg2rad;
L = ((279.69668 + ((36000.76892 * T) % 360.0) + 0.0003025 * (T*T) ) % 360) * constants.deg2rad;
e = 0.01675104 - (0.0000418 + 0.000000126 * T) * T;
C = ((1.919460 - (0.004789 + 0.000014 * T) * T) * Math.sin(M) + (0.020094 - 0.000100 * T) * Math.sin(2 * M) + 0.000293 * Math.sin(3 * M)) * constants.deg2rad;
O = ((259.18 - 1934.142 * T) % 360) * constants.deg2rad;
Lsa = (L + C -((0.00569 - 0.00479 * Math.sin(O)) * constants.deg2rad)) % (2*Math.PI);
nu = (M + C) % (2*Math.PI);
R = 1.0000002 * (1.0 - (e*e)) / (1.0 + e * Math.cos(nu));
eps = ((23.452294 - (0.0130125 + (0.00000164 - 0.000000503 * T) * T) * T + 0.00256 * Math.cos(O)) * constants.deg2rad);
R = constants.au * R;
var x = R * Math.cos (Lsa);
var y = R * Math.sin (Lsa) * Math.cos (eps);
var z = R * Math.sin (Lsa) * Math.sin (eps);
var w = R;
return { x : x, y : y, z : z, w : w }
};
var ECItoWGS84 = function ECItoWGS84(eci, time) {
var jd_utc = unix2jd( time / 1000 );
var theta = Math.atan2(eci.y, eci.x); // radians
var lon = (theta - thetaG_JD(jd_utc)) % (2*Math.PI); // radians
var r = Math.sqrt( (eci.x*eci.x) + (eci.y*eci.y) );
var e2 = constants.f * (2 - constants.f);
var lat = Math.atan2(eci.z, r); // radians
var sin_phi, phi, c;
do {
phi = lat;
sin_phi = Math.sin(phi);
c = 1 / Math.sqrt(1 - e2 * (sin_phi*sin_phi));
lat = Math.atan2(eci.z + constants.eqRearth * c * e2 * sin_phi, r);
} while (Math.abs(lat - phi) > 1e-10);
var alt = r / Math.cos(lat) - constants.eqRearth * c; // kilometers
if (lat > (Math.PI / 2)) {
lat -= (2 * Math.PI);
}
if (lon < -Math.PI) {
lon += 2*Math.PI;
}
return {
latitude: lat * constants.rad2deg,
longitude: lon * constants.rad2deg,
altitude: alt,
theta: theta * constants.rad2deg
};
};
// ** Astronomical, Geodetic & Mathematical Constants ** //
var constants = {
au: 149597870700, // [m] Astronomical unit
deltaUTCTT: 67.184,
deg2rad: 0.017453292519943295,
rad2deg: 57.29577951308232,
omega_E: 1.00273790934,
f: 1/298.257222101, // Earth, reciprocal of flattening IERS 2010
eqRearth: 6378.1366, // Equatorial radius
meanRearth: 6371.0, // Mean radius
meanRsun: 1.392684e8, // Mean radius sun
omega: 7.292115e-5, // Nominal mean angular vel. of Earth rotation
};
// Converts a UNIX timestamp to JD (Julian Date)
var unix2jd = function unix2jd(timestamp) {
return (timestamp / 86400.0) + 2440587.5;
};
var thetaG_JD = function thetaG_JD(jd) {
// Reference: The 1992 Astronomical Almanac, page B6.
var UT, TU, GMST;
UT = (jd + 0.5) % 1;
jd = jd - UT;
TU = (jd - 2451545.0) / 36525;
GMST = 24110.54841 + TU * (8640184.812866 + TU * (0.093104 - TU * 6.2e-6));
GMST = (GMST + 86400 * constants.omega_E * UT) % 86400;
return (2*Math.PI) * GMST / 86400;
};
</script>