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orbit.js
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orbit.js
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var Sylvester = require("sylvester");
var ParamHelper = require("./param-helper"),
constants = require("./constants"),
UniversalFormulation = require("./universal-formulation"),
Lagrange = require("./lagrange"),
Laguerre = require("./laguerre");
module.exports = Orbit;
function Orbit(r, v, opts) {
this.r = r;
this.v = v;
this.mu = (opts && opts.mu) || constants.MU;
this.centralBodyRadius = (opts && opts.centralBodyRadius) || constants.EARTH_RADIUS;
}
Orbit.fromParams = function fromParams(params) {
var state = ParamHelper.stateFromParams(params);
return new Orbit(state.r, state.v, {
mu: params.mu,
centralBodyRadius: params.centralBodyRadius
});
};
Orbit.prototype.angularMomentum = function angularMomentum() {
return this.r.cross(this.v);
};
Orbit.prototype.radialVelocity = function radialVelocity() {
return this.r.dot(this.v) / this.r.norm();
};
Orbit.prototype.eccentricity = function eccentricity() {
return this.r.x(
Math.pow(this.v.norm(), 2) - (this.mu / this.r.norm())
).subtract(
this.v.x(this.r.norm() * this.radialVelocity())
).x(1 / this.mu);
};
Orbit.prototype.semimajorAxis = function semimajorAxis() {
var h = this.angularMomentum().norm(),
e = this.eccentricity().norm();
return (Math.pow(h, 2) / this.mu) *
(1 / (1 - Math.pow(e, 2)));
};
Orbit.prototype.semiminorAxis = function semiminorAxis() {
var a = this.semimajorAxis(),
e = this.eccentricity().norm();
return a * Math.sqrt(1 - Math.pow(e, 2));
}
Orbit.prototype.semilatusRectum = function semilatusRectum() {
return Math.pow(this.angularMomentum().norm(), 2) / this.mu;
};
Orbit.prototype.inclination = function inclination() {
var h = this.angularMomentum();
return toDeg(Math.acos(constants.K.dot(h) / h.norm()));
};
Orbit.prototype.nodeLine = function nodeLine() {
return constants.K.cross(this.angularMomentum());
};
Orbit.prototype.rightAscension = function rightAscension() {
var n = this.nodeLine();
if (n.norm() === 0) { return 0; }
var omega = toDeg(Math.acos(n.elements[0] / n.norm()));
return n.elements[1] < 0 ? (360 - omega) : omega;
};
Orbit.prototype.argumentOfPeriapsis = function argumentOfPeriapsis() {
var n = this.nodeLine();
if (n.norm() === 0) { return 0; }
var e = this.eccentricity(),
w = toDeg(Math.acos(n.dot(e) / (n.norm() * e.norm())));
return n.elements[2] < 0 ? (360 - w) : w;
};
Orbit.prototype.trueAnomaly = function trueAnomaly() {
var e = this.eccentricity();
var u = toDeg(Math.acos(e.dot(this.r) / (e.norm() * this.r.norm())));
return this.r.dot(this.v) < 0 ? (360 - u) : u;
};
Orbit.prototype.periapsis = function periapsis() {
var h = this.angularMomentum(),
e = this.eccentricity();
return (Math.pow(h.norm(), 2) / this.mu) * (1 / (1 + e.norm() * Math.cos(0)));
};
Orbit.prototype.apoapsis = function apoapsis() {
var h = this.angularMomentum(),
e = this.eccentricity();
return (Math.pow(h.norm(), 2) / this.mu) * (1 / (1 + e.norm() * Math.cos(Math.PI)));
};
Orbit.prototype.period = function period() {
var a = this.semimajorAxis();
return (2 * Math.PI / Math.sqrt(this.mu)) * Math.sqrt(Math.pow(a, 3));
};
Orbit.prototype.universalAnomaly = function universalAnomaly(dt) {
var a = this.semimajorAxis(),
// initial guess of x
x = Math.sqrt(this.mu) * (dt / a),
r = this.r,
v = this.v,
mu = this.mu,
f = function(x) { return UniversalFormulation.f(x, a, r, v, mu, dt); },
df = function(x) { return UniversalFormulation.dfdt(x, a, r, v, mu); },
d2f = function(x) { return UniversalFormulation.d2fdt(x, a, r, v, mu); };
return Laguerre.solve(x, f, df, d2f);
};
Orbit.prototype.update = function update(dt) {
var x = this.universalAnomaly(dt),
a = this.semimajorAxis(),
z = UniversalFormulation.z(x, a),
r0 = this.r,
v0 = this.v,
mu = this.mu,
// make sure you use the same `z` for calculating `this.r` and
// `this.v`. this can be tricky because `z` depends on `this.r`
// via `a` so we must be careful to not recalculate `z` between
// updating `this.r` and updating `this.v`.
r = r0.x(Lagrange.f(x, z, this.r)).add(v0.x(Lagrange.g(x, z, mu, dt))),
v = r0.x(Lagrange.df(x, z, r, r0, mu)).add(v0.x(Lagrange.dg(x, z, r)));
return new Orbit(r, v, {
mu: mu,
centralBodyRadius: this.centralBodyRadius
});
};
function toDeg(rad) {
return rad * (180 / Math.PI);
}