JavaScript Library for Astronomical Calculations. Related to https://github.com/mgreter/ephem.js
Orbits can be created from orbital elements (6 independent parameters) or from state vectors (position and velocity). In both cases we need 6 arguments to fully define an orbit. Most related parameters will be calculated on construction. But certain parameters as the true anomaly are a bit more complex to calculate from orbital elements, if only the mean anomaly is given as initial parameters. They are lazy calculated on demand, either by using the getter or invoking updateElements(true).
To get state vectors for different times we just add a linear factor to the mean anomaly (related to mean motion and period). To get the actual state vectors from the mean anomaly we need to compute the solution for Kepler's Equation via Newton-Raphson solver loop.
Keep in mind that all angular parameters are in rads and that all
other units are linked to each other. This means that you can change
the units by adjusting the gravitational parameter. We use the solar
gravitational parameter by default with the units: au^3/(solm*day^2).
Normally in physics this parameter is measured in m^3/(kg*s^2). All
distance and time units must therefore be in the same units as GM.
// from standard orbital elements
// https://en.wikipedia.org/wiki/Orbital_elements
orbits.push({
name: 'Planet',
e: 0.09331680132087833, // unitless
a: 1.5236773948307722, // au
i: 0.032283817314135946, // rad
O: 0.8649518974751991, // rad
W: -0.4171558510055842, // rad
L: 6.203874882756421 // rad
// default GM is the sun with au and d
// GM: 2.9591220836841438269e-04
});
// satellite orbiting earth
var orbit = new Orbit({
x: 5052.4587, // km
y: 1056.2713, // km
z: 5011.6366, // km
X: 3.8589872, // km/s
Y: 4.2763114, // km/s
Z: -4.8070493, // km/s
// this GM is for the earth in km and s
GM: 398600.44
});
// from orbital state vectors
// https://en.wikipedia.org/wiki/Orbital_state_vectors
new Orbit({
name: 'State',
rx: 1.390712873654179, // au
ry: -0.013411960276849655, // au
rz: -0.034462732955625755, // au
vx: 0.0006714786862244502, // au/d
vy: 0.015187272121968753, // au/d
vz: 0.0003016547612144848, // au/d
});
// from VSOP parameters
// https://en.wikipedia.org/wiki/VSOP_(planets)
new Orbit({
name: 'VSOP',
a: 1.5236773948307722, // au
L: 6.203874882756421, // rad
h: -0.037808407518263365,
k: 0.08531441689241746,
q: 0.01047042574,
p: 0.01228449307
});After construction, most parameters are already calculated. You may access them directly, but it's recommended call their getters instead, to ensure the requested element was really calculated. If you want the most performance you may access them directly though (Just be careful!).
Pretty much every orbital element is stored as a one char parameter. Thus it is important that you make sure you access the correct variable, it is easy to confuse certain variables. Consult the following list if needed:
These can be used as orbital input arguments
i: inclination
e: eccentricity
a: semiMajorAxis
b: semiMinorAxis
l: semilatusRectum
L: meanLongitude
O: ascendingNode
w: argOfPeriapsis
T: timeOfPericenter
W: longitudeOfPericenter
n: meanMotion
M: meanAnomaly
P: orbitalPeriod
A: angularMomentum
GM: gravitationalParameter
PW: apsidalPrecession
PO: nodalPrecessionThese must not be used as orbital input arguments
m: trueAnomaly
B: radialVelocity
E: eccentricAnomalyOnly access them after calling their method once
C: apoapsis, aphelion, apocenter
c: periapsis, perhelion, pericenterAvailable after calling state method.
r: position
v: velocityIn orbital mechanics, eccentric anomaly (E) is an angular parameter that defines the position of a body that is moving along an elliptic Kepler orbit. The eccentric anomaly (E) is one of three angular parameters ("anomalies") that define a position along an orbit, the other two being the true anomaly (m) and the mean anomaly (M).
In celestial mechanics, true anomaly is an angular parameter that defines the position of a body moving along a Keplerian orbit. It is the angle between the direction of periapsis and the current position of the body, as seen from the main focus of the ellipse (the point around which the object orbits).
The radial velocity of an object with respect to a given point is the rate of change of the distance between the object and the point. That is, the radial velocity is the component of the object's velocity that points in the direction of the radius connecting the object and the point. In astronomy, the point is usually taken to be the observer on Earth, so the radial velocity then denotes the speed with which the object moves away from or approaches the Earth.
In celestial mechanics, the eccentricity vector of a Kepler orbit is the dimensionless vector with direction pointing from apoapsis to periapsis and with magnitude equal to the orbit's scalar eccentricity. For Kepler orbits the eccentricity vector is a constant of motion. Its main use is in the analysis of almost circular orbits, as perturbing (non-Keplerian) forces on an actual orbit will cause the osculating eccentricity vector to change continuously. For the eccentricity and argument of periapsis parameters, eccentricity zero (circular orbit) corresponds to a singularity.
Orbit inclination is the minimum angle between a reference plane and the orbital plane or axis of direction of an object in orbit around another object. The inclination is one of the six orbital parameters describing the shape and orientation of a celestial orbit. It is the angular distance of the orbital plane from the plane of reference (usually the primary's equator or the ecliptic), normally stated in degrees. In the Solar System, orbital inclination is usually stated with respect to Earth's orbit.
The orbital eccentricity of an astronomical object is a parameter that determines the amount by which its orbit around another body deviates from a perfect circle. A value of 0 is a circular orbit, values between 0 and 1 form an elliptical orbit, 1 is a parabolic escape orbit, and greater than 1 is a hyperbola. The term derives its name from the parameters of conic sections, as every Kepler orbit is a conic section. It is normally used for the isolated two-body problem, but extensions exist for objects following a rosette orbit through the galaxy.
In geometry, the major axis of an ellipse is its longest diameter: a line segment that runs through the center and both foci, with ends at the widest points of the perimeter. The semi-major axis is on half of the major axis, and thus runs from the centre, through a focus, and to the perimeter. Essentially, it is the radius of an orbit at the orbit's two most distant points. For the special case of a circle, the semi-major axis is the radius. One can think of the semi-major axis as an ellipse's long radius. The length of the semi-major axis a of an ellipse is related to the semi-minor axis's length b through the eccentricity e and the semilatus rectum ℓ.
The semi-minor axis b is related to the semi-major axis a through the eccentricity e and the semi-latus rectum ℓ.
The semi-latus rectum ℓ is related to the semi-major axis a through the eccentricity e and the semi-minor axis b.
The point of a body's elliptical orbit about the system's centre of mass where the distance between the body and the centre of mass is at its maximum. For some celestial bodies, specialised terms are used (aphelion/apogee).
The point of a body's elliptical orbit about the system's centre of mass where the distance between the body and the centre of mass is at its minimum. For some celestial bodies, specialised terms are used (perihelion/perigee).
Mean longitude is the ecliptic longitude at which an orbiting body could be found if its orbit were circular and free of perturbations. While nominally a simple longitude, in practice the mean longitude is a hybrid angle.
The longitude of the ascending node (☊ or Ω) is one of the orbital elements used to specify the orbit of an object in space. It is the angle from a reference direction, called the origin of longitude, to the direction of the ascending node, measured in a reference plane. The ascending node is the point where the orbit of the object passes through the plane of reference.
The argument of periapsis (also called argument of perifocus or argument of pericenter), is one of the orbital elements (ω) of an orbiting body. Parametrically, ω is the angle from the body's ascending node to its periapsis, measured in the direction of motion.
The time of pericenter passage when the orbiting body passes through the pericenter, closest to the central body. The mean anomaly is 0.0 when the orbiting body is at pericenter, so defining the orbital elements at the epoch T (the time of the pericenter passage) eliminates the need to determine the mean anomaly.
In celestial mechanics, the longitude of the periapsis (ϖ) of an orbiting body is the longitude (measured from the point of the vernal equinox) at which the periapsis (closest approach to the central body) would occur if the body's inclination were zero. For motion of a planet around the Sun, this position could be called longitude of perihelion. The longitude of periapsis is a compound angle, with part of it being measured in the plane of reference and the rest being measured in the plane of the orbit. Likewise, any angle derived from the longitude of periapsis (e.g. mean longitude and true longitude) will also be compound.
In orbital mechanics, mean motion is the angular speed required for a body to complete one orbit, assuming constant speed in a circular orbit which completes in the same time as the variable speed, elliptical orbit of the actual body.
In a closed system, no torque can be exerted on any matter without the exertion on some other matter of an equal and opposite torque. Hence, angular momentum can be exchanged between objects in a closed system, but total angular momentum before and after an exchange remains constant (is conserved)
In celestial mechanics, the mean anomaly is an angle used in calculating the position of a body in an elliptical orbit in the classical two-body problem. It is the angular distance from the pericenter which a fictitious body would have if it moved in a circular orbit, with constant speed, in the same orbital period as the actual body in its elliptical orbit. It is also the product of mean motion and time since pericenter passage.
The orbital period is the time taken for a given object to make one complete orbit around another object. When mentioned without further qualification in astronomy this refers to the sidereal period of an astronomical object, which is calculated with respect to the stars.
In celestial mechanics, the standard gravitational parameter μ of a celestial body is the product of the gravitational constant G and the mass M of the body. For several objects in the Solar System, the value of μ is known to greater accuracy than either G or M. The SI units of the standard gravitational parameter are m3 s−2. However, units of km3 s−2 are frequently used in the scientific literature and in spacecraft navigation. AstroJS normally will use units of AU3 and julian days or years (e.g. AstroJS.GMJY).
In celestial mechanics, apsidal precession (or apsidal advance) is the precession (gradual rotation) of the line connecting the apsides (line of apsides) of an astronomical body's orbit. The apsides are the orbital points closest (periapsis) and farthest (apoapsis) from its primary body. The apsidal precession is the first time derivative of the argument of periapsis, one of the six main orbital elements of an orbit. Apsidal precession is considered positive when the orbit's axis rotates in the same direction as the orbital motion. An apsidal period is the time interval required for an orbit to precess through 360°.
Nodal precession is the precession of the orbital plane of a satellite around the rotational axis of an astronomical body such as Earth. This precession is due to the non-spherical nature of a rotating body, which creates a non-uniform gravitational field. The direction of precession is opposite the direction of revolution.
In chronology and periodization, an epoch or reference epoch is an instant in time chosen as the origin of a particular calendar era. The "epoch" serves as a reference point from which time is measured.
// q: sin(i/2)*cos(O) (vsop)
q = function vsopPeriapsis()
// p: sin(i/2)*sin(O) (vsop)
p = function vsopApoapsis()
// k: e*cos(W) (vsop)
k = function vsopK()
// h: e*sin(W) (vsop)
h = function vsopH()
Descriptions taken from https://en.wikipedia.org
Calculate the apparent sidereal time at the meridian of Greenwich of a given date.
Calculate the mean sidereal time at the meridian of Greenwich of a given date.
Calculate nutation of longitude and obliquity in degrees from Julian Ephemeris Day
One to one implementations from libnova
- Cartesian (x, y, z)
- Spherical (r, θ, φ)
- Cylindrical (ρ, φ, z)
Some variables are the same in multiple representations (z and φ). For the
conversion between cylindrical and Cartesian coordinates, it is convenient to
assume that the reference plane of the former is the Cartesian x–y plane (with
equation z = 0), and the cylindrical axis is the Cartesian z axis. Then the z
coordinate is the same in both systems, and the correspondence between
cylindrical (ρ,φ) and Cartesian (x,y) are the same as for polar coordinates.
// cartesian (preferred)
new Coord({
x: 4.001168777115359,
y: 2.9385853724645656,
z: -0.10178505133708564
});
// spherical with elevation
// this is the VSOP87 format
new Coord({
r: 4.9653867444245865, // radius (r)
l: 36.29468623590961 * DEG2RAD, // phi (φ)
b: -1.1745809849948283 * DEG2RAD, // theta (θ)
});
// spherical with inclination
new Coord({
r: 4.9653797207164, // radius (r)
l: 36.29468623590961 * DEG2RAD, // phi (φ)
i: 91.17458536812916 * DEG2RAD, // theta (θ)
});
// cylindrical
new Coord({
p: 4.9643363679575, // radial dist (ρ)
l: 36.29474187359682 * DEG2RAD, // azimuth (φ)
z: -5.831853859137424 * DEG2RAD // height (z)
});p: radial distance ρ is the Euclidean distance from the z axis to the point P.l: The azimuth φ is the angle between the reference direction on the chosen plane and the line from the origin to the projection of P on the plane.z: The height z is the signed distance from the chosen plane to the point P. Same as the cartesian z value.x: Cartesian x value.y: Cartesian y value.b: Spherical θ as elevation.i: Spherical θ as inclination.r: Spherical radius.
Return Cartesian Coordinates
Return Spherical Coordinates
Return Cylindrical Coordinates
Ecliptic to Equatorial Coordinates; Pass obliquity of ecliptic (axial tilt)
Equatorial to Ecliptic Coordinates; Pass obliquity of ecliptic (axial tilt)
Galactic to Equatorial Coordinates
Equatorial to Galactic Coordinates