keplerjs/Core/keplerslv.js

Kepler solver to compute a celestial body position over the surface of the earth.

/**
 * Astrodynamics | Kepler Solver
 * Author: Edgar Gago Carrillo
 * Date 16/03/2021
 * 
 * Inputs:
 * obtj: {} object containing the celstial body main parameteres
 
 * Outputs:
 * JD: Julian Day
 * 
 * Description:
 * Euler iterative method to solve the kepler's equation
 * 
 */
const { deg2rad } = require("./deg2rad")

exports.keplerslv = (obt) => {

    // Inits
    const M = deg2rad(obt.ma); // Mean anomaly
    const e = obt.e; // eccensitricty

    const delta = 10e-7; // Error
    let t = 1;       // While initialization
    let i = 1;       // Variable to count the numer of iterations
    let E = M;       // Initialization
    const max = 50;   // Maximum iterations


    while (Math.abs(t) > delta) {

        let F = E - e * Math.sin(E) - M; // function to solve F(M) = E - e*sin(E) - M = 0
        let dF = 1.0 - e * Math.cos(E); // derivative of F(M)

        if (Math.abs(dF) < delta) {

            break;

        } else {

            t = F / dF;
            E = E - t;
            i = i + 1;

            if (i > max) {
                console.log(`no convergence after ${max} iterations`);
                break;
            }

        }
    }

    return E;
}