Sunny side of the Earth, for any date and time.

This interrupted Mollweide projection features the solar terminator for any date and time.

<!DOCTYPE html>
<meta charset="utf-8">
<style>

input { position: absolute; }
#d { left: 326px; top: 24px; }
#t { left: 370px; top: 61px; }

.night {
  stroke: rgb(35, 65, 90); /* steelblue at 50% brightness */
  fill: rgb(35, 65, 90);
  fill-opacity: .3;
}

.background {
  fill: #a4bac7;
}

.foreground {
  fill: none;
  stroke: #333;
  stroke-width: 1.5px;
}

.graticule {
  fill: none;
  stroke: #fff;
  stroke-width: .5px;
}

.graticule :nth-child(2n) {
  stroke-dasharray: 2,2;
}

.land {
  fill: #d7c7ad;
  stroke: #766951;
}

.boundary {
  fill: none;
  stroke: #a5967e;
}

</style>
<body marginwidth="0" marginheight="0">
<input type="date" id="d"/>
<input type="time" id="t"/>

var time = new Date, last = new Date
  , width = 960
  , height = 500
  ;

// Interrupted Mollweide, https://bl.ocks.org/4498187
var projection = d3.geo.interrupt(d3.geo.mollweide.raw)
    .lobes([[ // northern hemisphere
      [[-180,   0], [-100,  90], [ -40,   0]],
      [[ -40,   0], [  30,  90], [ 180,   0]]
    ], [ // southern hemisphere
      [[-180,   0], [-160, -90], [-100,   0]],
      [[-100,   0], [ -60, -90], [ -20,   0]],
      [[ -20,   0], [  20, -90], [  80,   0]],
      [[  80,   0], [ 140, -90], [ 180,   0]]
    ]])
    .translate([width / 2, height / 2]);

var circle = d3.geo.circle()
    .angle(89.9975572);

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);

var defs = svg.append("defs");

defs.append("path")
    .datum({type: "Sphere"})
    .attr("id", "sphere")
    .attr("d", path);

defs.append("clipPath")
    .attr("id", "clip")
  .append("use")
    .attr("xlink:href", "#sphere");

svg.append("use")
    .attr("class", "background")
    .attr("xlink:href", "#sphere");

svg.append("g")
    .attr("class", "graticule")
  .selectAll("path")
    .data(graticule.lines)
  .enter().append("path")
    .attr("d", path);

svg.append("use")
    .attr("class", "foreground")
    .attr("xlink:href", "#sphere");

d3.json("/d/4090846/world-50m.json", function(error, world) {
  svg.insert("path", ".graticule")
      .datum(topojson.object(world, world.objects.land))
      .attr("clip-path", "url(#clip)")
      .attr("class", "land")
      .attr("d", path);

svg.insert("path", ".graticule")
      .datum(topojson.mesh(world, world.objects.countries, function(a, b) { return a !== b; }))
      .attr("clip-path", "url(#clip)")
      .attr("class", "boundary")
      .attr("d", path);

var night = svg.append("path")
      .attr("class", "night")
      .attr("clip-path", "url(#clip)")
      .attr("d", path);

var at_d = document.querySelector('#d')
    , at_t = document.querySelector('#t')
    ;

update(time);
  redraw();
  setInterval(redraw, 1000);

at_d.addEventListener('input', redraw, false);
  at_t.addEventListener('input', redraw, false);

function z(n, z) { z = z || 2; return ('0000'+n).slice(-z); }

function date(t) {
    if (!t) t = document.querySelector('#d').value;
    if (typeof t === 'string') return t;
    return [z(t.getFullYear(), 4), z(t.getMonth()+1), z(t.getDate())].join('-');
  }

function hhmm(t) {
    if (!t) t = document.querySelector('#t').value;
    if (typeof t === 'string') return t;
    return z(t.getHours()) +':'+ z(t.getMinutes());
  }

function update(t) {
    at_d.value = date(t);
    at_t.value = hhmm(t);
  }

function redraw(e) {
    if (typeof e === 'object') {
      var t = (date() +' '+ hhmm()).split(/[- :]/).map(Number), y = t.shift();
      t = new Date(y, t.shift()-1, t.shift(), t.shift(), t.shift());
      t.setFullYear(y); // compensate for inane js year 0..99 handling
      if (!isNaN(t)) time = t;
    }
    else { // update clock display one tick (dt)
      var now = new Date, dt = now - last;
      time = new Date(time.getTime() + dt);
      update(time);
    }
    last = new Date;

var sunPos = getSolarWGSPosition(time);
    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 }
};

// ** 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>

Modified http://d3js.org/d3.v3.min.js to a secure url

Modified http://d3js.org/d3.geo.projection.v0.min.js to a secure url

Modified http://d3js.org/topojson.v0.min.js to a secure url

https://d3js.org/d3.v3.min.js

https://d3js.org/d3.geo.projection.v0.min.js

https://d3js.org/topojson.v0.min.js