virtualsky-planets.js

/*!
 * Virtual Sky add on to display planets without 
 * needing a file regularly updated from JPL Horizons
 * Written by Stuart Lowe (http://www.strudel.org.uk/)
 */

(function ($) {

	// An init function for the plugin
	function init(){
		// Attach a callback to the loadedPlanets event to calculate and draw the planets
		this.bind("loadedPlanets",function(d){
			this.jd = this.times.JD;
			var p = new Planets();
			var days = 365.25;
			this.planets = p.build(Math.floor(this.jd)-days*0.25,days*1.25);
			var loadtime = this.times.JD;
			var i = this.calendarevents.length;
			this.calendarevents.push(function(){
				if(Math.abs(loadtime-this.times.JD) >= days*0.25){
					this.calendarevents.splice(i,1);	// Remove this one-time event
					this.trigger('loadedPlanets');
					this.draw();
				}
			})
			this.draw();
		});
	}

	// Create an object to deal with planet ephemerides
	function Planets(){
		// Heliocentric Osculating Orbital Elements Referred to the Mean Equinox and Ecliptic of Date for 2013: http://asa.usno.navy.mil/static/files/2013/Osculating_Elements_2013.txt
		// Values of the Osculating Orbital Elements for 8th August 1997: http://www.stargazing.net/kepler/ellipse.html
		this.planets = [{
			"name": "Me",
			"radius":2439.7,	// km
			"interval": 0.5,
			"colour": "rgb(170,150,170)",
			"magnitude": function(d){ return -0.36 + 5*log10(d.r*d.R) + 0.027 * d.FV + 2.2E-13 * Math.pow(d.FV,6); },
			"elements": [
				{"jd":2456280.5,"i":7.0053,"o":48.485,"p":77.658,"a":0.387100,"n":4.09232,"e":0.205636,"L":191.7001},
				{"jd":2456320.5,"i":7.0052,"o":48.486,"p":77.661,"a":0.387097,"n":4.09236,"e":0.205644,"L":355.3943},
				{"jd":2456360.5,"i":7.0052,"o":48.487,"p":77.663,"a":0.387098,"n":4.09235,"e":0.205646,"L":159.0899},
				{"jd":2456400.5,"i":7.0052,"o":48.489,"p":77.665,"a":0.387097,"n":4.09236,"e":0.205649,"L":322.7854},
				{"jd":2456440.5,"i":7.0052,"o":48.490,"p":77.665,"a":0.387097,"n":4.09236,"e":0.205650,"L":126.4812},
				{"jd":2456480.5,"i":7.0052,"o":48.492,"p":77.667,"a":0.387098,"n":4.09235,"e":0.205645,"L":290.1771},
				{"jd":2456520.5,"i":7.0052,"o":48.493,"p":77.669,"a":0.387098,"n":4.09235,"e":0.205645,"L":93.8725},
				{"jd":2456560.5,"i":7.0052,"o":48.494,"p":77.671,"a":0.387098,"n":4.09235,"e":0.205642,"L":257.5683},
				{"jd":2456600.5,"i":7.0052,"o":48.495,"p":77.672,"a":0.387099,"n":4.09234,"e":0.205635,"L":61.2628},
				{"jd":2456640.5,"i":7.0052,"o":48.497,"p":77.674,"a":0.387099,"n":4.09233,"e":0.205635,"L":224.9579},
				{"jd":2456680.5,"i":7.0052,"o":48.498,"p":77.677,"a":0.387098,"n":4.09234,"e":0.205633,"L":28.6524}
			]
		},{
			"name": "V",
			"radius": 6051.9,	// km
			"interval": 1,
			"colour": "rgb(245,222,179)",
			"magnitude": function(d){ return -4.34 + 5*log10(d.a*d.R) + 0.013 * d.FV + 4.2E-7*Math.pow(d.FV,3); },
			"elements": [
				{"jd":2456280.5,"i":3.3949,"o":76.797,"p":132.00,"a":0.723328,"n":1.60214,"e":0.006777,"L":209.0515},
				{"jd":2456320.5,"i":3.3949,"o":76.798,"p":132.05,"a":0.723332,"n":1.60213,"e":0.006780,"L":273.1380},
				{"jd":2456360.5,"i":3.3949,"o":76.799,"p":132.07,"a":0.723327,"n":1.60215,"e":0.006787,"L":337.2248},
				{"jd":2456400.5,"i":3.3949,"o":76.801,"p":132.03,"a":0.723331,"n":1.60214,"e":0.006785,"L":41.3121},
				{"jd":2456440.5,"i":3.3949,"o":76.802,"p":131.97,"a":0.723333,"n":1.60213,"e":0.006780,"L":105.3980},
				{"jd":2456480.5,"i":3.3949,"o":76.803,"p":131.96,"a":0.723325,"n":1.60216,"e":0.006769,"L":169.4851},
				{"jd":2456520.5,"i":3.3949,"o":76.804,"p":131.99,"a":0.723327,"n":1.60215,"e":0.006769,"L":233.5729},
				{"jd":2456560.5,"i":3.3949,"o":76.806,"p":132.03,"a":0.723328,"n":1.60214,"e":0.006770,"L":297.6598},
				{"jd":2456600.5,"i":3.3949,"o":76.807,"p":132.03,"a":0.723326,"n":1.60215,"e":0.006775,"L":1.7475},
				{"jd":2456640.5,"i":3.3949,"o":76.808,"p":131.89,"a":0.723337,"n":1.60211,"e":0.006775,"L":65.8345},
				{"jd":2456680.5,"i":3.3948,"o":76.808,"p":131.63,"a":0.723345,"n":1.60209,"e":0.006770,"L":129.9169}
			]
		},{
			"name":"E",
			"elements" : [
				{"jd":2450680.5,"i":0.00041,"o":349.2,"p":102.8517,"a":1.0000200,"n":0.9855796,"e":0.0166967,"L":328.40353},
				{"jd":2456280.5,"i":0.0,"o":349.2,"p":103.042,"a":1.000008,"n":0.985598,"e":0.016703,"L":87.9950},
				{"jd":2456320.5,"i":0.0,"o":349.2,"p":103.005,"a":0.999986,"n":0.985631,"e":0.016682,"L":127.4201},
				{"jd":2456360.5,"i":0.0,"o":349.2,"p":102.990,"a":0.999978,"n":0.985642,"e":0.016675,"L":166.8472},
				{"jd":2456400.5,"i":0.0,"o":349.2,"p":103.022,"a":0.999987,"n":0.985630,"e":0.016677,"L":206.2740},
				{"jd":2456440.5,"i":0.0,"o":349.2,"p":103.077,"a":1.000000,"n":0.985611,"e":0.016677,"L":245.6993},
				{"jd":2456480.5,"i":0.0,"o":349.2,"p":103.119,"a":1.000005,"n":0.985603,"e":0.016675,"L":285.1238},
				{"jd":2456520.5,"i":0.0,"o":349.2,"p":103.147,"a":1.000000,"n":0.985611,"e":0.016679,"L":324.5489},
				{"jd":2456560.5,"i":0.0,"o":349.2,"p":103.161,"a":0.999995,"n":0.985618,"e":0.016682,"L":3.9752},
				{"jd":2456600.5,"i":0.0,"o":349.2,"p":103.146,"a":1.000002,"n":0.985608,"e":0.016690,"L":43.4020},
				{"jd":2456640.5,"i":0.0,"o":349.2,"p":103.135,"a":1.000010,"n":0.985596,"e":0.016698,"L":82.8279},
				{"jd":2456680.5,"i":0.0,"o":349.2,"p":103.166,"a":1.000005,"n":0.985603,"e":0.016693,"L":122.2544}
			]
		},{
			"name":"Ma",
			"radius": 3386,	// km
			"interval": 1,
			"colour": "rgb(255,50,50)",
			"magnitude": function(d){ return -1.51 + 5*log10(d.r*d.R) + 0.016 * d.FV; },
			"elements":[
				{"jd":2450680.5,"i":1.84992,"o":49.5664,"p":336.0882,"a":1.5236365,"n":0.5240613,"e":0.0934231,"L":262.42784},
				{"jd":2456280.5,"i":1.8497,"o":49.663,"p":336.246,"a":1.523624,"n":0.524069,"e":0.093285,"L":317.1847},
				{"jd":2456320.5,"i":1.8497,"o":49.664,"p":336.249,"a":1.523605,"n":0.524079,"e":0.093274,"L":338.1493},
				{"jd":2456360.5,"i":1.8497,"o":49.665,"p":336.255,"a":1.523601,"n":0.524081,"e":0.093269,"L":359.1150},
				{"jd":2456400.5,"i":1.8497,"o":49.666,"p":336.268,"a":1.523627,"n":0.524068,"e":0.093276,"L":20.0806},
				{"jd":2456440.5,"i":1.8497,"o":49.667,"p":336.287,"a":1.523678,"n":0.524041,"e":0.093292,"L":41.0443},
				{"jd":2456480.5,"i":1.8496,"o":49.668,"p":336.306,"a":1.523731,"n":0.524014,"e":0.093316,"L":62.0048},
				{"jd":2456520.5,"i":1.8496,"o":49.668,"p":336.322,"a":1.523762,"n":0.523998,"e":0.093346,"L":82.9625},
				{"jd":2456560.5,"i":1.8495,"o":49.666,"p":336.329,"a":1.523748,"n":0.524005,"e":0.093385,"L":103.9196},
				{"jd":2456600.5,"i":1.8495,"o":49.665,"p":336.333,"a":1.523709,"n":0.524025,"e":0.093425,"L":124.8784},
				{"jd":2456640.5,"i":1.8495,"o":49.665,"p":336.333,"a":1.523665,"n":0.524048,"e":0.093458,"L":145.8405},
				{"jd":2456680.5,"i":1.8495,"o":49.665,"p":336.330,"a":1.523631,"n":0.524066,"e":0.093482,"L":166.8051}
			]
		},{
			"name":"J",
			"radius": 69173,	// km
			"interval": 10,
			"colour": "rgb(255,150,150)",
			"magnitude": function(d){ return -9.25 + 5*log10(d.r*d.R) + 0.014 * d.FV; },
			"elements":[
				{"jd":2456280.5,"i":1.3033,"o":100.624,"p":14.604,"a":5.20269,"n":0.083094,"e":0.048895,"L":68.0222},
				{"jd":2456320.5,"i":1.3033,"o":100.624,"p":14.591,"a":5.20263,"n":0.083095,"e":0.048893,"L":71.3469},
				{"jd":2456360.5,"i":1.3033,"o":100.625,"p":14.588,"a":5.20262,"n":0.083095,"e":0.048895,"L":74.6719},
				{"jd":2456400.5,"i":1.3033,"o":100.626,"p":14.589,"a":5.20262,"n":0.083095,"e":0.048896,"L":77.9971},
				{"jd":2456440.5,"i":1.3033,"o":100.627,"p":14.586,"a":5.20259,"n":0.083096,"e":0.048892,"L":81.3228},
				{"jd":2456480.5,"i":1.3033,"o":100.628,"p":14.568,"a":5.20250,"n":0.083098,"e":0.048888,"L":84.6481},
				{"jd":2456520.5,"i":1.3033,"o":100.629,"p":14.556,"a":5.20245,"n":0.083099,"e":0.048892,"L":87.9728},
				{"jd":2456560.5,"i":1.3033,"o":100.630,"p":14.555,"a":5.20245,"n":0.083099,"e":0.048901,"L":91.2973},
				{"jd":2456600.5,"i":1.3033,"o":100.631,"p":14.576,"a":5.20254,"n":0.083097,"e":0.048907,"L":94.6223},
				{"jd":2456640.5,"i":1.3033,"o":100.632,"p":14.593,"a":5.20261,"n":0.083096,"e":0.048901,"L":97.9485},
				{"jd":2456680.5,"i":1.3033,"o":100.633,"p":14.592,"a":5.20259,"n":0.083096,"e":0.048891,"L":101.2751}
			]
		},{
			"name":"S",
			"radius": 57316,	// km
			"interval": 10,
			"colour": "rgb(200,150,150)",
			"magnitude": function(d){
				var slon = Math.atan2(d.y,d.x);
				var slat = Math.atan2(d.z, Math.sqrt(d.x*d.x + d.y*d.y));
				while(slon < 0) slon += 2*Math.PI;
				while(slon >= 360) slon -= 2*Math.PI;
				var ir = d.d2r*28.06;
				var Nr = d.d2r*(169.51 + 3.82E-5 * (d.jd-2451543.5));	// Compared to J2000 epoch
				var B = Math.asin(Math.sin(slat) * Math.cos(ir) - Math.cos(slat) * Math.sin(ir) * Math.sin(slon-Nr));
				return -9.0  + 5*log10(d.r*d.R) + 0.044 * d.FV + (-2.6 * Math.sin(Math.abs(B)) + 1.2 * Math.pow(Math.sin(B),2));
			},
			"elements":[
				{"jd":2456280.5,"i":2.4869,"o":113.732,"p":90.734,"a":9.51836,"n":0.033583,"e":0.055789,"L":208.6057},
				{"jd":2456320.5,"i":2.4869,"o":113.732,"p":90.856,"a":9.51931,"n":0.033578,"e":0.055791,"L":209.9430},
				{"jd":2456360.5,"i":2.4869,"o":113.732,"p":90.979,"a":9.52024,"n":0.033574,"e":0.055794,"L":211.2797},
				{"jd":2456400.5,"i":2.4869,"o":113.733,"p":91.105,"a":9.52121,"n":0.033568,"e":0.055793,"L":212.6162},
				{"jd":2456440.5,"i":2.4869,"o":113.732,"p":91.245,"a":9.52234,"n":0.033562,"e":0.055779,"L":213.9525},
				{"jd":2456480.5,"i":2.4869,"o":113.732,"p":91.380,"a":9.52349,"n":0.033556,"e":0.055750,"L":215.2901},
				{"jd":2456520.5,"i":2.4869,"o":113.732,"p":91.500,"a":9.52450,"n":0.033551,"e":0.055724,"L":216.6279},
				{"jd":2456560.5,"i":2.4870,"o":113.732,"p":91.611,"a":9.52541,"n":0.033546,"e":0.055704,"L":217.9654},
				{"jd":2456600.5,"i":2.4870,"o":113.732,"p":91.727,"a":9.52630,"n":0.033541,"e":0.055691,"L":219.3014},
				{"jd":2456640.5,"i":2.4870,"o":113.732,"p":91.870,"a":9.52748,"n":0.033535,"e":0.055657,"L":220.6368},
				{"jd":2456680.5,"i":2.4870,"o":113.733,"p":92.021,"a":9.52885,"n":0.033528,"e":0.055600,"L":221.9730}
			]
		},{
			"name":"U",
			"radius": 25266,	// km
			"interval": 20,
			"colour": "rgb(130,150,255)",
			"magnitude": function(d){ return -7.15 + 5*log10(d.r*d.R) + 0.001 * d.FV; },
			"elements":[
				{"jd":2456280.5,"i":0.7726,"o":74.004,"p":169.227,"a":19.2099,"n":0.011713,"e":0.046728,"L":9.1400},
				{"jd":2456320.5,"i":0.7727,"o":74.001,"p":169.271,"a":19.2064,"n":0.011716,"e":0.046913,"L":9.6133},
				{"jd":2456360.5,"i":0.7727,"o":73.997,"p":169.314,"a":19.2030,"n":0.011720,"e":0.047102,"L":10.0873},
				{"jd":2456400.5,"i":0.7727,"o":73.991,"p":169.364,"a":19.1994,"n":0.011723,"e":0.047297,"L":10.5610},
				{"jd":2456440.5,"i":0.7728,"o":73.989,"p":169.434,"a":19.1953,"n":0.011727,"e":0.047509,"L":11.0340},
				{"jd":2456480.5,"i":0.7728,"o":73.989,"p":169.522,"a":19.1916,"n":0.011730,"e":0.047703,"L":11.5048},
				{"jd":2456520.5,"i":0.7728,"o":73.989,"p":169.602,"a":19.1882,"n":0.011733,"e":0.047874,"L":11.9756},
				{"jd":2456560.5,"i":0.7728,"o":73.989,"p":169.674,"a":19.1850,"n":0.011736,"e":0.048035,"L":12.4470},
				{"jd":2456600.5,"i":0.7728,"o":73.985,"p":169.740,"a":19.1816,"n":0.011739,"e":0.048215,"L":12.9200},
				{"jd":2456640.5,"i":0.7728,"o":73.984,"p":169.836,"a":19.1774,"n":0.011743,"e":0.048431,"L":13.3920},
				{"jd":2456680.5,"i":0.7728,"o":73.983,"p":169.962,"a":19.1729,"n":0.011747,"e":0.048650,"L":13.8617}
			]
		},{
			"name":"N",
			"radius": 24553,	// km
			"interval": 20,
			"colour": "rgb(100,100,255)",
			"magnitude": function(d){ return -6.90 + 5*log10(d.r*d.R) + 0.001 * d.FV; },
			"elements":[
				{"jd":2456280.5,"i":1.7686,"o":131.930,"p":53.89,"a":30.0401,"n":0.005990,"e":0.010281,"L":333.6121},
				{"jd":2456320.5,"i":1.7687,"o":131.932,"p":55.15,"a":30.0331,"n":0.005992,"e":0.010207,"L":333.8487},
				{"jd":2456360.5,"i":1.7688,"o":131.935,"p":56.47,"a":30.0259,"n":0.005994,"e":0.010138,"L":334.0856},
				{"jd":2456400.5,"i":1.7688,"o":131.937,"p":57.82,"a":30.0185,"n":0.005996,"e":0.010067,"L":334.3220},
				{"jd":2456440.5,"i":1.7690,"o":131.940,"p":59.24,"a":30.0108,"n":0.005999,"e":0.009985,"L":334.5566},
				{"jd":2456480.5,"i":1.7691,"o":131.943,"p":60.44,"a":30.0044,"n":0.006000,"e":0.009894,"L":334.7895},
				{"jd":2456520.5,"i":1.7692,"o":131.946,"p":61.52,"a":29.9987,"n":0.006002,"e":0.009816,"L":335.0233},
				{"jd":2456560.5,"i":1.7693,"o":131.949,"p":62.57,"a":29.9932,"n":0.006004,"e":0.009748,"L":335.2581},
				{"jd":2456600.5,"i":1.7694,"o":131.951,"p":63.84,"a":29.9867,"n":0.006006,"e":0.009690,"L":335.4937},
				{"jd":2456640.5,"i":1.7695,"o":131.954,"p":65.29,"a":29.9793,"n":0.006008,"e":0.009609,"L":335.7265},
				{"jd":2456680.5,"i":1.7697,"o":131.957,"p":66.66,"a":29.9725,"n":0.006010,"e":0.009508,"L":335.9564}
			]
		}];
	
		this.d2r = Math.PI/180;
		this.r2d = 180/Math.PI;
		this.AUinkm = 149597870.700;
		return this;
	}

	// Build an array containing all the planets
	// Inputs:
	//  jd = the Julian Date to calculate from
	//  days = the number of days to calculate ephemerides for
	Planets.prototype.build = function(jd,days){
		var arr = new Array(this.planets.length-1);
		var b = 0;
		if(!days) days = 365.25;
		for(var a = 0 ; a < this.planets.length ; a++){
			if(this.planets[a].colour) arr[b++] = this.buildPlanet(a,jd,days);
		}
		return arr;
	}
	
	// Build the data array for a particular planet
	// Inputs:
	//  planet = the ID of the planet
	//  jd = the Julian Date to calculate from
	//  days = the number of days to calculate ephemerides for
	Planets.prototype.buildPlanet = function(planet,jd,days){
		var p,coord,interval,n,jdcurr;
		if(typeof planet==="number"){
			p = planet;
		}else{
			var match = -1;
			for(var a = 0 ; a < this.planets.length ; a++){
				if(this.planets[a].name==planet) match = a;
			}
			if(match < 0) return this;
			if(match == 2) return this;	// Can't calculate Earth
			p = match;
		}
	
		interval = (typeof this.planets[p].interval==="number" ? this.planets[p].interval : 1);
	
		// Build an array of the form:
		// [Planet name,colour,[jd_1, ra_1, dec_1, mag_1, jd_2, ra_2, dec_2, mag_2....]]
		n = Math.floor(days/interval);
		var arr = new Array(3);
		arr[0] = this.planets[p]["name"];
		arr[1] = this.planets[p]["colour"];
		arr[2] = new Array(n*4);

		jdcurr = jd;
		for(var i = 0 ; i < n; i++){
			jdcurr += interval;
			coord = this.getEphem(p,jdcurr);
			arr[2][i*4+0] = jdcurr;
			arr[2][i*4+1] = coord[0];
			arr[2][i*4+2] = coord[1];
			arr[2][i*4+3] = coord[2];
		}
		return arr;
	}
	
	
	// Get the ephemeris for the specified planet number
	// Input:
	//   planet = ID
	//   day = Julian Date to calculate the ephemeris for
	// Method from http://www.stargazing.net/kepler/ellipse.html#twig06
	Planets.prototype.getEphem = function(planet,day){
	
		var i,v,e,x,y,z,ec,q,ra,dc,R,mag,FV,phase;
	
		if(typeof planet==="number"){
			i = planet;
		}else{
			var match = -1;
			for(var a = 0 ; a < this.planets.length ; a++){
				if(this.planets[a].name==planet) match = a;
			}
			if(match < 0) return this;
			if(match == 2) return this;	// Can't calculate Earth
			i = match;
		}

		// Heliocentric coordinates of planet
		v = this.getHeliocentric(this.planets[i],day);
	
		// Heliocentric coordinates of Earth
		e = this.getHeliocentric(this.planets[2],day);
	
		// Geocentric ecliptic coordinates of the planet
		x = v.xyz[0] - e.xyz[0];
		y = v.xyz[1] - e.xyz[1];
		z = v.xyz[2] - e.xyz[2];
	
		// Geocentric equatorial coordinates of the planet
		ec = 23.439292*this.d2r; // obliquity of the ecliptic for the epoch the elements are referred to
		q = [x,y * Math.cos(ec) - z * Math.sin(ec),y * Math.sin(ec) + z * Math.cos(ec)];
	
		ra = Math.atan(q[1]/q[0])*this.r2d;
		if(q[0] < 0) ra += 180;
		if(q[0] >= 0 && q[1] < 0) ra += 360;
	
		dc = Math.atan(q[2] / Math.sqrt(q[0]*q[0] + q[1]*q[1]))*this.r2d;
	
		R = Math.sqrt(q[0]*q[0] + q[1]*q[1] + q[2]*q[2]);
	
		// Calculate the magnitude (http://stjarnhimlen.se/comp/tutorial.html)
		var angdiam = (this.planets[i].radius*2/(R*this.AUinkm));
		mag = 1;
	
		// planet's heliocentric distance, v.r, its geocentric distance, R, and the distance to the Sun, e.r.
		FV = Math.acos( ( v.r*v.r + R*R - e.r*e.r ) / (2*v.r*R) );
		phase = (1 + Math.cos(FV))/2;
		mag = this.planets[i].magnitude({a:v.r,r:v.r,R:R,FV:FV*this.r2d,x:x,y:y,z:z,jd:day,d2r:this.d2r});
	
		return [ra,dc,mag];
	}
	
	Planets.prototype.getHeliocentric = function(planet,jd,i){
		var min = 1e10;
		var mn,p,d,M,v,r;
	
		// Choose a set of orbital elements
		if(!i){
			// Loop over elements and pick the one closest in time
			for(var j = 0; j < planet.elements.length ;j++){
				mn = Math.abs(planet.elements[j].jd-jd);
				if(mn < min){
					i = j;
					min = mn;
				}
			}
		}
		p = planet.elements[i];

		// The day number is the number of days (decimal) since epoch of elements.
		d = (jd - p.jd);
	
		// Heliocentric coordinates of planet
		M = this.meanAnomaly(p.n,d,p.L,p.p)
		v = this.trueAnomaly(M*this.d2r,p.e,10);
		r = p.a * (1 - Math.pow(p.e,2)) / (1 + p.e * Math.cos(v*this.d2r));
		return {xyz: this.heliocentric(v*this.d2r,r,p.p*this.d2r,p.o*this.d2r,p.i*this.d2r), M:M, v:v, r:r, i:i, d:d, elements:p};
	}
	
	// Find the Mean Anomaly (M, degrees) of the planet where
	//  n is daily motion
	//  d is the number of days since the date of the elements
	//  L is the mean longitude (deg)
	//  p is the longitude of perihelion (deg) 
	//  M should be in range 0 to 360 degrees
	Planets.prototype.meanAnomaly = function(d,n,L,p){
		var M = n * d + L - p;
		while(M < 0) M += 360;
		while(M >= 360) M -= 360;
		return M;
	}
	
	// Heliocentric coordinates of the planet where:	
	//  o is longitude of ascending node (radians)
	//  p is longitude of perihelion (radians)
	//  i is inclination of plane of orbit (radians)
	// the quantity v + o - p is the angle of the planet measured in the plane of the orbit from the ascending node
	Planets.prototype.heliocentric = function(v,r,p,o,i){
		var vpo = v + p - o;
		var svpo = Math.sin(vpo);
		var cvpo = Math.cos(vpo);
		var co = Math.cos(o);
		var so = Math.sin(o);
		var ci = Math.cos(i);
		var si = Math.sin(i);
		return [r * (co * cvpo - so * svpo * ci),r * (so * cvpo + co * svpo * ci),r * (svpo * si)]
	}
	
	/*
		Find the True Anomaly given
		m  -  the 'mean anomaly' in orbit theory (in radians)
		ecc - the eccentricity of the orbit
	*/
	Planets.prototype.trueAnomaly = function(m,ecc,eps){
		var e = m;        // first guess
	
		if(typeof eps==="number"){
			var delta = 0.05; // set delta equal to a dummy value
			var eps = 10;     // eps - the precision parameter - solution will be within 10^-eps of the true value. Don't set eps above 14, as convergence can't be guaranteed
		
			while(Math.abs(delta) >= Math.pow(10,-eps)){    // converged?
				delta = e - ecc * Math.sin(e) - m;          // new error
				e -= delta / (1 - ecc * Math.cos(e));    // corrected guess
			}
			var v = 2 * Math.atan(Math.pow(((1 + ecc) / (1 - ecc)),0.5) * Math.tan(0.5 * e));
			if(v < 0) v+= Math.PI*2;
		}else{
			v = m + ( (2 * ecc - Math.pow(ecc,3)/4)*Math.sin(m) + 1.25*Math.pow(ecc,2)*Math.sin(2*m) + (13/12)*Math.pow(ecc,3)*Math.sin(3*m) );
		}
		return v*this.r2d; // return estimate
	}
	
	function formatRADec(ra,dec){
		var rah,ram,ras,dcd,dcm,dcs;
		ra /= 15;
		rah = Math.floor(ra);
		ram = Math.floor((ra-rah)*60);
		ras = (ra-rah-ram/60)*3600;
		dcd = Math.floor(dec);
		dcm = Math.floor((dec-dcd)*60);
		dcs = (dec-dcd-dcm/60)*3600;
		return (Math.abs(rah) < 10 ? "0":"")+rah+":"+(ram < 10 ? "0":"")+ram+":"+(ras < 10 ? "0":"")+ras.toFixed(2)+" "+(Math.abs(dcd) < 10 ? "0":"")+dcd+":"+(dcm < 10 ? "0":"")+dcm+":"+(dcs < 10 ? "0":"")+dcs.toFixed(2);
	}
	
	function getJD(today){
		if(!today) today = new Date();
		return ( today.getTime() / 86400000.0 ) + 2440587.5;
	}
	
	function rev(x) {
	  return  x - Math.floor(x/360.0)*360.0
	}
	
	function log10(x) {
		return Math.LOG10E * Math.log(x);
	}

	var match = false;
	for(var i = 0; i < $.virtualsky.plugins.length; i++){
		if($.virtualsky.plugins[i].name=="planets") match = true;
	}

	if(!match){
		$.virtualsky.plugins.push({
			init: init,
			name: 'planets',
			version: '1.0'
		});
	}

})(jQuery);