TDB top-level property

TimeInstantUnits TDB

Barycentric Dynamical Time (TDB): TDB varies from TDT by periodic variations

Implementation

// ignore: non_constant_identifier_names
final TimeInstantUnits TDB =
    TimeInstantUnits('Barycentric Dynamical Time', null, 'TDB', null, 1.0, false, -32.184, (dynamic val) {
  // TDB = TAI + 32.184 + 0.001658sin(g) + 0.000014sin(2g)...
  // where g = 357.53 deg + 0.9856003(JD - 2451545.0) deg... (Julian dates are in the TAI time scale)
  final d = val is num
      ? val.toDouble()
      : val is Number
          ? val.toDouble()
          : 0.0;
  final gRad = (357.53 + 0.9856003 * ((d / 86400.0) - 15341.0)) * (pi / 180.0);
  return Double(d + 32.184 + 0.001658 * sin(gRad) + 0.000014 * sin(2.0 * gRad));
}, (dynamic val) {
  // TAI = TDB - 32.184 - 0.001658sin(g) - 0.000014sin(2g)...
  // where g = 357.53 deg + 0.9856003(JD - 2451545.0) deg... (Julian dates are in the TAI time scale)

  final d = val is num
      ? val.toDouble()
      : val is Number
          ? val.toDouble()
          : 0.0;

  // Too convoluted to solve analytically (because g is a function of
  // the Julian Date in the TAI scale... instead, get close and then search).
  var taiTest = d;
  var step = 10.0;
  const epsilon = 1.0e-8;
  const maxCount = 10000;
  var count = 0;
  var tdbTest = TDB.fromMks(d).toDouble();
  var delta = tdbTest - taiTest;
  var prevDelta = double.maxFinite;
  while ((delta.abs() > epsilon) && (count < maxCount)) {
    // See if we got farther away (if so reverse and take smaller steps)
    if (delta.abs() > prevDelta.abs()) step *= -0.5;

    // Step
    taiTest += step;

    prevDelta = delta;
    count++;

    // value & delta
    tdbTest = TDB.fromMks(taiTest).toDouble();
    delta = tdbTest - d;
  }

  // taiTest now returns a tcb value within epsilon (or loop count ran out)
  return Double(taiTest);
});