ootk-core
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Orbital Object Toolkit. A modern typed replacement for satellite.js including SGP4 propagation, TLE parsing, Sun and Moon calculations, and more.
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JavaScript
/**
* @author Theodore Kruczek.
* @license MIT
* @copyright (c) 2022-2025 Theodore Kruczek Permission is
* hereby granted, free of charge, to any person obtaining a copy of this
* software and associated documentation files (the "Software"), to deal in the
* Software without restriction, including without limitation the rights to use,
* copy, modify, merge, publish, distribute, sublicense, and/or sell copies of
* the Software, and to permit persons to whom the Software is furnished to do
* so, subject to the following conditions:
*
* The above copyright notice and this permission notice shall be included in
* all copies or substantial portions of the Software.
*
* THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
* IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
* FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
* AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
* LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
* OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
* SOFTWARE.
*/
import { earthGravityParam, MINUTES_PER_DAY, TAU } from '../utils/constants.js';
import { newtonM } from '../utils/functions.js';
import { ClassicalElements } from './ClassicalElements.js';
/**
* Equinoctial elements are a set of orbital elements used to describe the
* orbits of celestial bodies, such as satellites around a planet. They provide
* an alternative to the traditional Keplerian elements and are especially
* useful for avoiding singularities and numerical issues in certain types of
* orbits.
*
* Unlike Keplerian elements, equinoctial elements don't suffer from
* singularities at zero eccentricity (circular orbits) or zero inclination
* (equatorial orbits). This makes them more reliable for numerical simulations
* and analytical studies, especially in these edge cases.
* @see https://faculty.nps.edu/dad/orbital/th0.pdf
*/
export class EquinoctialElements {
epoch;
/** The semi-major axis of the orbit in kilometers. */
a;
/** The h component of the eccentricity vector. */
h;
/** The k component of the eccentricity vector. */
k;
/** The p component of the ascending node vector. */
p;
/** The q component of the ascending node vector. */
q;
/** The mean longitude of the orbit in radians. */
lambda;
/** The gravitational parameter of the central body in km³/s². */
mu;
/** The retrograde factor. 1 for prograde orbits, -1 for retrograde orbits. */
I;
constructor({ epoch, h, k, lambda, a, p, q, mu, I }) {
this.epoch = epoch;
this.h = h;
this.k = k;
this.lambda = lambda;
this.a = a;
this.p = p;
this.q = q;
this.mu = mu ?? earthGravityParam;
this.I = I ?? 1;
}
/**
* Returns a string representation of the EquinoctialElements object.
* @returns A string representation of the EquinoctialElements object.
*/
toString() {
return [
'[EquinoctialElements]',
` Epoch: ${this.epoch}`,
` a: ${this.a} km`,
` h: ${this.h}`,
` k: ${this.k}`,
` p: ${this.p}`,
` q: ${this.q}`,
` lambda: ${this.lambda} rad`,
].join('\n');
}
/**
* Gets the semimajor axis.
* @returns The semimajor axis in kilometers.
*/
get semimajorAxis() {
return this.a;
}
/**
* Gets the mean longitude.
* @returns The mean longitude in radians.
*/
get meanLongitude() {
return this.lambda;
}
/**
* Calculates the mean motion of the celestial object.
* @returns The mean motion in units of radians per second.
*/
get meanMotion() {
return Math.sqrt(this.mu / this.a ** 3);
}
/**
* Gets the retrograde factor.
* @returns The retrograde factor.
*/
get retrogradeFactor() {
return this.I;
}
/**
* Checks if the orbit is prograde.
* @returns True if the orbit is prograde, false otherwise.
*/
isPrograde() {
return this.I === 1;
}
/**
* Checks if the orbit is retrograde.
* @returns True if the orbit is retrograde, false otherwise.
*/
isRetrograde() {
return this.I === -1;
}
/**
* Gets the period of the orbit.
* @returns The period in minutes.
*/
get period() {
const periodSec = (TAU * Math.sqrt(this.semimajorAxis ** 3 / this.mu));
return (periodSec / 60);
}
/**
* Gets the number of revolutions per day.
* @returns The number of revolutions per day.
*/
get revsPerDay() {
return MINUTES_PER_DAY / this.period;
}
/**
* Converts the equinoctial elements to classical elements.
* @returns The classical elements.
*/
toClassicalElements() {
const a = this.semimajorAxis;
const e = Math.sqrt(this.k * this.k + this.h * this.h);
const i = Math.PI * ((1.0 - this.I) * 0.5) + 2.0 * this.I * Math.atan(Math.sqrt(this.p * this.p + this.q * this.q));
const o = Math.atan2(this.p, this.q);
const w = Math.atan2(this.h, this.k) - this.I * Math.atan2(this.p, this.q);
const m = this.lambda - this.I * o - w;
const v = newtonM(e, m).nu;
return new ClassicalElements({
epoch: this.epoch,
semimajorAxis: a,
eccentricity: e,
inclination: i,
rightAscension: o,
argPerigee: w,
trueAnomaly: v,
mu: this.mu,
});
}
/**
* Converts the equinoctial elements to position and velocity.
* @returns The position and velocity in classical elements.
*/
toPositionVelocity() {
return this.toClassicalElements().toPositionVelocity();
}
}
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