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planetCoordinates.js
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planetCoordinates.js
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/*
Fitbit planets, calculates the position of the planets in our solar
system and their rise and set times based on the user's GPS
location.
Copyright (C) 2021 Chris Gorman
This program is free software: you can redistribute it and/or modify
it under the terms of the GNU General Public License as published by
the Free Software Foundation, either version 3 of the License, or
(at your option) any later version.
This program is distributed in the hope that it will be useful,
but WITHOUT ANY WARRANTY; without even the implied warranty of
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
GNU General Public License for more details.
You should have received a copy of the GNU General Public License
along with this program. If not, see <https://www.gnu.org/licenses/>.
*/
// Utility functions and variables
var radToDeg = 180.0 / Math.PI;
var degToRad = Math.PI / 180;
Math.sind = function(x) {
return Math.sin(x * degToRad);
}
Math.cosd = function(x) {
return Math.cos(x * degToRad);
}
Math.tand = function(x) {
return Math.tan(x * degToRad);
}
Math.asind = function(x) {
return Math.asin(x) * radToDeg;
}
Math.acosd = function(x) {
return Math.acos(x) * radToDeg;
}
Math.atand = function(x) {
return Math.atan(x) * radToDeg;
}
Math.atan2d = function(y, x) {
return Math.atan2(y, x) * radToDeg;
}
// Normalize degree of x to between 0 and 360
Math.revolveDegree = function (x) {
return x - Math.floor(x/360.0)*360.0;
}
// Normalize Hour Angle x to between 0 and 24
Math.revolveHourAngle = function (x) {
return x - Math.floor(x/24.0)*24.0;
}
// Helper functions
export function dayNumber (year, month, day, UT) {
let d = 367*year
- Math.floor(7 * (year + Math.floor((month+9)/12)) / 4)
- Math.floor(3 * ((year + Math.floor((month -9)/ 7)) / 100 + 1) / 4)
+ Math.floor(275*month/9) + day - 730515;
if (UT === undefined) {
let utc = new Date();
d = d + (utc.getUTCHours() + utc.getUTCMinutes()/60 +
utc.getUTCSeconds()/3600)/24;
} else {
d = d + UT/24;
}
return d;
}
export function eccentricAnomaly (M, e, tol) {
let e0 = M
+ (180/Math.PI) * e * Math.sind(M) * (1 + e + Math.cosd(M));
let e1 = e0 -
(e0 - (180/Math.PI) * e * Math.sind(e0) - M) / (1 - e *
Math.cosd(e0));
while (Math.abs(e0 - e1) > tol) {
e0 = e1;
e1 = e0 - (e0 - (180/Math.PI) * e * Math.sind(e0) - M) / (1 - e
* Math.cosd(e0));
}
return e1;
}
export function sidtime (day_number, longitude, UT) {
let sr = sunRectangular (day_number);
let gmst0 = Math.revolveDegree(sr.L + 180);
if (UT === undefined) {
let utc = new Date();
var st = gmst0/15 + (utc.getUTCHours() + utc.getUTCMinutes()/60 +
utc.getUTCSeconds()/3600) + longitude/15;
} else {
var st = gmst0/15 + UT + longitude/15;
}
return st;
}
export function sunRectangular (day_number) {
let w = 282.9404 + 4.70935e-5 * day_number; // longitude of perihelion
let a = 1; // mean distance, a.u.
let e = 0.016709 - 1.151e-9 * day_number; // eccentricity
let M = 356.0470 + 0.9856002585 * day_number; // mean anomaly
M = Math.revolveDegree(M);
let oblecl = 23.4393 - 3.563e-7 * day_number; // obliquity of the eliptic
let L = w + M; // sun's mean longitude
L = Math.revolveDegree(L);
// sun's eccentric anomaly
let E = M + (180/Math.PI) * e * Math.sind(M) * (1 + e * Math.cosd(M));
// sun's rectrangular coordinates
let x = Math.cosd(E) - e;
let y = Math.sind(E) * Math.sqrt(1 - e*e);
// convert to distance and true anomaly
let r = Math.sqrt(x*x + y*y);
let v = Math.atan2d(y, x);
// sun's longitude
let lon = v + w;
lon = Math.revolveDegree(lon);
// sun's ecliptic rectangular coordinates
let x1 = r * Math.cosd(lon);
let y1 = r * Math.sind(lon);
let z1 = 0;
return {
x1: x1,
y1: y1,
z1: z1,
oblecl: oblecl,
L: L,
lonsun: lon,
rs: r,
};
}
// sun and moon
export function sun (day_number, latitude, longitude, UT) {
// rotate equitorial coordinates
let sr = sunRectangular(day_number);
let xequat = sr.x1;
let yequat = sr.y1 * Math.cosd(sr.oblecl) - sr.z1 * Math.sind(sr.oblecl);
let zequat = sr.y1 * Math.sind(sr.oblecl) - sr.z1 * Math.cosd(sr.oblecl);
let right_ascension = Math.atan2d(yequat, xequat);
right_ascension = Math.revolveDegree(right_ascension);
// convert right_ascension to hours
right_ascension = right_ascension / 15;
let declination = Math.atan2d(zequat,
Math.sqrt(Math.pow(Math.abs(xequat), 2) + Math.pow(Math.abs(yequat), 2)));
let distance = Math.sqrt(Math.pow(Math.abs(xequat), 2) +
Math.pow(Math.abs(yequat), 2) + Math.pow(Math.abs(zequat), 2));
// calculate hour angle
let hour_angle = (sidtime(day_number, longitude, UT) - right_ascension) * 15;
// convert hour_angle and declination to rectangular system
let x2 = Math.cosd(hour_angle) * Math.cosd(declination);
let y2 = Math.sind(hour_angle) * Math.cosd(declination);
let z2 = Math.sind(declination);
// rotate this along the y2 axis
let xhor = x2 * Math.sind(latitude) - z2 * Math.cosd(latitude);
let yhor = y2;
let zhor = x2 * Math.cosd(latitude) + z2 * Math.sind(latitude);
// finally calculate azimuth and altitude
let azimuth = Math.atan2d(yhor, xhor) + 180;
let altitude = Math.atan2d(zhor, Math.sqrt(Math.pow(Math.abs(xhor), 2)
+ Math.pow(Math.abs(yhor), 2)));
return{
ra: right_ascension,
decl: declination,
dist: distance,
alt: altitude,
az: azimuth,
};
}
export function moon (day_number, latitude, longitude, UT) {
let N = 125.1228 - 0.0529538083 * day_number; // long asc. node
let i = 5.1454; // inclination
let w = 318.0634 + 0.1643573223 * day_number; // Arg. of perigree
let a = 60.2666; // mean distance
let e = 0.054900; // eccentricity
let M = 115.3654 + 13.0649929509 * day_number; // mean anomaly
M = Math.revolveDegree(M);
let oblecl = 23.4393 - 3.563e-7 * day_number; // obliquity of the eliptic
let E = eccentricAnomaly(M, e, 0.0005);
// moon's rectrangular coordinates
let x = a * (Math.cosd(E) - e);
let y = a * Math.sind(E) * Math.sqrt(1 - e*e);
// convert to distance and true anomaly
let distance = Math.sqrt(x*x + y*y);
let v = Math.atan2d(y, x);
// moon's position in ecliptic coordinates
let xeclip = distance * ( Math.cosd(N) * Math.cosd(v+w) -
Math.sind(N) * Math.sind(v+w) * Math.cosd(i));
let yeclip = distance * ( Math.sind(N) * Math.cosd(v+w) +
Math.cosd(N) * Math.sind(v+w) * Math.cosd(i));
let zeclip = distance * Math.sind(v+w) * Math.sind(i);
// convert to ecliptic longitude, latitude and distance
let lon = Math.atan2d(yeclip, xeclip);
lon = Math.revolveDegree(lon);
let lat = Math.atan2d(zeclip, Math.sqrt(xeclip*xeclip + yeclip*yeclip));
let Sw = 282.9404 + 4.70935e-5 * day_number; // sun's (longitude of
// perihelion)
let Ms = 356.0470 + 0.9856002585 * day_number; // sun's mean anomaly
let Ls = Sw + Ms;
Ls = Math.revolveDegree(Ls);
let Lm = N + w + M;
let Mm = M;
let D = Lm - Ls;
let F = Lm - N;
let perturbations_in_longitude = -1.274 * Math.sind(Mm - 2*D)
+0.658 * Math.sind(2*D)
-0.186 * Math.sind(Ms)
-0.059 * Math.sind(2*Mm - 2*D)
-0.057 * Math.sind(Mm - 2*D + Ms)
+0.053 * Math.sind(Mm + 2*D)
+0.046 * Math.sind(2*D - Ms)
+0.041 * Math.sind(Mm - Ms)
-0.035 * Math.sind(D)
-0.031 * Math.sind(Mm + Ms)
-0.015 * Math.sind(2*F - 2*D)
+0.011 * Math.sind(Mm - 4*D);
let perturbations_in_latitude = -0.173 * Math.sind(F - 2*D)
-0.055 * Math.sind(Mm - F - 2*D)
-0.046 * Math.sind(Mm + F - 2*D)
+0.033 * Math.sind(F + 2*D)
+0.017 * Math.sind(2*Mm + F);
let perturbations_in_distance = -0.58 * Math.cosd(Mm - 2*D)
-0.46 * Math.cosd(2*D);
lon = lon + perturbations_in_longitude;
lat = lat + perturbations_in_latitude;
distance = distance + perturbations_in_distance;
let x1 = Math.cosd(lon) * Math.cosd(lat);
let y1 = Math.cosd(lat) * Math.sind(lon);
let z1 = Math.sind(lat);
let x2 = x1;
let y2 = y1 * Math.cosd(oblecl) - z1 * Math.sind(oblecl);
let z2 = y1 * Math.sind(oblecl) + z1 * Math.cosd(oblecl);
let right_ascension = Math.atan2d(y2,x2);
let right_ascension1 = right_ascension;
right_ascension = right_ascension / 15;
right_ascension = Math.revolveHourAngle(right_ascension);
let declination = Math.atan2d(z2, Math.sqrt(x2*x2 + y2*y2));
let hour_angle = (sidtime(day_number, longitude, UT) - right_ascension) * 15;
hour_angle = Math.revolveDegree(hour_angle);
x = Math.cosd(hour_angle) * Math.cosd(declination);
y = Math.sind(hour_angle) * Math.cosd(declination);
let z = Math.sind(declination);
let xhor = x * Math.sind(latitude) - z * Math.cosd(latitude);
let yhor = y;
let zhor = x * Math.cosd(latitude) + z * Math.sind(latitude);
let azimuth = Math.atan2d( yhor, xhor ) + 180;
let altitude = Math.atan2d( zhor , Math.sqrt(xhor*xhor + yhor*yhor));
let mpar = Math.asind(1/distance);
let alt_geoc = altitude - mpar * Math.cosd(altitude);
let gclat = latitude - 0.1924 * Math.sind(2*latitude);
let rho = 0.99833 + 0.00167 * Math.cosd(2*latitude);
let g = Math.atand(Math.tand(gclat) / Math.cosd(hour_angle));
let topocentric_right_ascension = right_ascension1
- mpar * rho * Math.cosd(gclat)
* Math.sind(hour_angle) / Math.cosd(declination);
topocentric_right_ascension =
Math.revolveDegree(topocentric_right_ascension);
let topocentric_declination = declination
- mpar * rho * Math.sind(gclat) * Math.sind(g - declination) /
Math.sind(g);
return{
ra: topocentric_right_ascension,
decl: topocentric_declination,
dist: distance,
alt: alt_geoc,
az: azimuth,
};
}
// planets
export function mercury (day_number, latitude, longitude, UT) {
let N = 48.3313 + 3.24587e-5 * day_number; // (Long of asc. node)
let i = 7.0047 + 5.00e-8 * day_number; // (Inclination)
let w = 29.1241 + 1.01444e-5 * day_number; // (Argument of perihelion)
let a = 0.387098; // (Semi-major axis)
let e = 0.205635 + 5.59e-10 * day_number; // (Eccentricity)
let M = 168.6562 + 4.0923344368 * day_number; // (Mean anonaly)
M = Math.revolveDegree(M);
let oblecl = 23.4393 - 3.563e-7 * day_number; // obliquity of the eliptic
let E = eccentricAnomaly(M, e, 0.0005);
// mercury's rectrangular coordinates
let x = a * (Math.cosd(E) - e);
let y = a * Math.sind(E) * Math.sqrt(1 - e*e);
// convert to distance and true anomaly
let r = Math.sqrt(x*x + y*y);
let v = Math.atan2d(y, x);
// mercury's position in ecliptic coordinates
let xeclip = r * ( Math.cosd(N) * Math.cosd(v+w) - Math.sind(N) *
Math.sind(v+w) * Math.cosd(i));
let yeclip = r * ( Math.sind(N) * Math.cosd(v+w) + Math.cosd(N) *
Math.sind(v+w) * Math.cosd(i));
let zeclip = r * Math.sind(v+w) * Math.sind(i);
// sun's rectangular coordinates
let sr = sunRectangular(day_number);
// convert to ecliptic longitude and latitude
let lon = Math.atan2d(yeclip, xeclip);
let lat = Math.atan2d(zeclip, Math.sqrt(xeclip*xeclip + yeclip*yeclip));
// use lat and lon to produce RA and Dec
let xh = r * Math.cosd(lon) * Math.cosd(lat);
let yh = r * Math.sind(lon) * Math.cosd(lat);
let zh = r * Math.sind(lat);
// convert sun's position
let xs = sr.rs * Math.cosd(sr.lonsun);
let ys = sr.rs * Math.sind(sr.lonsun);
// convert from heliocentric to geocentric
let xg = xh + xs;
let yg = yh + ys;
let zg = zh;
// convert to equitorial
let xe = xg;
let ye = yg * Math.cosd(oblecl) - zg * Math.sind(oblecl);
let ze = yg * Math.sind(oblecl) + zg * Math.cosd(oblecl);
// RA and Decl
let RA = Math.atan2d(ye, xe);
RA = Math.revolveDegree(RA);
RA = RA/15;
let Dec = Math.atan2d(ze, Math.sqrt(xe*xe+ye*ye));
let rg = Math.sqrt(xe*xe+ye*ye+ze*ze);
// convert to azimuth and altitude
let HA = sidtime(day_number, longitude, UT) - RA;
HA = HA * 15;
HA = Math.revolveDegree(HA);
x = Math.cosd(HA) * Math.cosd(Dec);
y = Math.sind(HA) * Math.cosd(Dec);
let z = Math.sind(Dec);
let xhor = x * Math.sind(latitude) - z * Math.cosd(latitude);
let yhor = y;
let zhor = x * Math.cosd(latitude) + z * Math.sind(latitude);
let azimuth = Math.atan2d(yhor,xhor) + 180;
let altitude = Math.atan2d(zhor, Math.sqrt(Math.pow(Math.abs(xhor), 2)
+ Math.pow(Math.abs(yhor), 2)));
return{
ra: RA,
decl: Dec,
dist: rg,
alt: altitude,
az: azimuth,
};
}
export function venus (day_number, latitude, longitude, UT) {
let N = 76.6799 + 2.46590e-5 * day_number;
let i = 3.3946 + 2.75e-8 * day_number;
let w = 54.8910 + 1.38374e-5 * day_number;
let a = 0.723330;
let e = 0.006773 - 1.302e-9 * day_number;
let M = 48.0052 + 1.6021302244 * day_number;
M = Math.revolveDegree(M);
let oblecl = 23.4393 - 3.563e-7 * day_number; // obliquity of the eliptic
let E = eccentricAnomaly(M, e, 0.0005);
// venus's rectrangular coordinates
let x = a * (Math.cosd(E) - e);
let y = a * Math.sind(E) * Math.sqrt(1 - e*e);
// convert to distance and true anomaly
let r = Math.sqrt(x*x + y*y);
let v = Math.atan2d(y, x);
// venus's position in ecliptic coordinates
let xeclip = r * ( Math.cosd(N) * Math.cosd(v+w) - Math.sind(N) *
Math.sind(v+w) * Math.cosd(i));
let yeclip = r * ( Math.sind(N) * Math.cosd(v+w) + Math.cosd(N) *
Math.sind(v+w) * Math.cosd(i));
let zeclip = r * Math.sind(v+w) * Math.sind(i);
// sun's rectangular coordinates
let sr = sunRectangular(day_number);
// convert to ecliptic longitude and latitude
let lon = Math.atan2d(yeclip, xeclip);
lon = Math.revolveDegree(lon);
let lat = Math.atan2d(zeclip, Math.sqrt(xeclip*xeclip + yeclip*yeclip));
// use lat and lon to produce RA and Dec
let xh = r * Math.cosd(lon) * Math.cosd(lat);
let yh = r * Math.sind(lon) * Math.cosd(lat);
let zh = r * Math.sind(lat);
// convert sun's position
let xs = sr.rs * Math.cosd(sr.lonsun);
let ys = sr.rs * Math.sind(sr.lonsun);
// convert from heliocentric to geocentric
let xg = xh + xs;
let yg = yh + ys;
let zg = zh;
// convert to equitorial
let xe = xg;
let ye = yg * Math.cosd(oblecl) - zg * Math.sind(oblecl);
let ze = yg * Math.sind(oblecl) + zg * Math.cosd(oblecl);
// RA and Decl
let RA = Math.atan2d(ye, xe);
RA = Math.revolveDegree(RA);
RA = RA/15;
let Dec = Math.atan2d(ze, Math.sqrt(xe*xe+ye*ye));
let rg = Math.sqrt(xe*xe+ye*ye+ze*ze);
// convert to azimuth and altitude
let HA = sidtime(day_number, longitude, UT) - RA;
HA = HA * 15;
HA = Math.revolveDegree(HA);
x = Math.cosd(HA) * Math.cosd(Dec);
y = Math.sind(HA) * Math.cosd(Dec);
let z = Math.sind(Dec);
let xhor = x * Math.sind(latitude) - z * Math.cosd(latitude);
let yhor = y;
let zhor = x * Math.cosd(latitude) + z * Math.sind(latitude);
let azimuth = Math.atan2d(yhor,xhor) + 180;
let altitude = Math.atan2d(zhor, Math.sqrt(Math.pow(Math.abs(xhor), 2)
+ Math.pow(Math.abs(yhor), 2)));
return{
ra: RA,
decl: Dec,
dist: rg,
alt: altitude,
az: azimuth,
};
}
export function mars (day_number, latitude, longitude, UT) {
let N = 49.5574 + 2.11081e-5 * day_number;
let i = 1.8497 - 1.78e-8 * day_number;
let w = 286.5016 + 2.92961e-5 * day_number;
let a = 1.523688;
let e = 0.093405 + 2.516e-9 * day_number;
let M = 18.6021 + 0.5240207766 * day_number;
M = Math.revolveDegree(M);
let oblecl = 23.4393 - 3.563e-7 * day_number; // obliquity of the eliptic
let E = eccentricAnomaly(M, e, 0.0005);
// mars's rectrangular coordinates
let x = a * (Math.cosd(E) - e);
let y = a * Math.sind(E) * Math.sqrt(1 - e*e);
// convert to distance and true anomaly
let r = Math.sqrt(x*x + y*y);
let v = Math.atan2d(y, x);
// mars's position in ecliptic coordinates
let xeclip = r * ( Math.cosd(N) * Math.cosd(v+w)
- Math.sind(N) * Math.sind(v+w) * Math.cosd(i));
let yeclip = r * ( Math.sind(N) * Math.cosd(v+w)
+ Math.cosd(N) * Math.sind(v+w) * Math.cosd(i));
let zeclip = r * Math.sind(v+w) * Math.sind(i);
// sun's rectangular coordinates
let sr = sunRectangular(day_number);
// convert to ecliptic longitude and latitude
let lon = Math.atan2d(yeclip, xeclip);
lon = Math.revolveDegree(lon);
let lat = Math.atan2d(zeclip, Math.sqrt(xeclip*xeclip + yeclip*yeclip));
// use lat and lon to produce RA and Dec
let xh = r * Math.cosd(lon) * Math.cosd(lat);
let yh = r * Math.sind(lon) * Math.cosd(lat);
let zh = r * Math.sind(lat);
// convert sun's position
let xs = sr.rs * Math.cosd(sr.lonsun);
let ys = sr.rs * Math.sind(sr.lonsun);
// convert from heliocentric to geocentric
let xg = xh + xs;
let yg = yh + ys;
let zg = zh;
// convert to equitorial
let xe = xg;
let ye = yg * Math.cosd(oblecl) - zg * Math.sind(oblecl);
let ze = yg * Math.sind(oblecl) + zg * Math.cosd(oblecl);
// RA and Decl
let RA = Math.atan2d(ye, xe);
RA = Math.revolveDegree(RA);
RA = RA/15;
let Dec = Math.atan2d(ze, Math.sqrt(xe*xe+ye*ye));
let rg = Math.sqrt(xe*xe+ye*ye+ze*ze);
// convert to azimuth and altitude
let HA = sidtime(day_number, longitude, UT) - RA;
HA = HA * 15;
HA = Math.revolveDegree(HA);
x = Math.cosd(HA) * Math.cosd(Dec);
y = Math.sind(HA) * Math.cosd(Dec);
let z = Math.sind(Dec);
let xhor = x * Math.sind(latitude) - z * Math.cosd(latitude);
let yhor = y;
let zhor = x * Math.cosd(latitude) + z * Math.sind(latitude);
let azimuth = Math.atan2d(yhor,xhor) + 180;
let altitude = Math.atan2d(zhor, Math.sqrt(Math.pow(Math.abs(xhor), 2)
+ Math.pow(Math.abs(yhor), 2)));
return{
ra: RA,
decl: Dec,
dist: rg,
alt: altitude,
az: azimuth,
};
}
export function jupiter (day_number, latitude, longitude, UT) {
let N = 100.4542 + 2.76854e-5 * day_number; // Long of asc. node
let i = 1.3030 - 1.557e-7 * day_number; // Inclination
let w = 273.8777 + 1.64505e-5 * day_number; // Argument of perihelion
let a = 5.20256; // Semi-major axis
let e = 0.048498 + 4.469e-9 * day_number; // eccentricity
let M = 19.8950 + 0.0830853001 * day_number; // Mean anomaly Jupiter
M = Math.revolveDegree(M);
let Mj = M;
let Ms = 316.9670 + 0.0334442282 * day_number; // Mean anomaly Saturn
Ms = Math.revolveDegree(Ms);
let Mu = 142.5905 + 0.011725806 * day_number; // Mean anomaly Uranus
Mu = Math.revolveDegree(Mu);
let oblecl = 23.4393 - 3.563e-7 * day_number; // obliquity of the eliptic
let E = eccentricAnomaly(M, e, 0.0005);
// jupiter's rectrangular coordinates
let x = a * (Math.cosd(E) - e);
let y = a * Math.sind(E) * Math.sqrt(1 - e*e);
// convert to distance and true anomaly
let r = Math.sqrt(x*x + y*y);
let v = Math.atan2d(y, x);
// jupiter's position in ecliptic coordinates
let xeclip = r * ( Math.cosd(N) * Math.cosd(v+w) - Math.sind(N) * Math.sind(v+w) * Math.cosd(i));
let yeclip = r * ( Math.sind(N) * Math.cosd(v+w) + Math.cosd(N) * Math.sind(v+w) * Math.cosd(i));
let zeclip = r * Math.sind(v+w) * Math.sind(i);
// sun's rectangular coordinates
let sr = sunRectangular(day_number);
// convert to ecliptic longitude and latitude
let lon = Math.atan2d(yeclip, xeclip);
lon = Math.revolveDegree(lon);
let lat = Math.atan2d(zeclip, Math.sqrt(xeclip*xeclip +
yeclip*yeclip));
let perturbations_of_longitude = -0.332 * Math.sind(2*Mj - 5*Ms - 67.6)
-0.056 * Math.sind(2*Mj - 2*Ms + 21)
+0.042 * Math.sind(3*Mj - 5*Ms + 21)
-0.036 * Math.sind(Mj - 2*Ms)
+0.022 * Math.cosd(Mj - Ms)
+0.023 * Math.sind(2*Mj - 3*Ms + 52)
-0.016 * Math.sind(Mj - 5*Ms - 69);
lon = lon + perturbations_of_longitude;
lon = Math.revolveDegree(lon);
// use lat and lon to produce RA and Dec
let xh = r * Math.cosd(lon) * Math.cosd(lat);
let yh = r * Math.sind(lon) * Math.cosd(lat);
let zh = r * Math.sind(lat);
// convert sun's position
let xs = sr.rs * Math.cosd(sr.lonsun);
let ys = sr.rs * Math.sind(sr.lonsun);
// convert from heliocentric to geocentric
let xg = xh + xs;
let yg = yh + ys;
let zg = zh;
// convert to equitorial
let xe = xg;
let ye = yg * Math.cosd(oblecl) - zg * Math.sind(oblecl);
let ze = yg * Math.sind(oblecl) + zg * Math.cosd(oblecl);
// RA and Decl
let RA = Math.atan2d(ye, xe);
RA = Math.revolveDegree(RA);
RA = RA/15;
let Dec = Math.atan2d(ze, Math.sqrt(xe*xe+ye*ye));
let rg = Math.sqrt(xe*xe+ye*ye+ze*ze);
// convert to azimuth and altitude
let HA = sidtime(day_number, longitude, UT) - RA;
HA = HA * 15;
HA = Math.revolveDegree(HA);
x = Math.cosd(HA) * Math.cosd(Dec);
y = Math.sind(HA) * Math.cosd(Dec);
let z = Math.sind(Dec);
let xhor = x * Math.sind(latitude) - z * Math.cosd(latitude);
let yhor = y;
let zhor = x * Math.cosd(latitude) + z * Math.sind(latitude);
let azimuth = Math.atan2d(yhor,xhor) + 180;
let altitude = Math.atan2d(zhor, Math.sqrt(Math.pow(Math.abs(xhor), 2)
+ Math.pow(Math.abs(yhor), 2)));
return{
ra: RA,
decl: Dec,
dist: rg,
alt: altitude,
az: azimuth,
};
}
export function saturn (day_number, latitude, longitude, UT) {
let N = 113.6634 + 2.38980E-5 * day_number; // Long of asc. node
let i = 2.4886 - 1.081E-7 * day_number; // Inclination
let w = 339.3939 + 2.97661E-5 * day_number; // Argument of perihelion
let a = 9.55475; // Semi-major axis
let e = 0.055546 - 9.499E-9 * day_number; // eccentricity
let M = 316.9670 + 0.0334442282 * day_number; // Mean anomaly
M = Math.revolveDegree(M);
let Ms = M;
let Mj = 19.8950 + 0.0830853001 * day_number; // Mean anomaly Jupiter
Mj = Math.revolveDegree(Mj);
let Mu = 142.5905 + 0.011725806 * day_number; // Mean anomaly Uranus
Mu = Math.revolveDegree(Mu);
let oblecl = 23.4393 - 3.563e-7 * day_number; // obliquity of the eliptic
let E = eccentricAnomaly(M, e, 0.0005);
// saturn's rectrangular coordinates
let x = a * (Math.cosd(E) - e);
let y = a * Math.sind(E) * Math.sqrt(1 - e*e);
// convert to distance and true anomaly
let r = Math.sqrt(x*x + y*y);
let v = Math.atan2d(y, x);
// saturn's position in ecliptic coordinates
let xeclip = r * ( Math.cosd(N) * Math.cosd(v+w) - Math.sind(N) * Math.sind(v+w) * Math.cosd(i));
let yeclip = r * ( Math.sind(N) * Math.cosd(v+w) + Math.cosd(N) * Math.sind(v+w) * Math.cosd(i));
let zeclip = r * Math.sind(v+w) * Math.sind(i);
// add sun's rectangular coordinates
let sr = sunRectangular(day_number);
// convert to ecliptic longitude and latitude
let lon = Math.atan2d(yeclip, xeclip);
lon = Math.revolveDegree(lon);
let lat = Math.atan2d(zeclip, Math.sqrt(xeclip*xeclip + yeclip*yeclip));
let perturbations_in_longitude = 0.812 * Math.sind(2*Mj - 5*Ms - 67.6)
-0.229 * Math.cosd(2*Mj - 4*Ms - 2)
+0.119 * Math.sind(Mj - 2*Ms - 3)
+0.046 * Math.sind(2*Mj - 6*Ms - 69)
+0.014 * Math.sind(Mj - 3*Ms + 32);
let perturbations_in_latitude = -0.020 * Math.cosd(2*Mj - 4*Ms - 2)
+0.018 * Math.sind(2*Mj - 6*Ms - 49);
lon = lon + perturbations_in_longitude;
lon = Math.revolveDegree(lon);
lat = lat + perturbations_in_latitude;
lat = Math.revolveDegree(lat);
// use lat and lon to produce RA and Dec
let xh = r * Math.cosd(lon) * Math.cosd(lat);
let yh = r * Math.sind(lon) * Math.cosd(lat);
let zh = r * Math.sind(lat);
// convert sun's position
let xs = sr.rs * Math.cosd(sr.lonsun);
let ys = sr.rs * Math.sind(sr.lonsun);
// convert from heliocentric to geocentric
let xg = xh + xs;
let yg = yh + ys;
let zg = zh;
// convert to equitorial
let xe = xg;
let ye = yg * Math.cosd(oblecl) - zg * Math.sind(oblecl);
let ze = yg * Math.sind(oblecl) + zg * Math.cosd(oblecl);
// RA and Decl
let RA = Math.atan2d(ye, xe);
RA = Math.revolveDegree(RA);
RA = RA/15;
let Dec = Math.atan2d(ze, Math.sqrt(xe*xe+ye*ye));
let rg = Math.sqrt(xe*xe+ye*ye+ze*ze);
// convert to azimuth and altitude
let HA = sidtime(day_number, longitude, UT) - RA;
HA = HA * 15;
HA = Math.revolveDegree(HA);
x = Math.cosd(HA) * Math.cosd(Dec);
y = Math.sind(HA) * Math.cosd(Dec);
let z = Math.sind(Dec);
let xhor = x * Math.sind(latitude) - z * Math.cosd(latitude);
let yhor = y;
let zhor = x * Math.cosd(latitude) + z * Math.sind(latitude);
let azimuth = Math.atan2d(yhor,xhor) + 180;
let altitude = Math.atan2d(zhor, Math.sqrt(Math.pow(Math.abs(xhor), 2)
+ Math.pow(Math.abs(yhor), 2)));
return{
ra: RA,
decl: Dec,
dist: rg,
alt: altitude,
az: azimuth,
};
}
export function uranus (day_number, latitude, longitude, UT) {
let N = 74.0005 + 1.3978E-5 * day_number; // Long of asc. node
let i = 0.7733 + 1.9E-8 * day_number; // Inclination
let w = 96.6612 + 3.0565E-5 * day_number; // Argument of perihelion
let a = 19.18171 - 1.55E-8 * day_number; // Semi-major axis
let e = 0.047318 + 7.45E-9 * day_number; // eccentricity
let M = 142.5905 + 0.011725806 * day_number; // Mean anomaly Uranus
M = Math.revolveDegree(M);
let Mu = M;
let Ms = 316.9670 + 0.0334442282 * day_number; // Mean anomaly Saturn
Ms = Math.revolveDegree(Ms);
let Mj = 19.8950 + 0.0830853001 * day_number; // Mean anomaly Jupiter
Mj = Math.revolveDegree(Mj);
let oblecl = 23.4393 - 3.563e-7 * day_number; // obliquity of the eliptic
let E = eccentricAnomaly(M, e, 0.0005);
// uranus's rectrangular coordinates
let x = a * (Math.cosd(E) - e);
let y = a * Math.sind(E) * Math.sqrt(1 - e*e);
// convert to distance and true anomaly
let r = Math.sqrt(x*x + y*y);
let v = Math.atan2d(y, x);
// uranus's position in ecliptic coordinates
let xeclip = r * ( Math.cosd(N) * Math.cosd(v+w) - Math.sind(N) *
Math.sind(v+w) * Math.cosd(i));
let yeclip = r * ( Math.sind(N) * Math.cosd(v+w) + Math.cosd(N) *
Math.sind(v+w) * Math.cosd(i));
let zeclip = r * Math.sind(v+w) * Math.sind(i);
// sun's rectangular coordinates
let sr = sunRectangular(day_number);
// convert to ecliptic longitude and latitude
let lon = Math.atan2d(yeclip, xeclip);
lon = Math.revolveDegree(lon);
let lat = Math.atan2d(zeclip, Math.sqrt(Math.pow(Math.abs(xeclip), 2) +
Math.pow(Math.abs(yeclip), 2)));
let perturbations_in_longitude = +0.040 * Math.sind(Ms - 2*Mu + 6)
+0.035 * Math.sind(Ms - 3*Mu + 33)
-0.015 * Math.sind(Mj - Mu + 20);
lon = perturbations_in_longitude + lon;
lon = Math.revolveDegree(lon);
// use lat and lon to produce RA and Dec
let xh = r * Math.cosd(lon) * Math.cosd(lat);
let yh = r * Math.sind(lon) * Math.cosd(lat);
let zh = r * Math.sind(lat);
// convert sun's position
let xs = sr.rs * Math.cosd(sr.lonsun);
let ys = sr.rs * Math.sind(sr.lonsun);
// convert from heliocentric to geocentric
let xg = xh + xs;
let yg = yh + ys;
let zg = zh;
// convert to equitorial
let xe = xg;
let ye = yg * Math.cosd(oblecl) - zg * Math.sind(oblecl);
let ze = yg * Math.sind(oblecl) + zg * Math.cosd(oblecl);
// RA and Decl
let RA = Math.atan2d(ye, xe);
RA = Math.revolveDegree(RA);
RA = RA/15;
let Dec = Math.atan2d(ze, Math.sqrt(xe*xe+ye*ye));
let rg = Math.sqrt(xe*xe+ye*ye+ze*ze);
// convert to azimuth and altitude
let HA = sidtime(day_number, longitude, UT) - RA;
HA = HA * 15;
HA = Math.revolveDegree(HA);
x = Math.cosd(HA) * Math.cosd(Dec);
y = Math.sind(HA) * Math.cosd(Dec);
let z = Math.sind(Dec);
let xhor = x * Math.sind(latitude) - z * Math.cosd(latitude);
let yhor = y;
let zhor = x * Math.cosd(latitude) + z * Math.sind(latitude);
let azimuth = Math.atan2d(yhor,xhor) + 180;
let altitude = Math.atan2d(zhor, Math.sqrt(Math.pow(Math.abs(xhor), 2)
+ Math.pow(Math.abs(yhor), 2)));
return{
ra: RA,
decl: Dec,
dist: rg,
alt: altitude,
az: azimuth,
};
}
export function neptune (day_number, latitude, longitude, UT) {
let N = 131.7806 + 3.0173E-5 * day_number;
let i = 1.7700 - 2.55E-7 * day_number;
let w = 272.8461 - 6.027E-6 * day_number;
let a = 30.05826 + 3.313E-8 * day_number;
let e = 0.008606 + 2.15E-9 * day_number;
let M = 260.2471 + 0.005995147 * day_number;
M = Math.revolveDegree(M);
let oblecl = 23.4393 - 3.563e-7 * day_number; // obliquity of the eliptic
let E = eccentricAnomaly(M, e, 0.0005);
// neptune's rectrangular coordinates
let x = a * (Math.cosd(E) - e);
let y = a * Math.sind(E) * Math.sqrt(1 - e*e);
// convert to distance and true anomaly
let r = Math.sqrt(x*x + y*y);
let v = Math.atan2d(y, x);
// neptune's position in ecliptic coordinates
let xeclip = r * ( Math.cosd(N) * Math.cosd(v+w) - Math.sind(N) * Math.sind(v+w) * Math.cosd(i));
let yeclip = r * ( Math.sind(N) * Math.cosd(v+w) + Math.cosd(N) * Math.sind(v+w) * Math.cosd(i));
let zeclip = r * Math.sind(v+w) * Math.sind(i);
// sun's rectangular coordinates
let sr = sunRectangular(day_number);
// convert to ecliptic longitude and latitude
let lon = Math.atan2d(yeclip, xeclip);
lon = Math.revolveDegree(lon);
let lat = Math.atan2d(zeclip, Math.sqrt(xeclip*xeclip + yeclip*yeclip));
// use lat and lon to produce RA and Dec
let xh = r * Math.cosd(lon) * Math.cosd(lat);
let yh = r * Math.sind(lon) * Math.cosd(lat);
let zh = r * Math.sind(lat);
// convert sun's position
let xs = sr.rs * Math.cosd(sr.lonsun);
let ys = sr.rs * Math.sind(sr.lonsun);
// convert from heliocentric to geocentric
let xg = xh + xs;
let yg = yh + ys;
let zg = zh;
// convert to equitorial
let xe = xg;
let ye = yg * Math.cosd(oblecl) - zg * Math.sind(oblecl);
let ze = yg * Math.sind(oblecl) + zg * Math.cosd(oblecl);
// RA and Decl
let RA = Math.atan2d(ye, xe);
RA = Math.revolveDegree(RA);
RA = RA/15;
let Dec = Math.atan2d(ze, Math.sqrt(xe*xe+ye*ye));
let rg = Math.sqrt(xe*xe+ye*ye+ze*ze);
// convert to azimuth and altitude
let HA = sidtime(day_number, longitude, UT) - RA;
HA = HA * 15;
HA = Math.revolveDegree(HA);
x = Math.cosd(HA) * Math.cosd(Dec);
y = Math.sind(HA) * Math.cosd(Dec);
let z = Math.sind(Dec);
let xhor = x * Math.sind(latitude) - z * Math.cosd(latitude);
let yhor = y;
let zhor = x * Math.cosd(latitude) + z * Math.sind(latitude);
let azimuth = Math.atan2d(yhor,xhor) + 180;
let altitude = Math.atan2d(zhor, Math.sqrt(Math.pow(Math.abs(xhor), 2)
+ Math.pow(Math.abs(yhor), 2)));
return{
ra: RA,
decl: Dec,
dist: rg,
alt: altitude,
az: azimuth,
};
}
export function pluto (day_number, latitude, longitude, UT) {
let S = 50.03 + 0.033459652 * day_number;
let P = 238.95 + 0.003968789 * day_number;
let lonecl = 238.9508 + 0.00400703 * day_number
- 19.799 * Math.sind(P) + 19.848 * Math.cosd(P)
+ 0.897 * Math.sind(2*P) - 4.956 * Math.cosd(2*P)
+ 0.610 * Math.sind(3*P) + 1.211 * Math.cosd(3*P)
- 0.341 * Math.sind(4*P) - 0.190 * Math.cosd(4*P)
+ 0.128 * Math.sind(5*P) - 0.034 * Math.cosd(5*P)
- 0.038 * Math.sind(6*P) + 0.031 * Math.cosd(6*P)
+ 0.020 * Math.sind(S-P) - 0.010 * Math.cosd(S-P);
let latecl = -3.9082
- 5.453 * Math.sind(P) - 14.975 * Math.cosd(P)
+ 3.527 * Math.sind(2*P) + 1.673 * Math.cosd(2*P)
- 1.051 * Math.sind(3*P) + 0.328 * Math.cosd(3*P)
+ 0.179 * Math.sind(4*P) - 0.292 * Math.cosd(4*P)
+ 0.019 * Math.sind(5*P) + 0.100 * Math.cosd(5*P)
- 0.031 * Math.sind(6*P) - 0.026 * Math.cosd(6*P)
+ 0.011 * Math.cosd(S-P);
let r = 40.72
+ 6.68 * Math.sind(P) + 6.90 * Math.cosd(P)
- 1.18 * Math.sind(2*P) - 0.03 * Math.cosd(2*P)
+ 0.15 * Math.sind(3*P) - 0.14 * Math.cosd(3*P);
let xh = r * Math.cosd(lonecl) * Math.cosd(latecl);
let yh = r * Math.sind(lonecl) * Math.cosd(latecl);
let zh = r * Math.sind(latecl);
let sr = sunRectangular(day_number);
let xg = xh + sr.x1;
let yg = yh + sr.y1;
let zg = zh;
let xe = xg;
let ye = yg * Math.cosd(sr.oblecl) - zg * Math.sind(sr.oblecl);
let ze = yg * Math.sind(sr.oblecl) + zg * Math.cosd(sr.oblecl);
let RA = Math.atan2d( ye, xe );
RA = Math.revolveDegree(RA);
RA = RA/15;
let Dec = Math.atan2d( ze, Math.sqrt(xe*xe+ye*ye) );
let rg = Math.sqrt(xe*xe+ye*ye+ze*ze);
// convert to azimuth and altitude
let HA = sidtime(day_number, longitude, UT) - RA;
HA = HA * 15;
HA = Math.revolveDegree(HA);
let x = Math.cosd(HA)*Math.cosd(Dec);
let y = Math.sind(HA)*Math.cosd(Dec);
let z = Math.sind(Dec);
let xhor = x * Math.sind(latitude) - z * Math.cosd(latitude);
let yhor = y;
let zhor = x * Math.cosd(latitude) + z * Math.sind(latitude);
let azimuth = Math.atan2d(yhor,xhor) + 180;
let altitude = Math.atan2d(zhor,
Math.sqrt(Math.pow(Math.abs(xhor), 2) + Math.pow(Math.abs(yhor), 2)));
return{
ra: RA,
decl: Dec,
dist: rg,
alt: altitude,
az: azimuth,
};
}
// Helper functions for Rise and Set times
export function decimalToHM (time) {
let decimalTime = time;
if (decimalTime < 0) {
decimalTime = decimalTime + 24;
}
let hours = addZero(Math.floor(decimalTime) % 24);
let minutes = addZero(Math.floor((Math.round((decimalTime % 1)*100)/100)*60));
let formatted = hours + ":" + minutes;
return (formatted);
}
export function addZero (n) {
return (n < 10 ? '0' : '') + n;
}
// Rise and Set times for Celestial Bodies
export function sunRiseSet (year, month, day, UT, latitude, longitude) {
let h = -0.833;
let d = dayNumber(year, month, day, UT);
let sr = sunRectangular(d);
let sun1 = sun(d, latitude, longitude, UT);
let GMST0 = (sr.L + 180) / 15;
let UT_Sun_in_south = sun1.ra - (sr.L+180)/15 - longitude/15.0;
UT_Sun_in_south = Math.revolveHourAngle(UT_Sun_in_south);
let cos_lha = (Math.sind(h) -
Math.sind(latitude)*Math.sind(sun1.decl))/(Math.cosd(latitude) *
Math.cosd(sun1.decl));
if (cos_lha > 1) {
throw "Sun is always below our altitude limit.";
}
else if (cos_lha < -1) {
throw "Sun is always above our altitude limit.";
}
let LHA = Math.acosd(cos_lha)/15;
let time = new Date();
let srise = UT_Sun_in_south - LHA - time.getTimezoneOffset()/60;
let sset = UT_Sun_in_south + LHA - time.getTimezoneOffset()/60;
let srTime = decimalToHM(srise);
let ssTime = decimalToHM(sset);
return{
rise: srTime,
set: ssTime,
}
}
export function mercriset (year, month, day, UT, latitude, longitude) {
let h = -0.833;
let d = dayNumber(year, month, day, UT);
let sr = sunRectangular(d);
let Mercury = mercury(d, latitude, longitude, UT);
let UT_Planet_in_south = Mercury.ra - (sr.L+180)/15 - longitude/15.0;
UT_Planet_in_south = Math.revolveHourAngle(UT_Planet_in_south);
let cos_lha = (Math.sind(h) -
Math.sind(latitude)*Math.sind(Mercury.decl))/(Math.cosd(latitude) *
Math.cosd(Mercury.decl));
if (cos_lha > 1) {
throw "Mercury is always below our altitude limit.";
}
else if (cos_lha < -1) {
throw "Mercury is always above our altitude limit.";
}
let LHA = Math.acosd(cos_lha)/15.04107;
let mercuryrise = UT_Planet_in_south - LHA;
let mercuryset = UT_Planet_in_south + LHA;
return{
rise: mercuryrise,
set: mercuryset,
}
}
export function mercuryRiseSet (year, month, day, UT, latitude, longitude) {
let h = -0.833;
let d = dayNumber(year, month, day, UT);
let sr = sunRectangular(d);
let Mercury = mercury(d, latitude, longitude, UT);
let UT_Mercury_in_south = Mercury.ra - (sr.L+180)/15 - longitude/15.0;
UT_Mercury_in_south = Math.revolveHourAngle(UT_Mercury_in_south);
let cos_lha = (Math.sind(h) -
Math.sind(latitude)*Math.sind(Mercury.decl))/(Math.cosd(latitude) *
Math.cosd(Mercury.decl));
if (cos_lha > 1) {
throw "Mercury is always below our altitude limit.";
}
else if (cos_lha < -1) {
throw "Mercury is always above our altitude limit.";
}
let LHA = Math.acosd(cos_lha)/15.04107;
let time = new Date();
let mercuryrise = UT_Mercury_in_south - LHA;
let mr1 = mercriset(year,month,day,mercuryrise,latitude,longitude);
let mr2 = mercriset(year,month,day,mr1.rise,latitude,longitude);
let mr3 = mercriset(year,month,day,mr2.rise,latitude,longitude);
let mr4 = mercriset(year,month,day,mr3.rise,latitude,longitude);
let mr5 = mercriset(year,month,day,mr4.rise,latitude,longitude);
mercuryrise = mr5.rise - time.getTimezoneOffset()/60;
mercuryrise = decimalToHM(mercuryrise);
let mercuryset = UT_Mercury_in_south + LHA;
let ms1 = mercriset(year,month,day,mercuryset,latitude,longitude);
let ms2 = mercriset(year,month,day,ms1.set,latitude,longitude);
let ms3 = mercriset(year,month,day,ms2.set,latitude,longitude);
let ms4 = mercriset(year,month,day,ms3.set,latitude,longitude);
let ms5 = mercriset(year,month,day,ms4.set,latitude,longitude);
mercuryset = ms5.set - time.getTimezoneOffset()/60;
mercuryset = decimalToHM(mercuryset);