Planet Position Calculator in JavaScript
Keplerian Elements for Approximate Positions of the Major Planets Based on the paper written by E. M. Standish, Solar System Dynamics Group JPL/Caltech
https://ssd.jpl.nasa.gov/?planet_pos
Code is also available for download on GitHub
/*
* Keplerian Elements for Approximate Positions of the Major Planets
* Based on the paper written by E. M. Standish, Solar System Dynamics Group JPL/Caltech
* https://ssd.jpl.nasa.gov/?planet_pos
*
* Programmed by Daniel Brooke Peig (www.danbp.org), 02/06/2019
*/
function computeEclipticCoordinates(keplerianElementsTable, planetIndex, UNIXMilliTime){
let deg2rad = Math.PI/180;
let Teph = UNIXMilliTime/1000/86400 + 2440587.5; //Julian Ephemeris Date
let T = (Teph-2451545)/36525; //Centuries past J2000.0
//Calculations of the Keplerian elements
let a0 = keplerianElementsTable[planetIndex][1]; //semi-major axis (initial)
let at = keplerianElementsTable[planetIndex][7]; //semi-major axis (century variation)
let a = a0+at*T; //semi-major axis
let e0 = keplerianElementsTable[planetIndex][2]; //eccentricity (initial)
let et = keplerianElementsTable[planetIndex][8]; //eccentricity (century variation)
let e = e0+et*T; //eccentricity
let I0 = keplerianElementsTable[planetIndex][3]; //inclination (initial)
let It = keplerianElementsTable[planetIndex][9]; //inclination (century variation)
let I = I0 + It*T; //inclination
let L0 = keplerianElementsTable[planetIndex][4]; //mean longitude (initial)
let Lt = keplerianElementsTable[planetIndex][10]; //mean longitude (century variation)
let L = L0+Lt*T; //mean longitude
let W0 = keplerianElementsTable[planetIndex][5]; //longitude of perihelion (initial)
let Wt = keplerianElementsTable[planetIndex][11]; //longitude of perihelion (century variation)
let W = W0+Wt*T; //longitude of perihelion
let O0 = keplerianElementsTable[planetIndex][6]; //longitude of ascending node (initial)
let Ot = keplerianElementsTable[planetIndex][12]; //longitude of ascending node (century variation)
let O = O0+Ot*T; //longitude of ascending node
//Auxiliary parameters for the 3000 BC - 3000 AD period
let b = keplerianElementsTable[planetIndex][13];
let c = keplerianElementsTable[planetIndex][14];
let s = keplerianElementsTable[planetIndex][15];
let f = keplerianElementsTable[planetIndex][16];
//Argument of perihelion w
let w = W-O;
//Mean anomaly M
let M = L-W+b*Math.pow(T,2)+c*Math.cos(deg2rad*f*T)+s*Math.sin(deg2rad*f*T);
if(M < -180 || M > 180) M = M % 180; //Modulus M to be between -180 and 180
//Solve the Kepler Equation for the eccentric anomaly E
let E = solveKeplerEquation(M,e);
//Heliocentric coordinates
let x1 = a*(Math.cos(deg2rad*E)-e);
let y1 = a*Math.sqrt(1-(e*e))*Math.sin(deg2rad*E);
let z1 = 0;
//Auxiliary trigonometric calculations
let cosw = Math.cos(deg2rad*w);
let sinw = Math.sin(deg2rad*w);
let cosO = Math.cos(deg2rad*O);
let sinO = Math.sin(deg2rad*O);
let cosI = Math.cos(deg2rad*I);
let sinI = Math.sin(deg2rad*I);
//J2000 Ecliptic Plane Coordinates
let Xecl = (cosw*cosO - sinw*sinO*cosI)*x1 + (-sinw*cosO - cosw*sinO*cosI)*y1;
let Yecl = (cosw*sinO + sinw*cosO*cosI)*x1 + (-sinw*sinO + cosw*cosO*cosI)*y1;
let Zecl = (sinw*sinI)*x1 + (cosw*sinI)*y1;
//Result array
let EclipticCoordinates = [Xecl, Yecl, Zecl];
return EclipticCoordinates;
}
function convertToICRF(EclipticCoordinates){
let deg2rad = Math.PI/180;
let E = 23.43928;
let cosE = Math.cos(deg2rad*E);
let sinE = Math.sin(deg2rad*E);
let Xeq = EclipticCoordinates[0];
let Yeq = cosE*EclipticCoordinates[1]-sinE*EclipticCoordinates[2];
let Zeq = sinE*EclipticCoordinates[1]+cosE*EclipticCoordinates[2];
//Result array
let ICRFCoordinates = [Xeq, Yeq, Zeq];
return ICRFCoordinates;
}
function solveKeplerEquation(M,e) {
let e1 = 180/Math.PI*e;
let deg2rad = Math.PI/180;
let E0 = M+e1*Math.sin(M*deg2rad);
let tolerance = 10e-6;
let dE;
let dM;
let E1 = E0;
let E2 = 0;
let difE1E2 = 1;
for (let i=0; (i<1000) && (difE1E2 > tolerance); i++){
dM = M - (E1 - e1*Math.sin(deg2rad*E1));
dE = dM/(1-e*Math.cos(deg2rad*E1));
E2=E1+dE;
difE1E2 = Math.abs(E1-E2);
}
return E2;
}
//Keplerian elements and their rates, with respect to the mean ecliptic
//and equinox of J2000, valid for the time-interval 1800 AD - 2050 AD.
//
// a0 e0 I0 L0 W0 O0 at et It Lt Wt Ot b c s f
//--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
let keplerianElements2050 = [
["Mercury", 0.38709927, 0.20563593, 7.00497902, 252.25032350, 77.45779628, 48.33076593, 0.00000037 , 0.00001906 , -0.00594749, 149472.67411175, 0.16047689, -0.12534081, 0, 0, 0, 0],
["Venus", 0.72333566, 0.00677672, 3.39467605, 181.97909950, 131.60246718, 76.67984255, 0.00000390 , -0.00004107, -0.00078890, 58517.81538729 , 0.00268329, -0.27769418, 0, 0, 0, 0],
["EM Bary", 1.00000261, 0.01671123, -0.00001531, 100.46457166, 102.93768193, 0.0 , 0.00000562 , -0.00004392, -0.01294668, 35999.37244981 , 0.32327364, 0.0 , 0, 0, 0, 0],
["Mars", 1.52371034, 0.09339410, 1.84969142, -4.55343205, -23.94362959, 49.55953891, -0.00011607, -0.00013253 , -0.00183714, 3034.74612775 , 0.21252668, 0.20469106 , 0, 0, 0, 0],
["Jupiter", 5.20288700, 0.04838624, 1.30439695, 34.39644051, 14.72847983, 100.47390909, -0.00011607, -0.00013253 , -0.00183714, 3034.74612775 , 0.21252668, 0.20469106 , 0, 0, 0, 0],
["Saturn", 9.53667594, 0.05386179, 2.48599187, 49.95424423, 92.59887831, 113.66242448, -0.00125060, -0.00050991 , 0.00193609, 1222.49362201 , -0.41897216, -0.28867794, 0, 0, 0, 0],
["Uranus", 19.18916464, 0.04725744, 0.77263783, 313.23810451, 170.95427630, 74.01692503, -0.00196176, -0.00004397 , -0.00242939, 428.48202785 , 0.40805281, 0.04240589, 0, 0, 0, 0],
["Neptune", 30.06992276, 0.00859048, 1.77004347, -55.12002969, 44.96476227, 131.78422574, 0.00026291, 0.00005105 , 0.00035372, 218.45945325 , -0.32241464, -0.00508664, 0, 0, 0, 0],
["Pluto", 39.48211675, 0.24882730, 17.14001206, 238.92903833, 224.06891629, 110.30393684, -0.00031596, 0.00005170 , 0.00004818, 145.20780515 , -0.04062942, -0.01183482, 0, 0, 0, 0]
];
//Keplerian elements and their rates, with respect to the mean ecliptic and equinox of J2000,
//valid for the time-interval 3000 BC -- 3000 AD.
//
//
// a0 e0 I0 L0 W0 O0 at et It Lt Wt Ot b c s f
//---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
let keplerianElements3000 = [
["Mercury", 0.38709843, 0.20563661, 7.00559432, 252.25166724, 77.45771895, 48.33961819, 0.00000000, 0.00002123, -0.00590158, 149472.67486623, 0.15940013, -0.12214182, 0, 0, 0, 0],
["Venus", 0.72332102, 0.00676399, 3.39777545, 181.97970850, 131.76755713, 76.67261496, -0.00000026, -0.00005107, 0.00043494, 58517.81560260, 0.05679648, -0.27274174, 0, 0, 0, 0],
["EM Bary", 1.00000018, 0.01673163, -0.00054346, 100.46691572, 102.93005885, -5.11260389, -0.00000003, -0.00003661, -0.01337178, 35999.37306329, 0.31795260, -0.24123856, 0, 0, 0, 0],
["Mars", 1.52371243, 0.09336511, 1.85181869, -4.56813164, -23.91744784, 49.71320984, 0.00000097, 0.00009149, -0.00724757, 19140.29934243, 0.45223625, -0.26852431, 0, 0, 0, 0],
["Jupiter", 5.20248019, 0.04853590, 1.29861416, 34.33479152, 14.27495244, 100.29282654, -0.00002864, 0.00018026, -0.00322699, 3034.90371757, 0.18199196, 0.13024619, -0.00012452, 0.06064060, -0.35635438, 38.35125000],
["Saturn", 9.54149883, 0.05550825, 2.49424102, 50.07571329, 92.86136063, 113.63998702, -0.00003065, -0.00032044, 0.00451969, 1222.11494724, 0.54179478, -0.25015002, 0.00025899, -0.13434469, 0.87320147, 38.35125000],
["Uranus", 19.18797948, 0.04685740, 0.77298127, 314.20276625, 172.43404441, 73.96250215, -0.00020455, -0.00001550, -0.00180155, 428.49512595, 0.09266985, 0.05739699, 0.00058331, -0.97731848, 0.17689245, 7.67025000],
["Neptune", 30.06952752, 0.00895439, 1.77005520, 304.22289287, 46.68158724, 131.78635853, 0.00006447, 0.00000818, 0.00022400, 218.46515314, 0.01009938, -0.00606302, -0.00041348, 0.68346318, -0.10162547, 7.67025000],
["Pluto", 39.48686035, 0.24885238, 17.14104260, 238.96535011, 224.09702598, 110.30167986, 0.00449751, 0.00006016, 0.00000501, 145.18042903, -0.00968827, -0.00809981, -0.01262724, 0, 0, 0]
];
