satellite.js

/*!
 * satellite-js v4.0.0
 * (c) 2013 Shashwat Kandadai and UCSC
 * https://github.com/shashwatak/satellite-js
 * License: MIT
 */

(function (global, factory) {
  typeof exports === 'object' && typeof module !== 'undefined' ? module.exports = factory() :
  typeof define === 'function' && define.amd ? define(factory) :
  (global = global || self, global.satellite = factory());
}(this, (function () { 'use strict';

  var pi = Math.PI;
  var twoPi = pi * 2;
  var deg2rad = pi / 180.0;
  var rad2deg = 180 / pi;
  var minutesPerDay = 1440.0;
  var mu = 398600.5; // in km3 / s2

  var earthRadius = 6378.137; // in km

  var xke = 60.0 / Math.sqrt(earthRadius * earthRadius * earthRadius / mu);
  var vkmpersec = earthRadius * xke / 60.0;
  var tumin = 1.0 / xke;
  var j2 = 0.00108262998905;
  var j3 = -0.00000253215306;
  var j4 = -0.00000161098761;
  var j3oj2 = j3 / j2;
  var x2o3 = 2.0 / 3.0;

  var constants = /*#__PURE__*/Object.freeze({
    __proto__: null,
    pi: pi,
    twoPi: twoPi,
    deg2rad: deg2rad,
    rad2deg: rad2deg,
    minutesPerDay: minutesPerDay,
    mu: mu,
    earthRadius: earthRadius,
    xke: xke,
    vkmpersec: vkmpersec,
    tumin: tumin,
    j2: j2,
    j3: j3,
    j4: j4,
    j3oj2: j3oj2,
    x2o3: x2o3
  });

  /* -----------------------------------------------------------------------------
   *
   *                           procedure days2mdhms
   *
   *  this procedure converts the day of the year, days, to the equivalent month
   *    day, hour, minute and second.
   *
   *  algorithm     : set up array for the number of days per month
   *                  find leap year - use 1900 because 2000 is a leap year
   *                  loop through a temp value while the value is < the days
   *                  perform int conversions to the correct day and month
   *                  convert remainder into h m s using type conversions
   *
   *  author        : david vallado                  719-573-2600    1 mar 2001
   *
   *  inputs          description                    range / units
   *    year        - year                           1900 .. 2100
   *    days        - julian day of the year         0.0  .. 366.0
   *
   *  outputs       :
   *    mon         - month                          1 .. 12
   *    day         - day                            1 .. 28,29,30,31
   *    hr          - hour                           0 .. 23
   *    min         - minute                         0 .. 59
   *    sec         - second                         0.0 .. 59.999
   *
   *  locals        :
   *    dayofyr     - day of year
   *    temp        - temporary extended values
   *    inttemp     - temporary int value
   *    i           - index
   *    lmonth[12]  - int array containing the number of days per month
   *
   *  coupling      :
   *    none.
   * --------------------------------------------------------------------------- */
  function days2mdhms(year, days) {
    var lmonth = [31, year % 4 === 0 ? 29 : 28, 31, 30, 31, 30, 31, 31, 30, 31, 30, 31];
    var dayofyr = Math.floor(days); //  ----------------- find month and day of month ----------------

    var i = 1;
    var inttemp = 0;

    while (dayofyr > inttemp + lmonth[i - 1] && i < 12) {
      inttemp += lmonth[i - 1];
      i += 1;
    }

    var mon = i;
    var day = dayofyr - inttemp; //  ----------------- find hours minutes and seconds -------------

    var temp = (days - dayofyr) * 24.0;
    var hr = Math.floor(temp);
    temp = (temp - hr) * 60.0;
    var minute = Math.floor(temp);
    var sec = (temp - minute) * 60.0;
    return {
      mon: mon,
      day: day,
      hr: hr,
      minute: minute,
      sec: sec
    };
  }
  /* -----------------------------------------------------------------------------
   *
   *                           procedure jday
   *
   *  this procedure finds the julian date given the year, month, day, and time.
   *    the julian date is defined by each elapsed day since noon, jan 1, 4713 bc.
   *
   *  algorithm     : calculate the answer in one step for efficiency
   *
   *  author        : david vallado                  719-573-2600    1 mar 2001
   *
   *  inputs          description                    range / units
   *    year        - year                           1900 .. 2100
   *    mon         - month                          1 .. 12
   *    day         - day                            1 .. 28,29,30,31
   *    hr          - universal time hour            0 .. 23
   *    min         - universal time min             0 .. 59
   *    sec         - universal time sec             0.0 .. 59.999
   *
   *  outputs       :
   *    jd          - julian date                    days from 4713 bc
   *
   *  locals        :
   *    none.
   *
   *  coupling      :
   *    none.
   *
   *  references    :
   *    vallado       2007, 189, alg 14, ex 3-14
   *
   * --------------------------------------------------------------------------- */

  function jdayInternal(year, mon, day, hr, minute, sec) {
    var msec = arguments.length > 6 && arguments[6] !== undefined ? arguments[6] : 0;
    return 367.0 * year - Math.floor(7 * (year + Math.floor((mon + 9) / 12.0)) * 0.25) + Math.floor(275 * mon / 9.0) + day + 1721013.5 + ((msec / 60000 + sec / 60.0 + minute) / 60.0 + hr) / 24.0 // ut in days
    // # - 0.5*sgn(100.0*year + mon - 190002.5) + 0.5;
    ;
  }

  function jday(year, mon, day, hr, minute, sec, msec) {
    if (year instanceof Date) {
      var date = year;
      return jdayInternal(date.getUTCFullYear(), date.getUTCMonth() + 1, // Note, this function requires months in range 1-12.
      date.getUTCDate(), date.getUTCHours(), date.getUTCMinutes(), date.getUTCSeconds(), date.getUTCMilliseconds());
    }

    return jdayInternal(year, mon, day, hr, minute, sec, msec);
  }
  /* -----------------------------------------------------------------------------
   *
   *                           procedure invjday
   *
   *  this procedure finds the year, month, day, hour, minute and second
   *  given the julian date. tu can be ut1, tdt, tdb, etc.
   *
   *  algorithm     : set up starting values
   *                  find leap year - use 1900 because 2000 is a leap year
   *                  find the elapsed days through the year in a loop
   *                  call routine to find each individual value
   *
   *  author        : david vallado                  719-573-2600    1 mar 2001
   *
   *  inputs          description                    range / units
   *    jd          - julian date                    days from 4713 bc
   *
   *  outputs       :
   *    year        - year                           1900 .. 2100
   *    mon         - month                          1 .. 12
   *    day         - day                            1 .. 28,29,30,31
   *    hr          - hour                           0 .. 23
   *    min         - minute                         0 .. 59
   *    sec         - second                         0.0 .. 59.999
   *
   *  locals        :
   *    days        - day of year plus fractional
   *                  portion of a day               days
   *    tu          - julian centuries from 0 h
   *                  jan 0, 1900
   *    temp        - temporary double values
   *    leapyrs     - number of leap years from 1900
   *
   *  coupling      :
   *    days2mdhms  - finds month, day, hour, minute and second given days and year
   *
   *  references    :
   *    vallado       2007, 208, alg 22, ex 3-13
   * --------------------------------------------------------------------------- */

  function invjday(jd, asArray) {
    // --------------- find year and days of the year -
    var temp = jd - 2415019.5;
    var tu = temp / 365.25;
    var year = 1900 + Math.floor(tu);
    var leapyrs = Math.floor((year - 1901) * 0.25); // optional nudge by 8.64x10-7 sec to get even outputs

    var days = temp - ((year - 1900) * 365.0 + leapyrs) + 0.00000000001; // ------------ check for case of beginning of a year -----------

    if (days < 1.0) {
      year -= 1;
      leapyrs = Math.floor((year - 1901) * 0.25);
      days = temp - ((year - 1900) * 365.0 + leapyrs);
    } // ----------------- find remaing data  -------------------------


    var mdhms = days2mdhms(year, days);
    var mon = mdhms.mon,
        day = mdhms.day,
        hr = mdhms.hr,
        minute = mdhms.minute;
    var sec = mdhms.sec - 0.00000086400;

    if (asArray) {
      return [year, mon, day, hr, minute, Math.floor(sec)];
    }

    return new Date(Date.UTC(year, mon - 1, day, hr, minute, Math.floor(sec)));
  }

  /* -----------------------------------------------------------------------------
   *
   *                           procedure dpper
   *
   *  this procedure provides deep space long period periodic contributions
   *    to the mean elements.  by design, these periodics are zero at epoch.
   *    this used to be dscom which included initialization, but it's really a
   *    recurring function.
   *
   *  author        : david vallado                  719-573-2600   28 jun 2005
   *
   *  inputs        :
   *    e3          -
   *    ee2         -
   *    peo         -
   *    pgho        -
   *    pho         -
   *    pinco       -
   *    plo         -
   *    se2 , se3 , sgh2, sgh3, sgh4, sh2, sh3, si2, si3, sl2, sl3, sl4 -
   *    t           -
   *    xh2, xh3, xi2, xi3, xl2, xl3, xl4 -
   *    zmol        -
   *    zmos        -
   *    ep          - eccentricity                           0.0 - 1.0
   *    inclo       - inclination - needed for lyddane modification
   *    nodep       - right ascension of ascending node
   *    argpp       - argument of perigee
   *    mp          - mean anomaly
   *
   *  outputs       :
   *    ep          - eccentricity                           0.0 - 1.0
   *    inclp       - inclination
   *    nodep        - right ascension of ascending node
   *    argpp       - argument of perigee
   *    mp          - mean anomaly
   *
   *  locals        :
   *    alfdp       -
   *    betdp       -
   *    cosip  , sinip  , cosop  , sinop  ,
   *    dalf        -
   *    dbet        -
   *    dls         -
   *    f2, f3      -
   *    pe          -
   *    pgh         -
   *    ph          -
   *    pinc        -
   *    pl          -
   *    sel   , ses   , sghl  , sghs  , shl   , shs   , sil   , sinzf , sis   ,
   *    sll   , sls
   *    xls         -
   *    xnoh        -
   *    zf          -
   *    zm          -
   *
   *  coupling      :
   *    none.
   *
   *  references    :
   *    hoots, roehrich, norad spacetrack report #3 1980
   *    hoots, norad spacetrack report #6 1986
   *    hoots, schumacher and glover 2004
   *    vallado, crawford, hujsak, kelso  2006
   ----------------------------------------------------------------------------*/

  function dpper(satrec, options) {
    var e3 = satrec.e3,
        ee2 = satrec.ee2,
        peo = satrec.peo,
        pgho = satrec.pgho,
        pho = satrec.pho,
        pinco = satrec.pinco,
        plo = satrec.plo,
        se2 = satrec.se2,
        se3 = satrec.se3,
        sgh2 = satrec.sgh2,
        sgh3 = satrec.sgh3,
        sgh4 = satrec.sgh4,
        sh2 = satrec.sh2,
        sh3 = satrec.sh3,
        si2 = satrec.si2,
        si3 = satrec.si3,
        sl2 = satrec.sl2,
        sl3 = satrec.sl3,
        sl4 = satrec.sl4,
        t = satrec.t,
        xgh2 = satrec.xgh2,
        xgh3 = satrec.xgh3,
        xgh4 = satrec.xgh4,
        xh2 = satrec.xh2,
        xh3 = satrec.xh3,
        xi2 = satrec.xi2,
        xi3 = satrec.xi3,
        xl2 = satrec.xl2,
        xl3 = satrec.xl3,
        xl4 = satrec.xl4,
        zmol = satrec.zmol,
        zmos = satrec.zmos;
    var init = options.init,
        opsmode = options.opsmode;
    var ep = options.ep,
        inclp = options.inclp,
        nodep = options.nodep,
        argpp = options.argpp,
        mp = options.mp; // Copy satellite attributes into local variables for convenience
    // and symmetry in writing formulae.

    var alfdp;
    var betdp;
    var cosip;
    var sinip;
    var cosop;
    var sinop;
    var dalf;
    var dbet;
    var dls;
    var f2;
    var f3;
    var pe;
    var pgh;
    var ph;
    var pinc;
    var pl;
    var sinzf;
    var xls;
    var xnoh;
    var zf;
    var zm; //  ---------------------- constants -----------------------------

    var zns = 1.19459e-5;
    var zes = 0.01675;
    var znl = 1.5835218e-4;
    var zel = 0.05490; //  --------------- calculate time varying periodics -----------

    zm = zmos + zns * t; // be sure that the initial call has time set to zero

    if (init === 'y') {
      zm = zmos;
    }

    zf = zm + 2.0 * zes * Math.sin(zm);
    sinzf = Math.sin(zf);
    f2 = 0.5 * sinzf * sinzf - 0.25;
    f3 = -0.5 * sinzf * Math.cos(zf);
    var ses = se2 * f2 + se3 * f3;
    var sis = si2 * f2 + si3 * f3;
    var sls = sl2 * f2 + sl3 * f3 + sl4 * sinzf;
    var sghs = sgh2 * f2 + sgh3 * f3 + sgh4 * sinzf;
    var shs = sh2 * f2 + sh3 * f3;
    zm = zmol + znl * t;

    if (init === 'y') {
      zm = zmol;
    }

    zf = zm + 2.0 * zel * Math.sin(zm);
    sinzf = Math.sin(zf);
    f2 = 0.5 * sinzf * sinzf - 0.25;
    f3 = -0.5 * sinzf * Math.cos(zf);
    var sel = ee2 * f2 + e3 * f3;
    var sil = xi2 * f2 + xi3 * f3;
    var sll = xl2 * f2 + xl3 * f3 + xl4 * sinzf;
    var sghl = xgh2 * f2 + xgh3 * f3 + xgh4 * sinzf;
    var shll = xh2 * f2 + xh3 * f3;
    pe = ses + sel;
    pinc = sis + sil;
    pl = sls + sll;
    pgh = sghs + sghl;
    ph = shs + shll;

    if (init === 'n') {
      pe -= peo;
      pinc -= pinco;
      pl -= plo;
      pgh -= pgho;
      ph -= pho;
      inclp += pinc;
      ep += pe;
      sinip = Math.sin(inclp);
      cosip = Math.cos(inclp);
      /* ----------------- apply periodics directly ------------ */
      // sgp4fix for lyddane choice
      // strn3 used original inclination - this is technically feasible
      // gsfc used perturbed inclination - also technically feasible
      // probably best to readjust the 0.2 limit value and limit discontinuity
      // 0.2 rad = 11.45916 deg
      // use next line for original strn3 approach and original inclination
      // if (inclo >= 0.2)
      // use next line for gsfc version and perturbed inclination

      if (inclp >= 0.2) {
        ph /= sinip;
        pgh -= cosip * ph;
        argpp += pgh;
        nodep += ph;
        mp += pl;
      } else {
        //  ---- apply periodics with lyddane modification ----
        sinop = Math.sin(nodep);
        cosop = Math.cos(nodep);
        alfdp = sinip * sinop;
        betdp = sinip * cosop;
        dalf = ph * cosop + pinc * cosip * sinop;
        dbet = -ph * sinop + pinc * cosip * cosop;
        alfdp += dalf;
        betdp += dbet;
        nodep %= twoPi; //  sgp4fix for afspc written intrinsic functions
        //  nodep used without a trigonometric function ahead

        if (nodep < 0.0 && opsmode === 'a') {
          nodep += twoPi;
        }

        xls = mp + argpp + cosip * nodep;
        dls = pl + pgh - pinc * nodep * sinip;
        xls += dls;
        xnoh = nodep;
        nodep = Math.atan2(alfdp, betdp); //  sgp4fix for afspc written intrinsic functions
        //  nodep used without a trigonometric function ahead

        if (nodep < 0.0 && opsmode === 'a') {
          nodep += twoPi;
        }

        if (Math.abs(xnoh - nodep) > pi) {
          if (nodep < xnoh) {
            nodep += twoPi;
          } else {
            nodep -= twoPi;
          }
        }

        mp += pl;
        argpp = xls - mp - cosip * nodep;
      }
    }

    return {
      ep: ep,
      inclp: inclp,
      nodep: nodep,
      argpp: argpp,
      mp: mp
    };
  }

  /*-----------------------------------------------------------------------------
   *
   *                           procedure dscom
   *
   *  this procedure provides deep space common items used by both the secular
   *    and periodics subroutines.  input is provided as shown. this routine
   *    used to be called dpper, but the functions inside weren't well organized.
   *
   *  author        : david vallado                  719-573-2600   28 jun 2005
   *
   *  inputs        :
   *    epoch       -
   *    ep          - eccentricity
   *    argpp       - argument of perigee
   *    tc          -
   *    inclp       - inclination
   *    nodep       - right ascension of ascending node
   *    np          - mean motion
   *
   *  outputs       :
   *    sinim  , cosim  , sinomm , cosomm , snodm  , cnodm
   *    day         -
   *    e3          -
   *    ee2         -
   *    em          - eccentricity
   *    emsq        - eccentricity squared
   *    gam         -
   *    peo         -
   *    pgho        -
   *    pho         -
   *    pinco       -
   *    plo         -
   *    rtemsq      -
   *    se2, se3         -
   *    sgh2, sgh3, sgh4        -
   *    sh2, sh3, si2, si3, sl2, sl3, sl4         -
   *    s1, s2, s3, s4, s5, s6, s7          -
   *    ss1, ss2, ss3, ss4, ss5, ss6, ss7, sz1, sz2, sz3         -
   *    sz11, sz12, sz13, sz21, sz22, sz23, sz31, sz32, sz33        -
   *    xgh2, xgh3, xgh4, xh2, xh3, xi2, xi3, xl2, xl3, xl4         -
   *    nm          - mean motion
   *    z1, z2, z3, z11, z12, z13, z21, z22, z23, z31, z32, z33         -
   *    zmol        -
   *    zmos        -
   *
   *  locals        :
   *    a1, a2, a3, a4, a5, a6, a7, a8, a9, a10         -
   *    betasq      -
   *    cc          -
   *    ctem, stem        -
   *    x1, x2, x3, x4, x5, x6, x7, x8          -
   *    xnodce      -
   *    xnoi        -
   *    zcosg  , zsing  , zcosgl , zsingl , zcosh  , zsinh  , zcoshl , zsinhl ,
   *    zcosi  , zsini  , zcosil , zsinil ,
   *    zx          -
   *    zy          -
   *
   *  coupling      :
   *    none.
   *
   *  references    :
   *    hoots, roehrich, norad spacetrack report #3 1980
   *    hoots, norad spacetrack report #6 1986
   *    hoots, schumacher and glover 2004
   *    vallado, crawford, hujsak, kelso  2006
   ----------------------------------------------------------------------------*/

  function dscom(options) {
    var epoch = options.epoch,
        ep = options.ep,
        argpp = options.argpp,
        tc = options.tc,
        inclp = options.inclp,
        nodep = options.nodep,
        np = options.np;
    var a1;
    var a2;
    var a3;
    var a4;
    var a5;
    var a6;
    var a7;
    var a8;
    var a9;
    var a10;
    var cc;
    var x1;
    var x2;
    var x3;
    var x4;
    var x5;
    var x6;
    var x7;
    var x8;
    var zcosg;
    var zsing;
    var zcosh;
    var zsinh;
    var zcosi;
    var zsini;
    var ss1;
    var ss2;
    var ss3;
    var ss4;
    var ss5;
    var ss6;
    var ss7;
    var sz1;
    var sz2;
    var sz3;
    var sz11;
    var sz12;
    var sz13;
    var sz21;
    var sz22;
    var sz23;
    var sz31;
    var sz32;
    var sz33;
    var s1;
    var s2;
    var s3;
    var s4;
    var s5;
    var s6;
    var s7;
    var z1;
    var z2;
    var z3;
    var z11;
    var z12;
    var z13;
    var z21;
    var z22;
    var z23;
    var z31;
    var z32;
    var z33; // -------------------------- constants -------------------------

    var zes = 0.01675;
    var zel = 0.05490;
    var c1ss = 2.9864797e-6;
    var c1l = 4.7968065e-7;
    var zsinis = 0.39785416;
    var zcosis = 0.91744867;
    var zcosgs = 0.1945905;
    var zsings = -0.98088458; //  --------------------- local variables ------------------------

    var nm = np;
    var em = ep;
    var snodm = Math.sin(nodep);
    var cnodm = Math.cos(nodep);
    var sinomm = Math.sin(argpp);
    var cosomm = Math.cos(argpp);
    var sinim = Math.sin(inclp);
    var cosim = Math.cos(inclp);
    var emsq = em * em;
    var betasq = 1.0 - emsq;
    var rtemsq = Math.sqrt(betasq); //  ----------------- initialize lunar solar terms ---------------

    var peo = 0.0;
    var pinco = 0.0;
    var plo = 0.0;
    var pgho = 0.0;
    var pho = 0.0;
    var day = epoch + 18261.5 + tc / 1440.0;
    var xnodce = (4.5236020 - 9.2422029e-4 * day) % twoPi;
    var stem = Math.sin(xnodce);
    var ctem = Math.cos(xnodce);
    var zcosil = 0.91375164 - 0.03568096 * ctem;
    var zsinil = Math.sqrt(1.0 - zcosil * zcosil);
    var zsinhl = 0.089683511 * stem / zsinil;
    var zcoshl = Math.sqrt(1.0 - zsinhl * zsinhl);
    var gam = 5.8351514 + 0.0019443680 * day;
    var zx = 0.39785416 * stem / zsinil;
    var zy = zcoshl * ctem + 0.91744867 * zsinhl * stem;
    zx = Math.atan2(zx, zy);
    zx += gam - xnodce;
    var zcosgl = Math.cos(zx);
    var zsingl = Math.sin(zx); //  ------------------------- do solar terms ---------------------

    zcosg = zcosgs;
    zsing = zsings;
    zcosi = zcosis;
    zsini = zsinis;
    zcosh = cnodm;
    zsinh = snodm;
    cc = c1ss;
    var xnoi = 1.0 / nm;
    var lsflg = 0;

    while (lsflg < 2) {
      lsflg += 1;
      a1 = zcosg * zcosh + zsing * zcosi * zsinh;
      a3 = -zsing * zcosh + zcosg * zcosi * zsinh;
      a7 = -zcosg * zsinh + zsing * zcosi * zcosh;
      a8 = zsing * zsini;
      a9 = zsing * zsinh + zcosg * zcosi * zcosh;
      a10 = zcosg * zsini;
      a2 = cosim * a7 + sinim * a8;
      a4 = cosim * a9 + sinim * a10;
      a5 = -sinim * a7 + cosim * a8;
      a6 = -sinim * a9 + cosim * a10;
      x1 = a1 * cosomm + a2 * sinomm;
      x2 = a3 * cosomm + a4 * sinomm;
      x3 = -a1 * sinomm + a2 * cosomm;
      x4 = -a3 * sinomm + a4 * cosomm;
      x5 = a5 * sinomm;
      x6 = a6 * sinomm;
      x7 = a5 * cosomm;
      x8 = a6 * cosomm;
      z31 = 12.0 * x1 * x1 - 3.0 * x3 * x3;
      z32 = 24.0 * x1 * x2 - 6.0 * x3 * x4;
      z33 = 12.0 * x2 * x2 - 3.0 * x4 * x4;
      z1 = 3.0 * (a1 * a1 + a2 * a2) + z31 * emsq;
      z2 = 6.0 * (a1 * a3 + a2 * a4) + z32 * emsq;
      z3 = 3.0 * (a3 * a3 + a4 * a4) + z33 * emsq;
      z11 = -6.0 * a1 * a5 + emsq * (-24.0 * x1 * x7 - 6.0 * x3 * x5);
      z12 = -6.0 * (a1 * a6 + a3 * a5) + emsq * (-24.0 * (x2 * x7 + x1 * x8) + -6.0 * (x3 * x6 + x4 * x5));
      z13 = -6.0 * a3 * a6 + emsq * (-24.0 * x2 * x8 - 6.0 * x4 * x6);
      z21 = 6.0 * a2 * a5 + emsq * (24.0 * x1 * x5 - 6.0 * x3 * x7);
      z22 = 6.0 * (a4 * a5 + a2 * a6) + emsq * (24.0 * (x2 * x5 + x1 * x6) - 6.0 * (x4 * x7 + x3 * x8));
      z23 = 6.0 * a4 * a6 + emsq * (24.0 * x2 * x6 - 6.0 * x4 * x8);
      z1 = z1 + z1 + betasq * z31;
      z2 = z2 + z2 + betasq * z32;
      z3 = z3 + z3 + betasq * z33;
      s3 = cc * xnoi;
      s2 = -0.5 * s3 / rtemsq;
      s4 = s3 * rtemsq;
      s1 = -15.0 * em * s4;
      s5 = x1 * x3 + x2 * x4;
      s6 = x2 * x3 + x1 * x4;
      s7 = x2 * x4 - x1 * x3; //  ----------------------- do lunar terms -------------------

      if (lsflg === 1) {
        ss1 = s1;
        ss2 = s2;
        ss3 = s3;
        ss4 = s4;
        ss5 = s5;
        ss6 = s6;
        ss7 = s7;
        sz1 = z1;
        sz2 = z2;
        sz3 = z3;
        sz11 = z11;
        sz12 = z12;
        sz13 = z13;
        sz21 = z21;
        sz22 = z22;
        sz23 = z23;
        sz31 = z31;
        sz32 = z32;
        sz33 = z33;
        zcosg = zcosgl;
        zsing = zsingl;
        zcosi = zcosil;
        zsini = zsinil;
        zcosh = zcoshl * cnodm + zsinhl * snodm;
        zsinh = snodm * zcoshl - cnodm * zsinhl;
        cc = c1l;
      }
    }

    var zmol = (4.7199672 + (0.22997150 * day - gam)) % twoPi;
    var zmos = (6.2565837 + 0.017201977 * day) % twoPi; //  ------------------------ do solar terms ----------------------

    var se2 = 2.0 * ss1 * ss6;
    var se3 = 2.0 * ss1 * ss7;
    var si2 = 2.0 * ss2 * sz12;
    var si3 = 2.0 * ss2 * (sz13 - sz11);
    var sl2 = -2.0 * ss3 * sz2;
    var sl3 = -2.0 * ss3 * (sz3 - sz1);
    var sl4 = -2.0 * ss3 * (-21.0 - 9.0 * emsq) * zes;
    var sgh2 = 2.0 * ss4 * sz32;
    var sgh3 = 2.0 * ss4 * (sz33 - sz31);
    var sgh4 = -18.0 * ss4 * zes;
    var sh2 = -2.0 * ss2 * sz22;
    var sh3 = -2.0 * ss2 * (sz23 - sz21); //  ------------------------ do lunar terms ----------------------

    var ee2 = 2.0 * s1 * s6;
    var e3 = 2.0 * s1 * s7;
    var xi2 = 2.0 * s2 * z12;
    var xi3 = 2.0 * s2 * (z13 - z11);
    var xl2 = -2.0 * s3 * z2;
    var xl3 = -2.0 * s3 * (z3 - z1);
    var xl4 = -2.0 * s3 * (-21.0 - 9.0 * emsq) * zel;
    var xgh2 = 2.0 * s4 * z32;
    var xgh3 = 2.0 * s4 * (z33 - z31);
    var xgh4 = -18.0 * s4 * zel;
    var xh2 = -2.0 * s2 * z22;
    var xh3 = -2.0 * s2 * (z23 - z21);
    return {
      snodm: snodm,
      cnodm: cnodm,
      sinim: sinim,
      cosim: cosim,
      sinomm: sinomm,
      cosomm: cosomm,
      day: day,
      e3: e3,
      ee2: ee2,
      em: em,
      emsq: emsq,
      gam: gam,
      peo: peo,
      pgho: pgho,
      pho: pho,
      pinco: pinco,
      plo: plo,
      rtemsq: rtemsq,
      se2: se2,
      se3: se3,
      sgh2: sgh2,
      sgh3: sgh3,
      sgh4: sgh4,
      sh2: sh2,
      sh3: sh3,
      si2: si2,
      si3: si3,
      sl2: sl2,
      sl3: sl3,
      sl4: sl4,
      s1: s1,
      s2: s2,
      s3: s3,
      s4: s4,
      s5: s5,
      s6: s6,
      s7: s7,
      ss1: ss1,
      ss2: ss2,
      ss3: ss3,
      ss4: ss4,
      ss5: ss5,
      ss6: ss6,
      ss7: ss7,
      sz1: sz1,
      sz2: sz2,
      sz3: sz3,
      sz11: sz11,
      sz12: sz12,
      sz13: sz13,
      sz21: sz21,
      sz22: sz22,
      sz23: sz23,
      sz31: sz31,
      sz32: sz32,
      sz33: sz33,
      xgh2: xgh2,
      xgh3: xgh3,
      xgh4: xgh4,
      xh2: xh2,
      xh3: xh3,
      xi2: xi2,
      xi3: xi3,
      xl2: xl2,
      xl3: xl3,
      xl4: xl4,
      nm: nm,
      z1: z1,
      z2: z2,
      z3: z3,
      z11: z11,
      z12: z12,
      z13: z13,
      z21: z21,
      z22: z22,
      z23: z23,
      z31: z31,
      z32: z32,
      z33: z33,
      zmol: zmol,
      zmos: zmos
    };
  }

  /*-----------------------------------------------------------------------------
   *
   *                           procedure dsinit
   *
   *  this procedure provides deep space contributions to mean motion dot due
   *    to geopotential resonance with half day and one day orbits.
   *
   *  author        : david vallado                  719-573-2600   28 jun 2005
   *
   *  inputs        :
   *    cosim, sinim-
   *    emsq        - eccentricity squared
   *    argpo       - argument of perigee
   *    s1, s2, s3, s4, s5      -
   *    ss1, ss2, ss3, ss4, ss5 -
   *    sz1, sz3, sz11, sz13, sz21, sz23, sz31, sz33 -
   *    t           - time
   *    tc          -
   *    gsto        - greenwich sidereal time                   rad
   *    mo          - mean anomaly
   *    mdot        - mean anomaly dot (rate)
   *    no          - mean motion
   *    nodeo       - right ascension of ascending node
   *    nodedot     - right ascension of ascending node dot (rate)
   *    xpidot      -
   *    z1, z3, z11, z13, z21, z23, z31, z33 -
   *    eccm        - eccentricity
   *    argpm       - argument of perigee
   *    inclm       - inclination
   *    mm          - mean anomaly
   *    xn          - mean motion
   *    nodem       - right ascension of ascending node
   *
   *  outputs       :
   *    em          - eccentricity
   *    argpm       - argument of perigee
   *    inclm       - inclination
   *    mm          - mean anomaly
   *    nm          - mean motion
   *    nodem       - right ascension of ascending node
   *    irez        - flag for resonance           0-none, 1-one day, 2-half day
   *    atime       -
   *    d2201, d2211, d3210, d3222, d4410, d4422, d5220, d5232, d5421, d5433    -
   *    dedt        -
   *    didt        -
   *    dmdt        -
   *    dndt        -
   *    dnodt       -
   *    domdt       -
   *    del1, del2, del3        -
   *    ses  , sghl , sghs , sgs  , shl  , shs  , sis  , sls
   *    theta       -
   *    xfact       -
   *    xlamo       -
   *    xli         -
   *    xni
   *
   *  locals        :
   *    ainv2       -
   *    aonv        -
   *    cosisq      -
   *    eoc         -
   *    f220, f221, f311, f321, f322, f330, f441, f442, f522, f523, f542, f543  -
   *    g200, g201, g211, g300, g310, g322, g410, g422, g520, g521, g532, g533  -
   *    sini2       -
   *    temp        -
   *    temp1       -
   *    theta       -
   *    xno2        -
   *
   *  coupling      :
   *    getgravconst
   *
   *  references    :
   *    hoots, roehrich, norad spacetrack report #3 1980
   *    hoots, norad spacetrack report #6 1986
   *    hoots, schumacher and glover 2004
   *    vallado, crawford, hujsak, kelso  2006
   ----------------------------------------------------------------------------*/

  function dsinit(options) {
    var cosim = options.cosim,
        argpo = options.argpo,
        s1 = options.s1,
        s2 = options.s2,
        s3 = options.s3,
        s4 = options.s4,
        s5 = options.s5,
        sinim = options.sinim,
        ss1 = options.ss1,
        ss2 = options.ss2,
        ss3 = options.ss3,
        ss4 = options.ss4,
        ss5 = options.ss5,
        sz1 = options.sz1,
        sz3 = options.sz3,
        sz11 = options.sz11,
        sz13 = options.sz13,
        sz21 = options.sz21,
        sz23 = options.sz23,
        sz31 = options.sz31,
        sz33 = options.sz33,
        t = options.t,
        tc = options.tc,
        gsto = options.gsto,
        mo = options.mo,
        mdot = options.mdot,
        no = options.no,
        nodeo = options.nodeo,
        nodedot = options.nodedot,
        xpidot = options.xpidot,
        z1 = options.z1,
        z3 = options.z3,
        z11 = options.z11,
        z13 = options.z13,
        z21 = options.z21,
        z23 = options.z23,
        z31 = options.z31,
        z33 = options.z33,
        ecco = options.ecco,
        eccsq = options.eccsq;
    var emsq = options.emsq,
        em = options.em,
        argpm = options.argpm,
        inclm = options.inclm,
        mm = options.mm,
        nm = options.nm,
        nodem = options.nodem,
        irez = options.irez,
        atime = options.atime,
        d2201 = options.d2201,
        d2211 = options.d2211,
        d3210 = options.d3210,
        d3222 = options.d3222,
        d4410 = options.d4410,
        d4422 = options.d4422,
        d5220 = options.d5220,
        d5232 = options.d5232,
        d5421 = options.d5421,
        d5433 = options.d5433,
        dedt = options.dedt,
        didt = options.didt,
        dmdt = options.dmdt,
        dnodt = options.dnodt,
        domdt = options.domdt,
        del1 = options.del1,
        del2 = options.del2,
        del3 = options.del3,
        xfact = options.xfact,
        xlamo = options.xlamo,
        xli = options.xli,
        xni = options.xni;
    var f220;
    var f221;
    var f311;
    var f321;
    var f322;
    var f330;
    var f441;
    var f442;
    var f522;
    var f523;
    var f542;
    var f543;
    var g200;
    var g201;
    var g211;
    var g300;
    var g310;
    var g322;
    var g410;
    var g422;
    var g520;
    var g521;
    var g532;
    var g533;
    var sini2;
    var temp;
    var temp1;
    var xno2;
    var ainv2;
    var aonv;
    var cosisq;
    var eoc;
    var q22 = 1.7891679e-6;
    var q31 = 2.1460748e-6;
    var q33 = 2.2123015e-7;
    var root22 = 1.7891679e-6;
    var root44 = 7.3636953e-9;
    var root54 = 2.1765803e-9;
    var rptim = 4.37526908801129966e-3; // equates to 7.29211514668855e-5 rad/sec

    var root32 = 3.7393792e-7;
    var root52 = 1.1428639e-7;
    var znl = 1.5835218e-4;
    var zns = 1.19459e-5; // -------------------- deep space initialization ------------

    irez = 0;

    if (nm < 0.0052359877 && nm > 0.0034906585) {
      irez = 1;
    }

    if (nm >= 8.26e-3 && nm <= 9.24e-3 && em >= 0.5) {
      irez = 2;
    } // ------------------------ do solar terms -------------------


    var ses = ss1 * zns * ss5;
    var sis = ss2 * zns * (sz11 + sz13);
    var sls = -zns * ss3 * (sz1 + sz3 - 14.0 - 6.0 * emsq);
    var sghs = ss4 * zns * (sz31 + sz33 - 6.0);
    var shs = -zns * ss2 * (sz21 + sz23); // sgp4fix for 180 deg incl

    if (inclm < 5.2359877e-2 || inclm > pi - 5.2359877e-2) {
      shs = 0.0;
    }

    if (sinim !== 0.0) {
      shs /= sinim;
    }

    var sgs = sghs - cosim * shs; // ------------------------- do lunar terms ------------------

    dedt = ses + s1 * znl * s5;
    didt = sis + s2 * znl * (z11 + z13);
    dmdt = sls - znl * s3 * (z1 + z3 - 14.0 - 6.0 * emsq);
    var sghl = s4 * znl * (z31 + z33 - 6.0);
    var shll = -znl * s2 * (z21 + z23); // sgp4fix for 180 deg incl

    if (inclm < 5.2359877e-2 || inclm > pi - 5.2359877e-2) {
      shll = 0.0;
    }

    domdt = sgs + sghl;
    dnodt = shs;

    if (sinim !== 0.0) {
      domdt -= cosim / sinim * shll;
      dnodt += shll / sinim;
    } // ----------- calculate deep space resonance effects --------


    var dndt = 0.0;
    var theta = (gsto + tc * rptim) % twoPi;
    em += dedt * t;
    inclm += didt * t;
    argpm += domdt * t;
    nodem += dnodt * t;
    mm += dmdt * t; // sgp4fix for negative inclinations
    // the following if statement should be commented out
    // if (inclm < 0.0)
    // {
    //   inclm  = -inclm;
    //   argpm  = argpm - pi;
    //   nodem = nodem + pi;
    // }
    // -------------- initialize the resonance terms -------------

    if (irez !== 0) {
      aonv = Math.pow(nm / xke, x2o3); // ---------- geopotential resonance for 12 hour orbits ------

      if (irez === 2) {
        cosisq = cosim * cosim;
        var emo = em;
        em = ecco;
        var emsqo = emsq;
        emsq = eccsq;
        eoc = em * emsq;
        g201 = -0.306 - (em - 0.64) * 0.440;

        if (em <= 0.65) {
          g211 = 3.616 - 13.2470 * em + 16.2900 * emsq;
          g310 = -19.302 + 117.3900 * em - 228.4190 * emsq + 156.5910 * eoc;
          g322 = -18.9068 + 109.7927 * em - 214.6334 * emsq + 146.5816 * eoc;
          g410 = -41.122 + 242.6940 * em - 471.0940 * emsq + 313.9530 * eoc;
          g422 = -146.407 + 841.8800 * em - 1629.014 * emsq + 1083.4350 * eoc;
          g520 = -532.114 + 3017.977 * em - 5740.032 * emsq + 3708.2760 * eoc;
        } else {
          g211 = -72.099 + 331.819 * em - 508.738 * emsq + 266.724 * eoc;
          g310 = -346.844 + 1582.851 * em - 2415.925 * emsq + 1246.113 * eoc;
          g322 = -342.585 + 1554.908 * em - 2366.899 * emsq + 1215.972 * eoc;
          g410 = -1052.797 + 4758.686 * em - 7193.992 * emsq + 3651.957 * eoc;
          g422 = -3581.690 + 16178.110 * em - 24462.770 * emsq + 12422.520 * eoc;

          if (em > 0.715) {
            g520 = -5149.66 + 29936.92 * em - 54087.36 * emsq + 31324.56 * eoc;
          } else {
            g520 = 1464.74 - 4664.75 * em + 3763.64 * emsq;
          }
        }

        if (em < 0.7) {
          g533 = -919.22770 + 4988.6100 * em - 9064.7700 * emsq + 5542.21 * eoc;
          g521 = -822.71072 + 4568.6173 * em - 8491.4146 * emsq + 5337.524 * eoc;
          g532 = -853.66600 + 4690.2500 * em - 8624.7700 * emsq + 5341.4 * eoc;
        } else {
          g533 = -37995.780 + 161616.52 * em - 229838.20 * emsq + 109377.94 * eoc;
          g521 = -51752.104 + 218913.95 * em - 309468.16 * emsq + 146349.42 * eoc;
          g532 = -40023.880 + 170470.89 * em - 242699.48 * emsq + 115605.82 * eoc;
        }

        sini2 = sinim * sinim;
        f220 = 0.75 * (1.0 + 2.0 * cosim + cosisq);
        f221 = 1.5 * sini2;
        f321 = 1.875 * sinim * (1.0 - 2.0 * cosim - 3.0 * cosisq);
        f322 = -1.875 * sinim * (1.0 + 2.0 * cosim - 3.0 * cosisq);
        f441 = 35.0 * sini2 * f220;
        f442 = 39.3750 * sini2 * sini2;
        f522 = 9.84375 * sinim * (sini2 * (1.0 - 2.0 * cosim - 5.0 * cosisq) + 0.33333333 * (-2.0 + 4.0 * cosim + 6.0 * cosisq));
        f523 = sinim * (4.92187512 * sini2 * (-2.0 - 4.0 * cosim + 10.0 * cosisq) + 6.56250012 * (1.0 + 2.0 * cosim - 3.0 * cosisq));
        f542 = 29.53125 * sinim * (2.0 - 8.0 * cosim + cosisq * (-12.0 + 8.0 * cosim + 10.0 * cosisq));
        f543 = 29.53125 * sinim * (-2.0 - 8.0 * cosim + cosisq * (12.0 + 8.0 * cosim - 10.0 * cosisq));
        xno2 = nm * nm;
        ainv2 = aonv * aonv;
        temp1 = 3.0 * xno2 * ainv2;
        temp = temp1 * root22;
        d2201 = temp * f220 * g201;
        d2211 = temp * f221 * g211;
        temp1 *= aonv;
        temp = temp1 * root32;
        d3210 = temp * f321 * g310;
        d3222 = temp * f322 * g322;
        temp1 *= aonv;
        temp = 2.0 * temp1 * root44;
        d4410 = temp * f441 * g410;
        d4422 = temp * f442 * g422;
        temp1 *= aonv;
        temp = temp1 * root52;
        d5220 = temp * f522 * g520;
        d5232 = temp * f523 * g532;
        temp = 2.0 * temp1 * root54;
        d5421 = temp * f542 * g521;
        d5433 = temp * f543 * g533;
        xlamo = (mo + nodeo + nodeo - (theta + theta)) % twoPi;
        xfact = mdot + dmdt + 2.0 * (nodedot + dnodt - rptim) - no;
        em = emo;
        emsq = emsqo;
      } //  ---------------- synchronous resonance terms --------------


      if (irez === 1) {
        g200 = 1.0 + emsq * (-2.5 + 0.8125 * emsq);
        g310 = 1.0 + 2.0 * emsq;
        g300 = 1.0 + emsq * (-6.0 + 6.60937 * emsq);
        f220 = 0.75 * (1.0 + cosim) * (1.0 + cosim);
        f311 = 0.9375 * sinim * sinim * (1.0 + 3.0 * cosim) - 0.75 * (1.0 + cosim);
        f330 = 1.0 + cosim;
        f330 *= 1.875 * f330 * f330;
        del1 = 3.0 * nm * nm * aonv * aonv;
        del2 = 2.0 * del1 * f220 * g200 * q22;
        del3 = 3.0 * del1 * f330 * g300 * q33 * aonv;
        del1 = del1 * f311 * g310 * q31 * aonv;
        xlamo = (mo + nodeo + argpo - theta) % twoPi;
        xfact = mdot + xpidot + dmdt + domdt + dnodt - (no + rptim);
      } //  ------------ for sgp4, initialize the integrator ----------


      xli = xlamo;
      xni = no;
      atime = 0.0;
      nm = no + dndt;
    }

    return {
      em: em,
      argpm: argpm,
      inclm: inclm,
      mm: mm,
      nm: nm,
      nodem: nodem,
      irez: irez,
      atime: atime,
      d2201: d2201,
      d2211: d2211,
      d3210: d3210,
      d3222: d3222,
      d4410: d4410,
      d4422: d4422,
      d5220: d5220,
      d5232: d5232,
      d5421: d5421,
      d5433: d5433,
      dedt: dedt,
      didt: didt,
      dmdt: dmdt,
      dndt: dndt,
      dnodt: dnodt,
      domdt: domdt,
      del1: del1,
      del2: del2,
      del3: del3,
      xfact: xfact,
      xlamo: xlamo,
      xli: xli,
      xni: xni
    };
  }

  /* -----------------------------------------------------------------------------
   *
   *                           function gstime
   *
   *  this function finds the greenwich sidereal time.
   *
   *  author        : david vallado                  719-573-2600    1 mar 2001
   *
   *  inputs          description                    range / units
   *    jdut1       - julian date in ut1             days from 4713 bc
   *
   *  outputs       :
   *    gstime      - greenwich sidereal time        0 to 2pi rad
   *
   *  locals        :
   *    temp        - temporary variable for doubles   rad
   *    tut1        - julian centuries from the
   *                  jan 1, 2000 12 h epoch (ut1)
   *
   *  coupling      :
   *    none
   *
   *  references    :
   *    vallado       2004, 191, eq 3-45
   * --------------------------------------------------------------------------- */

  function gstimeInternal(jdut1) {
    var tut1 = (jdut1 - 2451545.0) / 36525.0;
    var temp = -6.2e-6 * tut1 * tut1 * tut1 + 0.093104 * tut1 * tut1 + (876600.0 * 3600 + 8640184.812866) * tut1 + 67310.54841; // # sec

    temp = temp * deg2rad / 240.0 % twoPi; // 360/86400 = 1/240, to deg, to rad
    //  ------------------------ check quadrants ---------------------

    if (temp < 0.0) {
      temp += twoPi;
    }

    return temp;
  }

  function gstime() {
    if ((arguments.length <= 0 ? undefined : arguments[0]) instanceof Date || arguments.length > 1) {
      return gstimeInternal(jday.apply(void 0, arguments));
    }

    return gstimeInternal.apply(void 0, arguments);
  }

  /*-----------------------------------------------------------------------------
   *
   *                           procedure initl
   *
   *  this procedure initializes the sgp4 propagator. all the initialization is
   *    consolidated here instead of having multiple loops inside other routines.
   *
   *  author        : david vallado                  719-573-2600   28 jun 2005
   *
   *  inputs        :
   *    ecco        - eccentricity                           0.0 - 1.0
   *    epoch       - epoch time in days from jan 0, 1950. 0 hr
   *    inclo       - inclination of satellite
   *    no          - mean motion of satellite
   *    satn        - satellite number
   *
   *  outputs       :
   *    ainv        - 1.0 / a
   *    ao          - semi major axis
   *    con41       -
   *    con42       - 1.0 - 5.0 cos(i)
   *    cosio       - cosine of inclination
   *    cosio2      - cosio squared
   *    eccsq       - eccentricity squared
   *    method      - flag for deep space                    'd', 'n'
   *    omeosq      - 1.0 - ecco * ecco
   *    posq        - semi-parameter squared
   *    rp          - radius of perigee
   *    rteosq      - square root of (1.0 - ecco*ecco)
   *    sinio       - sine of inclination
   *    gsto        - gst at time of observation               rad
   *    no          - mean motion of satellite
   *
   *  locals        :
   *    ak          -
   *    d1          -
   *    del         -
   *    adel        -
   *    po          -
   *
   *  coupling      :
   *    getgravconst
   *    gstime      - find greenwich sidereal time from the julian date
   *
   *  references    :
   *    hoots, roehrich, norad spacetrack report #3 1980
   *    hoots, norad spacetrack report #6 1986
   *    hoots, schumacher and glover 2004
   *    vallado, crawford, hujsak, kelso  2006
   ----------------------------------------------------------------------------*/

  function initl(options) {
    var ecco = options.ecco,
        epoch = options.epoch,
        inclo = options.inclo,
        opsmode = options.opsmode;
    var no = options.no; // sgp4fix use old way of finding gst
    // ----------------------- earth constants ---------------------
    // sgp4fix identify constants and allow alternate values
    // ------------- calculate auxillary epoch quantities ----------

    var eccsq = ecco * ecco;
    var omeosq = 1.0 - eccsq;
    var rteosq = Math.sqrt(omeosq);
    var cosio = Math.cos(inclo);
    var cosio2 = cosio * cosio; // ------------------ un-kozai the mean motion -----------------

    var ak = Math.pow(xke / no, x2o3);
    var d1 = 0.75 * j2 * (3.0 * cosio2 - 1.0) / (rteosq * omeosq);
    var delPrime = d1 / (ak * ak);
    var adel = ak * (1.0 - delPrime * delPrime - delPrime * (1.0 / 3.0 + 134.0 * delPrime * delPrime / 81.0));
    delPrime = d1 / (adel * adel);
    no /= 1.0 + delPrime;
    var ao = Math.pow(xke / no, x2o3);
    var sinio = Math.sin(inclo);
    var po = ao * omeosq;
    var con42 = 1.0 - 5.0 * cosio2;
    var con41 = -con42 - cosio2 - cosio2;
    var ainv = 1.0 / ao;
    var posq = po * po;
    var rp = ao * (1.0 - ecco);
    var method = 'n'; //  sgp4fix modern approach to finding sidereal time

    var gsto;

    if (opsmode === 'a') {
      //  sgp4fix use old way of finding gst
      //  count integer number of days from 0 jan 1970
      var ts70 = epoch - 7305.0;
      var ds70 = Math.floor(ts70 + 1.0e-8);
      var tfrac = ts70 - ds70; //  find greenwich location at epoch

      var c1 = 1.72027916940703639e-2;
      var thgr70 = 1.7321343856509374;
      var fk5r = 5.07551419432269442e-15;
      var c1p2p = c1 + twoPi;
      gsto = (thgr70 + c1 * ds70 + c1p2p * tfrac + ts70 * ts70 * fk5r) % twoPi;

      if (gsto < 0.0) {
        gsto += twoPi;
      }
    } else {
      gsto = gstime(epoch + 2433281.5);
    }

    return {
      no: no,
      method: method,
      ainv: ainv,
      ao: ao,
      con41: con41,
      con42: con42,
      cosio: cosio,
      cosio2: cosio2,
      eccsq: eccsq,
      omeosq: omeosq,
      posq: posq,
      rp: rp,
      rteosq: rteosq,
      sinio: sinio,
      gsto: gsto
    };
  }

  /*-----------------------------------------------------------------------------
   *
   *                           procedure dspace
   *
   *  this procedure provides deep space contributions to mean elements for
   *    perturbing third body.  these effects have been averaged over one
   *    revolution of the sun and moon.  for earth resonance effects, the
   *    effects have been averaged over no revolutions of the satellite.
   *    (mean motion)
   *
   *  author        : david vallado                  719-573-2600   28 jun 2005
   *
   *  inputs        :
   *    d2201, d2211, d3210, d3222, d4410, d4422, d5220, d5232, d5421, d5433 -
   *    dedt        -
   *    del1, del2, del3  -
   *    didt        -
   *    dmdt        -
   *    dnodt       -
   *    domdt       -
   *    irez        - flag for resonance           0-none, 1-one day, 2-half day
   *    argpo       - argument of perigee
   *    argpdot     - argument of perigee dot (rate)
   *    t           - time
   *    tc          -
   *    gsto        - gst
   *    xfact       -
   *    xlamo       -
   *    no          - mean motion
   *    atime       -
   *    em          - eccentricity
   *    ft          -
   *    argpm       - argument of perigee
   *    inclm       - inclination
   *    xli         -
   *    mm          - mean anomaly
   *    xni         - mean motion
   *    nodem       - right ascension of ascending node
   *
   *  outputs       :
   *    atime       -
   *    em          - eccentricity
   *    argpm       - argument of perigee
   *    inclm       - inclination
   *    xli         -
   *    mm          - mean anomaly
   *    xni         -
   *    nodem       - right ascension of ascending node
   *    dndt        -
   *    nm          - mean motion
   *
   *  locals        :
   *    delt        -
   *    ft          -
   *    theta       -
   *    x2li        -
   *    x2omi       -
   *    xl          -
   *    xldot       -
   *    xnddt       -
   *    xndt        -
   *    xomi        -
   *
   *  coupling      :
   *    none        -
   *
   *  references    :
   *    hoots, roehrich, norad spacetrack report #3 1980
   *    hoots, norad spacetrack report #6 1986
   *    hoots, schumacher and glover 2004
   *    vallado, crawford, hujsak, kelso  2006
   ----------------------------------------------------------------------------*/

  function dspace(options) {
    var irez = options.irez,
        d2201 = options.d2201,
        d2211 = options.d2211,
        d3210 = options.d3210,
        d3222 = options.d3222,
        d4410 = options.d4410,
        d4422 = options.d4422,
        d5220 = options.d5220,
        d5232 = options.d5232,
        d5421 = options.d5421,
        d5433 = options.d5433,
        dedt = options.dedt,
        del1 = options.del1,
        del2 = options.del2,
        del3 = options.del3,
        didt = options.didt,
        dmdt = options.dmdt,
        dnodt = options.dnodt,
        domdt = options.domdt,
        argpo = options.argpo,
        argpdot = options.argpdot,
        t = options.t,
        tc = options.tc,
        gsto = options.gsto,
        xfact = options.xfact,
        xlamo = options.xlamo,
        no = options.no;
    var atime = options.atime,
        em = options.em,
        argpm = options.argpm,
        inclm = options.inclm,
        xli = options.xli,
        mm = options.mm,
        xni = options.xni,
        nodem = options.nodem,
        nm = options.nm;
    var fasx2 = 0.13130908;
    var fasx4 = 2.8843198;
    var fasx6 = 0.37448087;
    var g22 = 5.7686396;
    var g32 = 0.95240898;
    var g44 = 1.8014998;
    var g52 = 1.0508330;
    var g54 = 4.4108898;
    var rptim = 4.37526908801129966e-3; // equates to 7.29211514668855e-5 rad/sec

    var stepp = 720.0;
    var stepn = -720.0;
    var step2 = 259200.0;
    var delt;
    var x2li;
    var x2omi;
    var xl;
    var xldot;
    var xnddt;
    var xndt;
    var xomi;
    var dndt = 0.0;
    var ft = 0.0; //  ----------- calculate deep space resonance effects -----------

    var theta = (gsto + tc * rptim) % twoPi;
    em += dedt * t;
    inclm += didt * t;
    argpm += domdt * t;
    nodem += dnodt * t;
    mm += dmdt * t; // sgp4fix for negative inclinations
    // the following if statement should be commented out
    // if (inclm < 0.0)
    // {
    //   inclm = -inclm;
    //   argpm = argpm - pi;
    //   nodem = nodem + pi;
    // }

    /* - update resonances : numerical (euler-maclaurin) integration - */

    /* ------------------------- epoch restart ----------------------  */
    //   sgp4fix for propagator problems
    //   the following integration works for negative time steps and periods
    //   the specific changes are unknown because the original code was so convoluted
    // sgp4fix take out atime = 0.0 and fix for faster operation

    if (irez !== 0) {
      //  sgp4fix streamline check
      if (atime === 0.0 || t * atime <= 0.0 || Math.abs(t) < Math.abs(atime)) {
        atime = 0.0;
        xni = no;
        xli = xlamo;
      } // sgp4fix move check outside loop


      if (t > 0.0) {
        delt = stepp;
      } else {
        delt = stepn;
      }

      var iretn = 381; // added for do loop

      while (iretn === 381) {
        //  ------------------- dot terms calculated -------------
        //  ----------- near - synchronous resonance terms -------
        if (irez !== 2) {
          xndt = del1 * Math.sin(xli - fasx2) + del2 * Math.sin(2.0 * (xli - fasx4)) + del3 * Math.sin(3.0 * (xli - fasx6));
          xldot = xni + xfact;
          xnddt = del1 * Math.cos(xli - fasx2) + 2.0 * del2 * Math.cos(2.0 * (xli - fasx4)) + 3.0 * del3 * Math.cos(3.0 * (xli - fasx6));
          xnddt *= xldot;
        } else {
          // --------- near - half-day resonance terms --------
          xomi = argpo + argpdot * atime;
          x2omi = xomi + xomi;
          x2li = xli + xli;
          xndt = d2201 * Math.sin(x2omi + xli - g22) + d2211 * Math.sin(xli - g22) + d3210 * Math.sin(xomi + xli - g32) + d3222 * Math.sin(-xomi + xli - g32) + d4410 * Math.sin(x2omi + x2li - g44) + d4422 * Math.sin(x2li - g44) + d5220 * Math.sin(xomi + xli - g52) + d5232 * Math.sin(-xomi + xli - g52) + d5421 * Math.sin(xomi + x2li - g54) + d5433 * Math.sin(-xomi + x2li - g54);
          xldot = xni + xfact;
          xnddt = d2201 * Math.cos(x2omi + xli - g22) + d2211 * Math.cos(xli - g22) + d3210 * Math.cos(xomi + xli - g32) + d3222 * Math.cos(-xomi + xli - g32) + d5220 * Math.cos(xomi + xli - g52) + d5232 * Math.cos(-xomi + xli - g52) + 2.0 * d4410 * Math.cos(x2omi + x2li - g44) + d4422 * Math.cos(x2li - g44) + d5421 * Math.cos(xomi + x2li - g54) + d5433 * Math.cos(-xomi + x2li - g54);
          xnddt *= xldot;
        } //  ----------------------- integrator -------------------
        //  sgp4fix move end checks to end of routine


        if (Math.abs(t - atime) >= stepp) {
          iretn = 381;
        } else {
          ft = t - atime;
          iretn = 0;
        }

        if (iretn === 381) {
          xli += xldot * delt + xndt * step2;
          xni += xndt * delt + xnddt * step2;
          atime += delt;
        }
      }

      nm = xni + xndt * ft + xnddt * ft * ft * 0.5;
      xl = xli + xldot * ft + xndt * ft * ft * 0.5;

      if (irez !== 1) {
        mm = xl - 2.0 * nodem + 2.0 * theta;
        dndt = nm - no;
      } else {
        mm = xl - nodem - argpm + theta;
        dndt = nm - no;
      }

      nm = no + dndt;
    }

    return {
      atime: atime,
      em: em,
      argpm: argpm,
      inclm: inclm,
      xli: xli,
      mm: mm,
      xni: xni,
      nodem: nodem,
      dndt: dndt,
      nm: nm
    };
  }

  /*----------------------------------------------------------------------------
   *
   *                             procedure sgp4
   *
   *  this procedure is the sgp4 prediction model from space command. this is an
   *    updated and combined version of sgp4 and sdp4, which were originally
   *    published separately in spacetrack report //3. this version follows the
   *    methodology from the aiaa paper (2006) describing the history and
   *    development of the code.
   *
   *  author        : david vallado                  719-573-2600   28 jun 2005
   *
   *  inputs        :
   *    satrec  - initialised structure from sgp4init() call.
   *    tsince  - time since epoch (minutes)
   *
   *  outputs       :
   *    r           - position vector                     km
   *    v           - velocity                            km/sec
   *  return code - non-zero on error.
   *                   1 - mean elements, ecc >= 1.0 or ecc < -0.001 or a < 0.95 er
   *                   2 - mean motion less than 0.0
   *                   3 - pert elements, ecc < 0.0  or  ecc > 1.0
   *                   4 - semi-latus rectum < 0.0
   *                   5 - epoch elements are sub-orbital
   *                   6 - satellite has decayed
   *
   *  locals        :
   *    am          -
   *    axnl, aynl        -
   *    betal       -
   *    cosim   , sinim   , cosomm  , sinomm  , cnod    , snod    , cos2u   ,
   *    sin2u   , coseo1  , sineo1  , cosi    , sini    , cosip   , sinip   ,
   *    cosisq  , cossu   , sinsu   , cosu    , sinu
   *    delm        -
   *    delomg      -
   *    dndt        -
   *    eccm        -
   *    emsq        -
   *    ecose       -
   *    el2         -
   *    eo1         -
   *    eccp        -
   *    esine       -
   *    argpm       -
   *    argpp       -
   *    omgadf      -
   *    pl          -
   *    r           -
   *    rtemsq      -
   *    rdotl       -
   *    rl          -
   *    rvdot       -
   *    rvdotl      -
   *    su          -
   *    t2  , t3   , t4    , tc
   *    tem5, temp , temp1 , temp2  , tempa  , tempe  , templ
   *    u   , ux   , uy    , uz     , vx     , vy     , vz
   *    inclm       - inclination
   *    mm          - mean anomaly
   *    nm          - mean motion
   *    nodem       - right asc of ascending node
   *    xinc        -
   *    xincp       -
   *    xl          -
   *    xlm         -
   *    mp          -
   *    xmdf        -
   *    xmx         -
   *    xmy         -
   *    nodedf      -
   *    xnode       -
   *    nodep       -
   *    np          -
   *
   *  coupling      :
   *    getgravconst-
   *    dpper
   *    dspace
   *
   *  references    :
   *    hoots, roehrich, norad spacetrack report //3 1980
   *    hoots, norad spacetrack report //6 1986
   *    hoots, schumacher and glover 2004
   *    vallado, crawford, hujsak, kelso  2006
   ----------------------------------------------------------------------------*/

  function sgp4(satrec, tsince) {
    /* eslint-disable no-param-reassign */
    var coseo1;
    var sineo1;
    var cosip;
    var sinip;
    var cosisq;
    var delm;
    var delomg;
    var eo1;
    var argpm;
    var argpp;
    var su;
    var t3;
    var t4;
    var tc;
    var tem5;
    var temp;
    var tempa;
    var tempe;
    var templ;
    var inclm;
    var mm;
    var nm;
    var nodem;
    var xincp;
    var xlm;
    var mp;
    var nodep;
    /* ------------------ set mathematical constants --------------- */
    // sgp4fix divisor for divide by zero check on inclination
    // the old check used 1.0 + cos(pi-1.0e-9), but then compared it to
    // 1.5 e-12, so the threshold was changed to 1.5e-12 for consistency

    var temp4 = 1.5e-12; // --------------------- clear sgp4 error flag -----------------

    satrec.t = tsince;
    satrec.error = 0; //  ------- update for secular gravity and atmospheric drag -----

    var xmdf = satrec.mo + satrec.mdot * satrec.t;
    var argpdf = satrec.argpo + satrec.argpdot * satrec.t;
    var nodedf = satrec.nodeo + satrec.nodedot * satrec.t;
    argpm = argpdf;
    mm = xmdf;
    var t2 = satrec.t * satrec.t;
    nodem = nodedf + satrec.nodecf * t2;
    tempa = 1.0 - satrec.cc1 * satrec.t;
    tempe = satrec.bstar * satrec.cc4 * satrec.t;
    templ = satrec.t2cof * t2;

    if (satrec.isimp !== 1) {
      delomg = satrec.omgcof * satrec.t; //  sgp4fix use mutliply for speed instead of pow

      var delmtemp = 1.0 + satrec.eta * Math.cos(xmdf);
      delm = satrec.xmcof * (delmtemp * delmtemp * delmtemp - satrec.delmo);
      temp = delomg + delm;
      mm = xmdf + temp;
      argpm = argpdf - temp;
      t3 = t2 * satrec.t;
      t4 = t3 * satrec.t;
      tempa = tempa - satrec.d2 * t2 - satrec.d3 * t3 - satrec.d4 * t4;
      tempe += satrec.bstar * satrec.cc5 * (Math.sin(mm) - satrec.sinmao);
      templ = templ + satrec.t3cof * t3 + t4 * (satrec.t4cof + satrec.t * satrec.t5cof);
    }

    nm = satrec.no;
    var em = satrec.ecco;
    inclm = satrec.inclo;

    if (satrec.method === 'd') {
      tc = satrec.t;
      var dspaceOptions = {
        irez: satrec.irez,
        d2201: satrec.d2201,
        d2211: satrec.d2211,
        d3210: satrec.d3210,
        d3222: satrec.d3222,
        d4410: satrec.d4410,
        d4422: satrec.d4422,
        d5220: satrec.d5220,
        d5232: satrec.d5232,
        d5421: satrec.d5421,
        d5433: satrec.d5433,
        dedt: satrec.dedt,
        del1: satrec.del1,
        del2: satrec.del2,
        del3: satrec.del3,
        didt: satrec.didt,
        dmdt: satrec.dmdt,
        dnodt: satrec.dnodt,
        domdt: satrec.domdt,
        argpo: satrec.argpo,
        argpdot: satrec.argpdot,
        t: satrec.t,
        tc: tc,
        gsto: satrec.gsto,
        xfact: satrec.xfact,
        xlamo: satrec.xlamo,
        no: satrec.no,
        atime: satrec.atime,
        em: em,
        argpm: argpm,
        inclm: inclm,
        xli: satrec.xli,
        mm: mm,
        xni: satrec.xni,
        nodem: nodem,
        nm: nm
      };
      var dspaceResult = dspace(dspaceOptions);
      em = dspaceResult.em;
      argpm = dspaceResult.argpm;
      inclm = dspaceResult.inclm;
      mm = dspaceResult.mm;
      nodem = dspaceResult.nodem;
      nm = dspaceResult.nm;
    }

    if (nm <= 0.0) {
      // printf("// error nm %f\n", nm);
      satrec.error = 2; // sgp4fix add return

      return [false, false];
    }

    var am = Math.pow(xke / nm, x2o3) * tempa * tempa;
    nm = xke / Math.pow(am, 1.5);
    em -= tempe; // fix tolerance for error recognition
    // sgp4fix am is fixed from the previous nm check

    if (em >= 1.0 || em < -0.001) {
      // || (am < 0.95)
      // printf("// error em %f\n", em);
      satrec.error = 1; // sgp4fix to return if there is an error in eccentricity

      return [false, false];
    } //  sgp4fix fix tolerance to avoid a divide by zero


    if (em < 1.0e-6) {
      em = 1.0e-6;
    }

    mm += satrec.no * templ;
    xlm = mm + argpm + nodem;
    nodem %= twoPi;
    argpm %= twoPi;
    xlm %= twoPi;
    mm = (xlm - argpm - nodem) % twoPi; // ----------------- compute extra mean quantities -------------

    var sinim = Math.sin(inclm);
    var cosim = Math.cos(inclm); // -------------------- add lunar-solar periodics --------------

    var ep = em;
    xincp = inclm;
    argpp = argpm;
    nodep = nodem;
    mp = mm;
    sinip = sinim;
    cosip = cosim;

    if (satrec.method === 'd') {
      var dpperParameters = {
        inclo: satrec.inclo,
        init: 'n',
        ep: ep,
        inclp: xincp,
        nodep: nodep,
        argpp: argpp,
        mp: mp,
        opsmode: satrec.operationmode
      };
      var dpperResult = dpper(satrec, dpperParameters);
      ep = dpperResult.ep;
      nodep = dpperResult.nodep;
      argpp = dpperResult.argpp;
      mp = dpperResult.mp;
      xincp = dpperResult.inclp;

      if (xincp < 0.0) {
        xincp = -xincp;
        nodep += pi;
        argpp -= pi;
      }

      if (ep < 0.0 || ep > 1.0) {
        //  printf("// error ep %f\n", ep);
        satrec.error = 3; //  sgp4fix add return

        return [false, false];
      }
    } //  -------------------- long period periodics ------------------


    if (satrec.method === 'd') {
      sinip = Math.sin(xincp);
      cosip = Math.cos(xincp);
      satrec.aycof = -0.5 * j3oj2 * sinip; //  sgp4fix for divide by zero for xincp = 180 deg

      if (Math.abs(cosip + 1.0) > 1.5e-12) {
        satrec.xlcof = -0.25 * j3oj2 * sinip * (3.0 + 5.0 * cosip) / (1.0 + cosip);
      } else {
        satrec.xlcof = -0.25 * j3oj2 * sinip * (3.0 + 5.0 * cosip) / temp4;
      }
    }

    var axnl = ep * Math.cos(argpp);
    temp = 1.0 / (am * (1.0 - ep * ep));
    var aynl = ep * Math.sin(argpp) + temp * satrec.aycof;
    var xl = mp + argpp + nodep + temp * satrec.xlcof * axnl; // --------------------- solve kepler's equation ---------------

    var u = (xl - nodep) % twoPi;
    eo1 = u;
    tem5 = 9999.9;
    var ktr = 1; //    sgp4fix for kepler iteration
    //    the following iteration needs better limits on corrections

    while (Math.abs(tem5) >= 1.0e-12 && ktr <= 10) {
      sineo1 = Math.sin(eo1);
      coseo1 = Math.cos(eo1);
      tem5 = 1.0 - coseo1 * axnl - sineo1 * aynl;
      tem5 = (u - aynl * coseo1 + axnl * sineo1 - eo1) / tem5;

      if (Math.abs(tem5) >= 0.95) {
        if (tem5 > 0.0) {
          tem5 = 0.95;
        } else {
          tem5 = -0.95;
        }
      }

      eo1 += tem5;
      ktr += 1;
    } //  ------------- short period preliminary quantities -----------


    var ecose = axnl * coseo1 + aynl * sineo1;
    var esine = axnl * sineo1 - aynl * coseo1;
    var el2 = axnl * axnl + aynl * aynl;
    var pl = am * (1.0 - el2);

    if (pl < 0.0) {
      //  printf("// error pl %f\n", pl);
      satrec.error = 4; //  sgp4fix add return

      return [false, false];
    }

    var rl = am * (1.0 - ecose);
    var rdotl = Math.sqrt(am) * esine / rl;
    var rvdotl = Math.sqrt(pl) / rl;
    var betal = Math.sqrt(1.0 - el2);
    temp = esine / (1.0 + betal);
    var sinu = am / rl * (sineo1 - aynl - axnl * temp);
    var cosu = am / rl * (coseo1 - axnl + aynl * temp);
    su = Math.atan2(sinu, cosu);
    var sin2u = (cosu + cosu) * sinu;
    var cos2u = 1.0 - 2.0 * sinu * sinu;
    temp = 1.0 / pl;
    var temp1 = 0.5 * j2 * temp;
    var temp2 = temp1 * temp; // -------------- update for short period periodics ------------

    if (satrec.method === 'd') {
      cosisq = cosip * cosip;
      satrec.con41 = 3.0 * cosisq - 1.0;
      satrec.x1mth2 = 1.0 - cosisq;
      satrec.x7thm1 = 7.0 * cosisq - 1.0;
    }

    var mrt = rl * (1.0 - 1.5 * temp2 * betal * satrec.con41) + 0.5 * temp1 * satrec.x1mth2 * cos2u; // sgp4fix for decaying satellites

    if (mrt < 1.0) {
      // printf("// decay condition %11.6f \n",mrt);
      satrec.error = 6;
      return {
        position: false,
        velocity: false
      };
    }

    su -= 0.25 * temp2 * satrec.x7thm1 * sin2u;
    var xnode = nodep + 1.5 * temp2 * cosip * sin2u;
    var xinc = xincp + 1.5 * temp2 * cosip * sinip * cos2u;
    var mvt = rdotl - nm * temp1 * satrec.x1mth2 * sin2u / xke;
    var rvdot = rvdotl + nm * temp1 * (satrec.x1mth2 * cos2u + 1.5 * satrec.con41) / xke; // --------------------- orientation vectors -------------------

    var sinsu = Math.sin(su);
    var cossu = Math.cos(su);
    var snod = Math.sin(xnode);
    var cnod = Math.cos(xnode);
    var sini = Math.sin(xinc);
    var cosi = Math.cos(xinc);
    var xmx = -snod * cosi;
    var xmy = cnod * cosi;
    var ux = xmx * sinsu + cnod * cossu;
    var uy = xmy * sinsu + snod * cossu;
    var uz = sini * sinsu;
    var vx = xmx * cossu - cnod * sinsu;
    var vy = xmy * cossu - snod * sinsu;
    var vz = sini * cossu; // --------- position and velocity (in km and km/sec) ----------

    var r = {
      x: mrt * ux * earthRadius,
      y: mrt * uy * earthRadius,
      z: mrt * uz * earthRadius
    };
    var v = {
      x: (mvt * ux + rvdot * vx) * vkmpersec,
      y: (mvt * uy + rvdot * vy) * vkmpersec,
      z: (mvt * uz + rvdot * vz) * vkmpersec
    };
    return {
      position: r,
      velocity: v
    };
    /* eslint-enable no-param-reassign */
  }

  /*-----------------------------------------------------------------------------
   *
   *                             procedure sgp4init
   *
   *  this procedure initializes variables for sgp4.
   *
   *  author        : david vallado                  719-573-2600   28 jun 2005
   *  author        : david vallado                  719-573-2600   28 jun 2005
   *
   *  inputs        :
   *    opsmode     - mode of operation afspc or improved 'a', 'i'
   *    satn        - satellite number
   *    bstar       - sgp4 type drag coefficient              kg/m2er
   *    ecco        - eccentricity
   *    epoch       - epoch time in days from jan 0, 1950. 0 hr
   *    argpo       - argument of perigee (output if ds)
   *    inclo       - inclination
   *    mo          - mean anomaly (output if ds)
   *    no          - mean motion
   *    nodeo       - right ascension of ascending node
   *
   *  outputs       :
   *    rec      - common values for subsequent calls
   *    return code - non-zero on error.
   *                   1 - mean elements, ecc >= 1.0 or ecc < -0.001 or a < 0.95 er
   *                   2 - mean motion less than 0.0
   *                   3 - pert elements, ecc < 0.0  or  ecc > 1.0
   *                   4 - semi-latus rectum < 0.0
   *                   5 - epoch elements are sub-orbital
   *                   6 - satellite has decayed
   *
   *  locals        :
   *    cnodm  , snodm  , cosim  , sinim  , cosomm , sinomm
   *    cc1sq  , cc2    , cc3
   *    coef   , coef1
   *    cosio4      -
   *    day         -
   *    dndt        -
   *    em          - eccentricity
   *    emsq        - eccentricity squared
   *    eeta        -
   *    etasq       -
   *    gam         -
   *    argpm       - argument of perigee
   *    nodem       -
   *    inclm       - inclination
   *    mm          - mean anomaly
   *    nm          - mean motion
   *    perige      - perigee
   *    pinvsq      -
   *    psisq       -
   *    qzms24      -
   *    rtemsq      -
   *    s1, s2, s3, s4, s5, s6, s7          -
   *    sfour       -
   *    ss1, ss2, ss3, ss4, ss5, ss6, ss7         -
   *    sz1, sz2, sz3
   *    sz11, sz12, sz13, sz21, sz22, sz23, sz31, sz32, sz33        -
   *    tc          -
   *    temp        -
   *    temp1, temp2, temp3       -
   *    tsi         -
   *    xpidot      -
   *    xhdot1      -
   *    z1, z2, z3          -
   *    z11, z12, z13, z21, z22, z23, z31, z32, z33         -
   *
   *  coupling      :
   *    getgravconst-
   *    initl       -
   *    dscom       -
   *    dpper       -
   *    dsinit      -
   *    sgp4        -
   *
   *  references    :
   *    hoots, roehrich, norad spacetrack report #3 1980
   *    hoots, norad spacetrack report #6 1986
   *    hoots, schumacher and glover 2004
   *    vallado, crawford, hujsak, kelso  2006
   ----------------------------------------------------------------------------*/

  function sgp4init(satrec, options) {
    /* eslint-disable no-param-reassign */
    var opsmode = options.opsmode,
        satn = options.satn,
        epoch = options.epoch,
        xbstar = options.xbstar,
        xecco = options.xecco,
        xargpo = options.xargpo,
        xinclo = options.xinclo,
        xmo = options.xmo,
        xno = options.xno,
        xnodeo = options.xnodeo;
    var cosim;
    var sinim;
    var cc1sq;
    var cc2;
    var cc3;
    var coef;
    var coef1;
    var cosio4;
    var em;
    var emsq;
    var eeta;
    var etasq;
    var argpm;
    var nodem;
    var inclm;
    var mm;
    var nm;
    var perige;
    var pinvsq;
    var psisq;
    var qzms24;
    var s1;
    var s2;
    var s3;
    var s4;
    var s5;
    var sfour;
    var ss1;
    var ss2;
    var ss3;
    var ss4;
    var ss5;
    var sz1;
    var sz3;
    var sz11;
    var sz13;
    var sz21;
    var sz23;
    var sz31;
    var sz33;
    var tc;
    var temp;
    var temp1;
    var temp2;
    var temp3;
    var tsi;
    var xpidot;
    var xhdot1;
    var z1;
    var z3;
    var z11;
    var z13;
    var z21;
    var z23;
    var z31;
    var z33;
    /* ------------------------ initialization --------------------- */
    // sgp4fix divisor for divide by zero check on inclination
    // the old check used 1.0 + Math.cos(pi-1.0e-9), but then compared it to
    // 1.5 e-12, so the threshold was changed to 1.5e-12 for consistency

    var temp4 = 1.5e-12; // ----------- set all near earth variables to zero ------------

    satrec.isimp = 0;
    satrec.method = 'n';
    satrec.aycof = 0.0;
    satrec.con41 = 0.0;
    satrec.cc1 = 0.0;
    satrec.cc4 = 0.0;
    satrec.cc5 = 0.0;
    satrec.d2 = 0.0;
    satrec.d3 = 0.0;
    satrec.d4 = 0.0;
    satrec.delmo = 0.0;
    satrec.eta = 0.0;
    satrec.argpdot = 0.0;
    satrec.omgcof = 0.0;
    satrec.sinmao = 0.0;
    satrec.t = 0.0;
    satrec.t2cof = 0.0;
    satrec.t3cof = 0.0;
    satrec.t4cof = 0.0;
    satrec.t5cof = 0.0;
    satrec.x1mth2 = 0.0;
    satrec.x7thm1 = 0.0;
    satrec.mdot = 0.0;
    satrec.nodedot = 0.0;
    satrec.xlcof = 0.0;
    satrec.xmcof = 0.0;
    satrec.nodecf = 0.0; // ----------- set all deep space variables to zero ------------

    satrec.irez = 0;
    satrec.d2201 = 0.0;
    satrec.d2211 = 0.0;
    satrec.d3210 = 0.0;
    satrec.d3222 = 0.0;
    satrec.d4410 = 0.0;
    satrec.d4422 = 0.0;
    satrec.d5220 = 0.0;
    satrec.d5232 = 0.0;
    satrec.d5421 = 0.0;
    satrec.d5433 = 0.0;
    satrec.dedt = 0.0;
    satrec.del1 = 0.0;
    satrec.del2 = 0.0;
    satrec.del3 = 0.0;
    satrec.didt = 0.0;
    satrec.dmdt = 0.0;
    satrec.dnodt = 0.0;
    satrec.domdt = 0.0;
    satrec.e3 = 0.0;
    satrec.ee2 = 0.0;
    satrec.peo = 0.0;
    satrec.pgho = 0.0;
    satrec.pho = 0.0;
    satrec.pinco = 0.0;
    satrec.plo = 0.0;
    satrec.se2 = 0.0;
    satrec.se3 = 0.0;
    satrec.sgh2 = 0.0;
    satrec.sgh3 = 0.0;
    satrec.sgh4 = 0.0;
    satrec.sh2 = 0.0;
    satrec.sh3 = 0.0;
    satrec.si2 = 0.0;
    satrec.si3 = 0.0;
    satrec.sl2 = 0.0;
    satrec.sl3 = 0.0;
    satrec.sl4 = 0.0;
    satrec.gsto = 0.0;
    satrec.xfact = 0.0;
    satrec.xgh2 = 0.0;
    satrec.xgh3 = 0.0;
    satrec.xgh4 = 0.0;
    satrec.xh2 = 0.0;
    satrec.xh3 = 0.0;
    satrec.xi2 = 0.0;
    satrec.xi3 = 0.0;
    satrec.xl2 = 0.0;
    satrec.xl3 = 0.0;
    satrec.xl4 = 0.0;
    satrec.xlamo = 0.0;
    satrec.zmol = 0.0;
    satrec.zmos = 0.0;
    satrec.atime = 0.0;
    satrec.xli = 0.0;
    satrec.xni = 0.0; // sgp4fix - note the following variables are also passed directly via satrec.
    // it is possible to streamline the sgp4init call by deleting the "x"
    // variables, but the user would need to set the satrec.* values first. we
    // include the additional assignments in case twoline2rv is not used.

    satrec.bstar = xbstar;
    satrec.ecco = xecco;
    satrec.argpo = xargpo;
    satrec.inclo = xinclo;
    satrec.mo = xmo;
    satrec.no = xno;
    satrec.nodeo = xnodeo; //  sgp4fix add opsmode

    satrec.operationmode = opsmode; // ------------------------ earth constants -----------------------
    // sgp4fix identify constants and allow alternate values

    var ss = 78.0 / earthRadius + 1.0; // sgp4fix use multiply for speed instead of pow

    var qzms2ttemp = (120.0 - 78.0) / earthRadius;
    var qzms2t = qzms2ttemp * qzms2ttemp * qzms2ttemp * qzms2ttemp;
    satrec.init = 'y';
    satrec.t = 0.0;
    var initlOptions = {
      satn: satn,
      ecco: satrec.ecco,
      epoch: epoch,
      inclo: satrec.inclo,
      no: satrec.no,
      method: satrec.method,
      opsmode: satrec.operationmode
    };
    var initlResult = initl(initlOptions);
    var ao = initlResult.ao,
        con42 = initlResult.con42,
        cosio = initlResult.cosio,
        cosio2 = initlResult.cosio2,
        eccsq = initlResult.eccsq,
        omeosq = initlResult.omeosq,
        posq = initlResult.posq,
        rp = initlResult.rp,
        rteosq = initlResult.rteosq,
        sinio = initlResult.sinio;
    satrec.no = initlResult.no;
    satrec.con41 = initlResult.con41;
    satrec.gsto = initlResult.gsto;
    satrec.error = 0; // sgp4fix remove this check as it is unnecessary
    // the mrt check in sgp4 handles decaying satellite cases even if the starting
    // condition is below the surface of te earth
    // if (rp < 1.0)
    // {
    //   printf("// *** satn%d epoch elts sub-orbital ***\n", satn);
    //   satrec.error = 5;
    // }

    if (omeosq >= 0.0 || satrec.no >= 0.0) {
      satrec.isimp = 0;

      if (rp < 220.0 / earthRadius + 1.0) {
        satrec.isimp = 1;
      }

      sfour = ss;
      qzms24 = qzms2t;
      perige = (rp - 1.0) * earthRadius; // - for perigees below 156 km, s and qoms2t are altered -

      if (perige < 156.0) {
        sfour = perige - 78.0;

        if (perige < 98.0) {
          sfour = 20.0;
        } // sgp4fix use multiply for speed instead of pow


        var qzms24temp = (120.0 - sfour) / earthRadius;
        qzms24 = qzms24temp * qzms24temp * qzms24temp * qzms24temp;
        sfour = sfour / earthRadius + 1.0;
      }

      pinvsq = 1.0 / posq;
      tsi = 1.0 / (ao - sfour);
      satrec.eta = ao * satrec.ecco * tsi;
      etasq = satrec.eta * satrec.eta;
      eeta = satrec.ecco * satrec.eta;
      psisq = Math.abs(1.0 - etasq);
      coef = qzms24 * Math.pow(tsi, 4.0);
      coef1 = coef / Math.pow(psisq, 3.5);
      cc2 = coef1 * satrec.no * (ao * (1.0 + 1.5 * etasq + eeta * (4.0 + etasq)) + 0.375 * j2 * tsi / psisq * satrec.con41 * (8.0 + 3.0 * etasq * (8.0 + etasq)));
      satrec.cc1 = satrec.bstar * cc2;
      cc3 = 0.0;

      if (satrec.ecco > 1.0e-4) {
        cc3 = -2.0 * coef * tsi * j3oj2 * satrec.no * sinio / satrec.ecco;
      }

      satrec.x1mth2 = 1.0 - cosio2;
      satrec.cc4 = 2.0 * satrec.no * coef1 * ao * omeosq * (satrec.eta * (2.0 + 0.5 * etasq) + satrec.ecco * (0.5 + 2.0 * etasq) - j2 * tsi / (ao * psisq) * (-3.0 * satrec.con41 * (1.0 - 2.0 * eeta + etasq * (1.5 - 0.5 * eeta)) + 0.75 * satrec.x1mth2 * (2.0 * etasq - eeta * (1.0 + etasq)) * Math.cos(2.0 * satrec.argpo)));
      satrec.cc5 = 2.0 * coef1 * ao * omeosq * (1.0 + 2.75 * (etasq + eeta) + eeta * etasq);
      cosio4 = cosio2 * cosio2;
      temp1 = 1.5 * j2 * pinvsq * satrec.no;
      temp2 = 0.5 * temp1 * j2 * pinvsq;
      temp3 = -0.46875 * j4 * pinvsq * pinvsq * satrec.no;
      satrec.mdot = satrec.no + 0.5 * temp1 * rteosq * satrec.con41 + 0.0625 * temp2 * rteosq * (13.0 - 78.0 * cosio2 + 137.0 * cosio4);
      satrec.argpdot = -0.5 * temp1 * con42 + 0.0625 * temp2 * (7.0 - 114.0 * cosio2 + 395.0 * cosio4) + temp3 * (3.0 - 36.0 * cosio2 + 49.0 * cosio4);
      xhdot1 = -temp1 * cosio;
      satrec.nodedot = xhdot1 + (0.5 * temp2 * (4.0 - 19.0 * cosio2) + 2.0 * temp3 * (3.0 - 7.0 * cosio2)) * cosio;
      xpidot = satrec.argpdot + satrec.nodedot;
      satrec.omgcof = satrec.bstar * cc3 * Math.cos(satrec.argpo);
      satrec.xmcof = 0.0;

      if (satrec.ecco > 1.0e-4) {
        satrec.xmcof = -x2o3 * coef * satrec.bstar / eeta;
      }

      satrec.nodecf = 3.5 * omeosq * xhdot1 * satrec.cc1;
      satrec.t2cof = 1.5 * satrec.cc1; // sgp4fix for divide by zero with xinco = 180 deg

      if (Math.abs(cosio + 1.0) > 1.5e-12) {
        satrec.xlcof = -0.25 * j3oj2 * sinio * (3.0 + 5.0 * cosio) / (1.0 + cosio);
      } else {
        satrec.xlcof = -0.25 * j3oj2 * sinio * (3.0 + 5.0 * cosio) / temp4;
      }

      satrec.aycof = -0.5 * j3oj2 * sinio; // sgp4fix use multiply for speed instead of pow

      var delmotemp = 1.0 + satrec.eta * Math.cos(satrec.mo);
      satrec.delmo = delmotemp * delmotemp * delmotemp;
      satrec.sinmao = Math.sin(satrec.mo);
      satrec.x7thm1 = 7.0 * cosio2 - 1.0; // --------------- deep space initialization -------------

      if (2 * pi / satrec.no >= 225.0) {
        satrec.method = 'd';
        satrec.isimp = 1;
        tc = 0.0;
        inclm = satrec.inclo;
        var dscomOptions = {
          epoch: epoch,
          ep: satrec.ecco,
          argpp: satrec.argpo,
          tc: tc,
          inclp: satrec.inclo,
          nodep: satrec.nodeo,
          np: satrec.no,
          e3: satrec.e3,
          ee2: satrec.ee2,
          peo: satrec.peo,
          pgho: satrec.pgho,
          pho: satrec.pho,
          pinco: satrec.pinco,
          plo: satrec.plo,
          se2: satrec.se2,
          se3: satrec.se3,
          sgh2: satrec.sgh2,
          sgh3: satrec.sgh3,
          sgh4: satrec.sgh4,
          sh2: satrec.sh2,
          sh3: satrec.sh3,
          si2: satrec.si2,
          si3: satrec.si3,
          sl2: satrec.sl2,
          sl3: satrec.sl3,
          sl4: satrec.sl4,
          xgh2: satrec.xgh2,
          xgh3: satrec.xgh3,
          xgh4: satrec.xgh4,
          xh2: satrec.xh2,
          xh3: satrec.xh3,
          xi2: satrec.xi2,
          xi3: satrec.xi3,
          xl2: satrec.xl2,
          xl3: satrec.xl3,
          xl4: satrec.xl4,
          zmol: satrec.zmol,
          zmos: satrec.zmos
        };
        var dscomResult = dscom(dscomOptions);
        satrec.e3 = dscomResult.e3;
        satrec.ee2 = dscomResult.ee2;
        satrec.peo = dscomResult.peo;
        satrec.pgho = dscomResult.pgho;
        satrec.pho = dscomResult.pho;
        satrec.pinco = dscomResult.pinco;
        satrec.plo = dscomResult.plo;
        satrec.se2 = dscomResult.se2;
        satrec.se3 = dscomResult.se3;
        satrec.sgh2 = dscomResult.sgh2;
        satrec.sgh3 = dscomResult.sgh3;
        satrec.sgh4 = dscomResult.sgh4;
        satrec.sh2 = dscomResult.sh2;
        satrec.sh3 = dscomResult.sh3;
        satrec.si2 = dscomResult.si2;
        satrec.si3 = dscomResult.si3;
        satrec.sl2 = dscomResult.sl2;
        satrec.sl3 = dscomResult.sl3;
        satrec.sl4 = dscomResult.sl4;
        sinim = dscomResult.sinim;
        cosim = dscomResult.cosim;
        em = dscomResult.em;
        emsq = dscomResult.emsq;
        s1 = dscomResult.s1;
        s2 = dscomResult.s2;
        s3 = dscomResult.s3;
        s4 = dscomResult.s4;
        s5 = dscomResult.s5;
        ss1 = dscomResult.ss1;
        ss2 = dscomResult.ss2;
        ss3 = dscomResult.ss3;
        ss4 = dscomResult.ss4;
        ss5 = dscomResult.ss5;
        sz1 = dscomResult.sz1;
        sz3 = dscomResult.sz3;
        sz11 = dscomResult.sz11;
        sz13 = dscomResult.sz13;
        sz21 = dscomResult.sz21;
        sz23 = dscomResult.sz23;
        sz31 = dscomResult.sz31;
        sz33 = dscomResult.sz33;
        satrec.xgh2 = dscomResult.xgh2;
        satrec.xgh3 = dscomResult.xgh3;
        satrec.xgh4 = dscomResult.xgh4;
        satrec.xh2 = dscomResult.xh2;
        satrec.xh3 = dscomResult.xh3;
        satrec.xi2 = dscomResult.xi2;
        satrec.xi3 = dscomResult.xi3;
        satrec.xl2 = dscomResult.xl2;
        satrec.xl3 = dscomResult.xl3;
        satrec.xl4 = dscomResult.xl4;
        satrec.zmol = dscomResult.zmol;
        satrec.zmos = dscomResult.zmos;
        nm = dscomResult.nm;
        z1 = dscomResult.z1;
        z3 = dscomResult.z3;
        z11 = dscomResult.z11;
        z13 = dscomResult.z13;
        z21 = dscomResult.z21;
        z23 = dscomResult.z23;
        z31 = dscomResult.z31;
        z33 = dscomResult.z33;
        var dpperOptions = {
          inclo: inclm,
          init: satrec.init,
          ep: satrec.ecco,
          inclp: satrec.inclo,
          nodep: satrec.nodeo,
          argpp: satrec.argpo,
          mp: satrec.mo,
          opsmode: satrec.operationmode
        };
        var dpperResult = dpper(satrec, dpperOptions);
        satrec.ecco = dpperResult.ep;
        satrec.inclo = dpperResult.inclp;
        satrec.nodeo = dpperResult.nodep;
        satrec.argpo = dpperResult.argpp;
        satrec.mo = dpperResult.mp;
        argpm = 0.0;
        nodem = 0.0;
        mm = 0.0;
        var dsinitOptions = {
          cosim: cosim,
          emsq: emsq,
          argpo: satrec.argpo,
          s1: s1,
          s2: s2,
          s3: s3,
          s4: s4,
          s5: s5,
          sinim: sinim,
          ss1: ss1,
          ss2: ss2,
          ss3: ss3,
          ss4: ss4,
          ss5: ss5,
          sz1: sz1,
          sz3: sz3,
          sz11: sz11,
          sz13: sz13,
          sz21: sz21,
          sz23: sz23,
          sz31: sz31,
          sz33: sz33,
          t: satrec.t,
          tc: tc,
          gsto: satrec.gsto,
          mo: satrec.mo,
          mdot: satrec.mdot,
          no: satrec.no,
          nodeo: satrec.nodeo,
          nodedot: satrec.nodedot,
          xpidot: xpidot,
          z1: z1,
          z3: z3,
          z11: z11,
          z13: z13,
          z21: z21,
          z23: z23,
          z31: z31,
          z33: z33,
          ecco: satrec.ecco,
          eccsq: eccsq,
          em: em,
          argpm: argpm,
          inclm: inclm,
          mm: mm,
          nm: nm,
          nodem: nodem,
          irez: satrec.irez,
          atime: satrec.atime,
          d2201: satrec.d2201,
          d2211: satrec.d2211,
          d3210: satrec.d3210,
          d3222: satrec.d3222,
          d4410: satrec.d4410,
          d4422: satrec.d4422,
          d5220: satrec.d5220,
          d5232: satrec.d5232,
          d5421: satrec.d5421,
          d5433: satrec.d5433,
          dedt: satrec.dedt,
          didt: satrec.didt,
          dmdt: satrec.dmdt,
          dnodt: satrec.dnodt,
          domdt: satrec.domdt,
          del1: satrec.del1,
          del2: satrec.del2,
          del3: satrec.del3,
          xfact: satrec.xfact,
          xlamo: satrec.xlamo,
          xli: satrec.xli,
          xni: satrec.xni
        };
        var dsinitResult = dsinit(dsinitOptions);
        satrec.irez = dsinitResult.irez;
        satrec.atime = dsinitResult.atime;
        satrec.d2201 = dsinitResult.d2201;
        satrec.d2211 = dsinitResult.d2211;
        satrec.d3210 = dsinitResult.d3210;
        satrec.d3222 = dsinitResult.d3222;
        satrec.d4410 = dsinitResult.d4410;
        satrec.d4422 = dsinitResult.d4422;
        satrec.d5220 = dsinitResult.d5220;
        satrec.d5232 = dsinitResult.d5232;
        satrec.d5421 = dsinitResult.d5421;
        satrec.d5433 = dsinitResult.d5433;
        satrec.dedt = dsinitResult.dedt;
        satrec.didt = dsinitResult.didt;
        satrec.dmdt = dsinitResult.dmdt;
        satrec.dnodt = dsinitResult.dnodt;
        satrec.domdt = dsinitResult.domdt;
        satrec.del1 = dsinitResult.del1;
        satrec.del2 = dsinitResult.del2;
        satrec.del3 = dsinitResult.del3;
        satrec.xfact = dsinitResult.xfact;
        satrec.xlamo = dsinitResult.xlamo;
        satrec.xli = dsinitResult.xli;
        satrec.xni = dsinitResult.xni;
      } // ----------- set variables if not deep space -----------


      if (satrec.isimp !== 1) {
        cc1sq = satrec.cc1 * satrec.cc1;
        satrec.d2 = 4.0 * ao * tsi * cc1sq;
        temp = satrec.d2 * tsi * satrec.cc1 / 3.0;
        satrec.d3 = (17.0 * ao + sfour) * temp;
        satrec.d4 = 0.5 * temp * ao * tsi * (221.0 * ao + 31.0 * sfour) * satrec.cc1;
        satrec.t3cof = satrec.d2 + 2.0 * cc1sq;
        satrec.t4cof = 0.25 * (3.0 * satrec.d3 + satrec.cc1 * (12.0 * satrec.d2 + 10.0 * cc1sq));
        satrec.t5cof = 0.2 * (3.0 * satrec.d4 + 12.0 * satrec.cc1 * satrec.d3 + 6.0 * satrec.d2 * satrec.d2 + 15.0 * cc1sq * (2.0 * satrec.d2 + cc1sq));
      }
      /* finally propogate to zero epoch to initialize all others. */
      // sgp4fix take out check to let satellites process until they are actually below earth surface
      // if(satrec.error == 0)

    }

    sgp4(satrec, 0);
    satrec.init = 'n';
    /* eslint-enable no-param-reassign */
  }

  /* -----------------------------------------------------------------------------
   *
   *                           function twoline2rv
   *
   *  this function converts the two line element set character string data to
   *    variables and initializes the sgp4 variables. several intermediate varaibles
   *    and quantities are determined. note that the result is a structure so multiple
   *    satellites can be processed simultaneously without having to reinitialize. the
   *    verification mode is an important option that permits quick checks of any
   *    changes to the underlying technical theory. this option works using a
   *    modified tle file in which the start, stop, and delta time values are
   *    included at the end of the second line of data. this only works with the
   *    verification mode. the catalog mode simply propagates from -1440 to 1440 min
   *    from epoch and is useful when performing entire catalog runs.
   *
   *  author        : david vallado                  719-573-2600    1 mar 2001
   *
   *  inputs        :
   *    longstr1    - first line of the tle
   *    longstr2    - second line of the tle
   *    typerun     - type of run                    verification 'v', catalog 'c',
   *                                                 manual 'm'
   *    typeinput   - type of manual input           mfe 'm', epoch 'e', dayofyr 'd'
   *    opsmode     - mode of operation afspc or improved 'a', 'i'
   *    whichconst  - which set of constants to use  72, 84
   *
   *  outputs       :
   *    satrec      - structure containing all the sgp4 satellite information
   *
   *  coupling      :
   *    getgravconst-
   *    days2mdhms  - conversion of days to month, day, hour, minute, second
   *    jday        - convert day month year hour minute second into julian date
   *    sgp4init    - initialize the sgp4 variables
   *
   *  references    :
   *    norad spacetrack report #3
   *    vallado, crawford, hujsak, kelso  2006
   --------------------------------------------------------------------------- */

  /**
   * Return a Satellite imported from two lines of TLE data.
   *
   * Provide the two TLE lines as strings `longstr1` and `longstr2`,
   * and select which standard set of gravitational constants you want
   * by providing `gravity_constants`:
   *
   * `sgp4.propagation.wgs72` - Standard WGS 72 model
   * `sgp4.propagation.wgs84` - More recent WGS 84 model
   * `sgp4.propagation.wgs72old` - Legacy support for old SGP4 behavior
   *
   * Normally, computations are made using letious recent improvements
   * to the algorithm.  If you want to turn some of these off and go
   * back into "afspc" mode, then set `afspc_mode` to `True`.
   */

  function twoline2satrec(longstr1, longstr2) {
    var opsmode = 'i';
    var xpdotp = 1440.0 / (2.0 * pi); // 229.1831180523293;

    var year = 0;
    var satrec = {};
    satrec.error = 0;
    satrec.satnum = longstr1.substring(2, 7);
    satrec.epochyr = parseInt(longstr1.substring(18, 20), 10);
    satrec.epochdays = parseFloat(longstr1.substring(20, 32));
    satrec.ndot = parseFloat(longstr1.substring(33, 43));
    satrec.nddot = parseFloat(".".concat(parseInt(longstr1.substring(44, 50), 10), "E").concat(longstr1.substring(50, 52)));
    satrec.bstar = parseFloat("".concat(longstr1.substring(53, 54), ".").concat(parseInt(longstr1.substring(54, 59), 10), "E").concat(longstr1.substring(59, 61))); // satrec.satnum = longstr2.substring(2, 7);

    satrec.inclo = parseFloat(longstr2.substring(8, 16));
    satrec.nodeo = parseFloat(longstr2.substring(17, 25));
    satrec.ecco = parseFloat(".".concat(longstr2.substring(26, 33)));
    satrec.argpo = parseFloat(longstr2.substring(34, 42));
    satrec.mo = parseFloat(longstr2.substring(43, 51));
    satrec.no = parseFloat(longstr2.substring(52, 63)); // ---- find no, ndot, nddot ----

    satrec.no /= xpdotp; //   rad/min
    // satrec.nddot= satrec.nddot * Math.pow(10.0, nexp);
    // satrec.bstar= satrec.bstar * Math.pow(10.0, ibexp);
    // ---- convert to sgp4 units ----

    satrec.a = Math.pow(satrec.no * tumin, -2.0 / 3.0);
    satrec.ndot /= xpdotp * 1440.0; // ? * minperday

    satrec.nddot /= xpdotp * 1440.0 * 1440; // ---- find standard orbital elements ----

    satrec.inclo *= deg2rad;
    satrec.nodeo *= deg2rad;
    satrec.argpo *= deg2rad;
    satrec.mo *= deg2rad;
    satrec.alta = satrec.a * (1.0 + satrec.ecco) - 1.0;
    satrec.altp = satrec.a * (1.0 - satrec.ecco) - 1.0; // ----------------------------------------------------------------
    // find sgp4epoch time of element set
    // remember that sgp4 uses units of days from 0 jan 1950 (sgp4epoch)
    // and minutes from the epoch (time)
    // ----------------------------------------------------------------
    // ---------------- temp fix for years from 1957-2056 -------------------
    // --------- correct fix will occur when year is 4-digit in tle ---------

    if (satrec.epochyr < 57) {
      year = satrec.epochyr + 2000;
    } else {
      year = satrec.epochyr + 1900;
    }

    var mdhmsResult = days2mdhms(year, satrec.epochdays);
    var mon = mdhmsResult.mon,
        day = mdhmsResult.day,
        hr = mdhmsResult.hr,
        minute = mdhmsResult.minute,
        sec = mdhmsResult.sec;
    satrec.jdsatepoch = jday(year, mon, day, hr, minute, sec); //  ---------------- initialize the orbit at sgp4epoch -------------------

    sgp4init(satrec, {
      opsmode: opsmode,
      satn: satrec.satnum,
      epoch: satrec.jdsatepoch - 2433281.5,
      xbstar: satrec.bstar,
      xecco: satrec.ecco,
      xargpo: satrec.argpo,
      xinclo: satrec.inclo,
      xmo: satrec.mo,
      xno: satrec.no,
      xnodeo: satrec.nodeo
    });
    return satrec;
  }

  function _toConsumableArray(arr) {
    return _arrayWithoutHoles(arr) || _iterableToArray(arr) || _unsupportedIterableToArray(arr) || _nonIterableSpread();
  }

  function _arrayWithoutHoles(arr) {
    if (Array.isArray(arr)) return _arrayLikeToArray(arr);
  }

  function _iterableToArray(iter) {
    if (typeof Symbol !== "undefined" && Symbol.iterator in Object(iter)) return Array.from(iter);
  }

  function _unsupportedIterableToArray(o, minLen) {
    if (!o) return;
    if (typeof o === "string") return _arrayLikeToArray(o, minLen);
    var n = Object.prototype.toString.call(o).slice(8, -1);
    if (n === "Object" && o.constructor) n = o.constructor.name;
    if (n === "Map" || n === "Set") return Array.from(o);
    if (n === "Arguments" || /^(?:Ui|I)nt(?:8|16|32)(?:Clamped)?Array$/.test(n)) return _arrayLikeToArray(o, minLen);
  }

  function _arrayLikeToArray(arr, len) {
    if (len == null || len > arr.length) len = arr.length;

    for (var i = 0, arr2 = new Array(len); i < len; i++) arr2[i] = arr[i];

    return arr2;
  }

  function _nonIterableSpread() {
    throw new TypeError("Invalid attempt to spread non-iterable instance.\nIn order to be iterable, non-array objects must have a [Symbol.iterator]() method.");
  }

  function propagate() {
    for (var _len = arguments.length, args = new Array(_len), _key = 0; _key < _len; _key++) {
      args[_key] = arguments[_key];
    }

    // Return a position and velocity vector for a given date and time.
    var satrec = args[0];
    var date = Array.prototype.slice.call(args, 1);
    var j = jday.apply(void 0, _toConsumableArray(date));
    var m = (j - satrec.jdsatepoch) * minutesPerDay;
    return sgp4(satrec, m);
  }

  function dopplerFactor(location, position, velocity) {
    var currentRange = Math.sqrt(Math.pow(position.x - location.x, 2) + Math.pow(position.y - location.y, 2) + Math.pow(position.z - location.z, 2));
    var nextPos = {
      x: position.x + velocity.x,
      y: position.y + velocity.y,
      z: position.z + velocity.z
    };
    var nextRange = Math.sqrt(Math.pow(nextPos.x - location.x, 2) + Math.pow(nextPos.y - location.y, 2) + Math.pow(nextPos.z - location.z, 2));
    var rangeRate = nextRange - currentRange;

    function sign(value) {
      return value >= 0 ? 1 : -1;
    }

    rangeRate *= sign(rangeRate);
    var c = 299792.458; // Speed of light in km/s

    return 1 + rangeRate / c;
  }

  function radiansToDegrees(radians) {
    return radians * rad2deg;
  }
  function degreesToRadians(degrees) {
    return degrees * deg2rad;
  }
  function degreesLat(radians) {
    if (radians < -pi / 2 || radians > pi / 2) {
      throw new RangeError('Latitude radians must be in range [-pi/2; pi/2].');
    }

    return radiansToDegrees(radians);
  }
  function degreesLong(radians) {
    if (radians < -pi || radians > pi) {
      throw new RangeError('Longitude radians must be in range [-pi; pi].');
    }

    return radiansToDegrees(radians);
  }
  function radiansLat(degrees) {
    if (degrees < -90 || degrees > 90) {
      throw new RangeError('Latitude degrees must be in range [-90; 90].');
    }

    return degreesToRadians(degrees);
  }
  function radiansLong(degrees) {
    if (degrees < -180 || degrees > 180) {
      throw new RangeError('Longitude degrees must be in range [-180; 180].');
    }

    return degreesToRadians(degrees);
  }
  function geodeticToEcf(geodetic) {
    var longitude = geodetic.longitude,
        latitude = geodetic.latitude,
        height = geodetic.height;
    var a = 6378.137;
    var b = 6356.7523142;
    var f = (a - b) / a;
    var e2 = 2 * f - f * f;
    var normal = a / Math.sqrt(1 - e2 * (Math.sin(latitude) * Math.sin(latitude)));
    var x = (normal + height) * Math.cos(latitude) * Math.cos(longitude);
    var y = (normal + height) * Math.cos(latitude) * Math.sin(longitude);
    var z = (normal * (1 - e2) + height) * Math.sin(latitude);
    return {
      x: x,
      y: y,
      z: z
    };
  }
  function eciToGeodetic(eci, gmst) {
    // http://www.celestrak.com/columns/v02n03/
    var a = 6378.137;
    var b = 6356.7523142;
    var R = Math.sqrt(eci.x * eci.x + eci.y * eci.y);
    var f = (a - b) / a;
    var e2 = 2 * f - f * f;
    var longitude = Math.atan2(eci.y, eci.x) - gmst;

    while (longitude < -pi) {
      longitude += twoPi;
    }

    while (longitude > pi) {
      longitude -= twoPi;
    }

    var kmax = 20;
    var k = 0;
    var latitude = Math.atan2(eci.z, Math.sqrt(eci.x * eci.x + eci.y * eci.y));
    var C;

    while (k < kmax) {
      C = 1 / Math.sqrt(1 - e2 * (Math.sin(latitude) * Math.sin(latitude)));
      latitude = Math.atan2(eci.z + a * C * e2 * Math.sin(latitude), R);
      k += 1;
    }

    var height = R / Math.cos(latitude) - a * C;
    return {
      longitude: longitude,
      latitude: latitude,
      height: height
    };
  }
  function ecfToEci(ecf, gmst) {
    // ccar.colorado.edu/ASEN5070/handouts/coordsys.doc
    //
    // [X]     [C -S  0][X]
    // [Y]  =  [S  C  0][Y]
    // [Z]eci  [0  0  1][Z]ecf
    //
    var X = ecf.x * Math.cos(gmst) - ecf.y * Math.sin(gmst);
    var Y = ecf.x * Math.sin(gmst) + ecf.y * Math.cos(gmst);
    var Z = ecf.z;
    return {
      x: X,
      y: Y,
      z: Z
    };
  }
  function eciToEcf(eci, gmst) {
    // ccar.colorado.edu/ASEN5070/handouts/coordsys.doc
    //
    // [X]     [C -S  0][X]
    // [Y]  =  [S  C  0][Y]
    // [Z]eci  [0  0  1][Z]ecf
    //
    //
    // Inverse:
    // [X]     [C  S  0][X]
    // [Y]  =  [-S C  0][Y]
    // [Z]ecf  [0  0  1][Z]eci
    var x = eci.x * Math.cos(gmst) + eci.y * Math.sin(gmst);
    var y = eci.x * -Math.sin(gmst) + eci.y * Math.cos(gmst);
    var z = eci.z;
    return {
      x: x,
      y: y,
      z: z
    };
  }

  function topocentric(observerGeodetic, satelliteEcf) {
    // http://www.celestrak.com/columns/v02n02/
    // TS Kelso's method, except I'm using ECF frame
    // and he uses ECI.
    var longitude = observerGeodetic.longitude,
        latitude = observerGeodetic.latitude;
    var observerEcf = geodeticToEcf(observerGeodetic);
    var rx = satelliteEcf.x - observerEcf.x;
    var ry = satelliteEcf.y - observerEcf.y;
    var rz = satelliteEcf.z - observerEcf.z;
    var topS = Math.sin(latitude) * Math.cos(longitude) * rx + Math.sin(latitude) * Math.sin(longitude) * ry - Math.cos(latitude) * rz;
    var topE = -Math.sin(longitude) * rx + Math.cos(longitude) * ry;
    var topZ = Math.cos(latitude) * Math.cos(longitude) * rx + Math.cos(latitude) * Math.sin(longitude) * ry + Math.sin(latitude) * rz;
    return {
      topS: topS,
      topE: topE,
      topZ: topZ
    };
  }
  /**
   * @param {Object} tc
   * @param {Number} tc.topS Positive horizontal vector S due south.
   * @param {Number} tc.topE Positive horizontal vector E due east.
   * @param {Number} tc.topZ Vector Z normal to the surface of the earth (up).
   * @returns {Object}
   */


  function topocentricToLookAngles(tc) {
    var topS = tc.topS,
        topE = tc.topE,
        topZ = tc.topZ;
    var rangeSat = Math.sqrt(topS * topS + topE * topE + topZ * topZ);
    var El = Math.asin(topZ / rangeSat);
    var Az = Math.atan2(-topE, topS) + pi;
    return {
      azimuth: Az,
      elevation: El,
      rangeSat: rangeSat // Range in km

    };
  }

  function ecfToLookAngles(observerGeodetic, satelliteEcf) {
    var topocentricCoords = topocentric(observerGeodetic, satelliteEcf);
    return topocentricToLookAngles(topocentricCoords);
  }

  var indexUmd = {
    constants: constants,
    // Propagation
    propagate: propagate,
    sgp4: sgp4,
    twoline2satrec: twoline2satrec,
    gstime: gstime,
    jday: jday,
    invjday: invjday,
    dopplerFactor: dopplerFactor,
    // Coordinate transforms
    radiansToDegrees: radiansToDegrees,
    degreesToRadians: degreesToRadians,
    degreesLat: degreesLat,
    degreesLong: degreesLong,
    radiansLat: radiansLat,
    radiansLong: radiansLong,
    geodeticToEcf: geodeticToEcf,
    eciToGeodetic: eciToGeodetic,
    eciToEcf: eciToEcf,
    ecfToEci: ecfToEci,
    ecfToLookAngles: ecfToLookAngles
  };

  return indexUmd;

})));