Celestial Programming : Illuminated Fraction of the Moon

    /*
    Greg Miller gmiller@gregmiller.net 2021
    http://www.celestialprogramming.com/
    Released as public domain
    */
    
    function JulianDateFromUnixTime(t){
        //Not valid for dates before Oct 15, 1582
        return (t / 86400000) + 2440587.5;
    }
    
    function UnixTimeFromJulianDate(jd){
        //Not valid for dates before Oct 15, 1582
        return (jd-2440587.5)*86400000;
    }	
    
    function constrain(d){
        let t=d%360;
        if(t<0){t+=360;}
        return t;
    }
    
      function getIlluminatedFractionOfMoon(jd){
        const toRad=Math.PI/180.0;
        const T=(jd-2451545)/36525.0;
    
        const D = constrain(297.8501921 + 445267.1114034*T - 0.0018819*T*T + 1.0/545868.0*T*T*T - 1.0/113065000.0*T*T*T*T)*toRad; //47.2
        const M = constrain(357.5291092 + 35999.0502909*T - 0.0001536*T*T + 1.0/24490000.0*T*T*T)*toRad; //47.3
        const Mp = constrain(134.9633964 + 477198.8675055*T + 0.0087414*T*T + 1.0/69699.0*T*T*T - 1.0/14712000.0*T*T*T*T)*toRad; //47.4
    
        //48.4
        const i=constrain(180 - D*180/Math.PI - 6.289 * Math.sin(Mp) + 2.1 * Math.sin(M) -1.274 * Math.sin(2*D - Mp) -0.658 * Math.sin(2*D) -0.214 * Math.sin(2*Mp) -0.11 * Math.sin(D))*toRad;
    
        const k=(1+Math.cos(i))/2;
        return k;
    }