# Orbital Elements

Creation date: 2018-09-24 16:07:14 Update date: 2018-09-27 18:25:00

Policy: Expert Review

Authority: CCSDS.MOIMS.NAV

OID: 1.3.112.4.57.5

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## Contents

15 records in registry

1.3.112.4.57.5
Orbital Elements

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Details Status Name Description And Reference Nomenclature Default Units/Type References OID

Provisional

Spherical 6-element set comprised of: right ascension +E°, declination +N°, inertial flight path angle measured from the radial direction to inertial velocity direction (e.g. 90° for circular orbit), inertial azimuth angle measured from local North to projection of inertial velocity in local horizontal plane, radius magnitude, and velocity magnitude.

$$\alpha, \delta, \beta, A, r, v$$

$$4 \times degrees,$$
$$1 \times km,$$
$$1 \times \frac{km}{s}$$

1.3.112.4.57.5.1

Provisional

CARTP

Cartesian 3-element position (only) orbit state

X, Y, Z

$$3 \times km$$

1.3.112.4.57.5.2

Provisional

KEPLERIAN

Keplerian 6-element classical set (semi-major axis, eccentricity, inclination, right ascension of the ascending node, argument of perigee, and true anomaly).

$$a, e, i, \Omega, \omega, \nu$$

$$1 \times km,$$
$$1 \times NonDim,$$
$$4 \times degrees$$

1.3.112.4.57.5.11

Provisional

CARTPV

Cartesian 6-element position and velocity orbit state

X, Y, Z,
XD, YD, ZD

$$3 \times km,$$
$$3 \times \frac{km}{s}$$

1.3.112.4.57.5.3

Provisional

CARTPVA

Cartesian 9-element position, velocity, and acceleration orbit state

X, Y, Z,
XD, YD, ZD, XDD, YDD, ZDD

$$3 \times km,$$
$$3 \times \frac{km}{s},$$
$$3 \times \frac{km}{s^2}$$

1.3.112.4.57.5.4

Provisional

DELAUNAY

Delaunay elements employ a set of canonical action-angle variables, which are commonly used in general perturbation theories. The element set consists of three conjugate action-angle pairs. Lower case letters represent the angles while upper case letters represent the conjugate actions. Delaunay variables coordinate type is not available if a fixed coordinate system is selected. Elements L, G, and H are expressed in terms of distance squared divided by time, where distance is measured in standard units and time is measured in seconds, where “L” is related to the two-body orbital energy, “G” is the magnitude of the orbital angular momentum, “H” is the Z component of the orbital angular momentum. The elements l, g, and h are angles, where l is the mean anomaly, g is the argument of perigee, and h is the right ascension of the ascending node.

L, G, H,
l, g, h

$$3 \times \frac{km^2}{s},$$
$$3 \times degrees$$

1.3.112.4.57.5.5

Provisional

DELAUNAYMOD

Modified Delaunay variables, where the L, G, and H “action” variables of the Delaunay element set defined above are divided by the square root of the central-body gravitational constant, yielding a geometric version of the Delaunay set that is independent of the central body.

Lm, Gm, Hm,
lm, gm, hm

$$3 \times \sqrt{km},$$
$$3 \times degrees$$

1.3.112.4.57.5.6

Provisional

EIGVAL3EIGVEC3

12-element eigenvalue/eigenvector representation time history corresponding to the 3x3 position covariance time history. The set consists of the three (major, medium, and minor) eigenvalues in descending order, and the corresponding three eigenvectors matching the major, medium, and minor eigenvalues.

EigMaj,
EigMed,
EigMin,
EigVecMaj,
EigVecMed,
EigVecMin

$$3 \times km,$$
$$9 \times NonDim$$

1.3.112.4.57.5.7

Provisional

GEODETIC

Geodetic elements (longitude, geodetic latitude, fixed frame flight path angle, fixed frame azimuth, altitude above oblate spheroid, and velocity relative to the fixed frame.

$$\lambda, \Phi_{GD}, \beta, A, h, v_{rel}$$

$$4 \times degrees,$$
$$1 \times km,$$
$$1 \times \frac{km}{s}$$

1.3.112.4.57.5.10

Provisional

EQUINOCTIALMOD

Modified equinoctial seven-element set, where semi-major axis has been replaced by semi-latus rectum “p” = a (1-$$e^2$$), and where Mean Anomaly has been replaced by True Anomaly in the “L” term. The seventh element specifies the retrograde factor [$$f_r$$ = ±1] as defined in David A. Vallado, Fundamentals of Astrodynamics and Applications, 4th Ed., Microcosm Press and Springer, ISBN 978-1881883180.

$$[p=a(1-e^2)], a_f, a_g, \left\{ L' = (\nu+\omega+f_r\Omega)\right\}, \chi, \psi, f_r$$

$$1 \times km,$$
$$2 \times NonDim,$$
$$1 \times degrees,$$
$$2 \times NonDim,$$
$$1 \times (\pm1)$$

1.3.112.4.57.5.9

Provisional

KEPLERIANMEAN

Keplerian 6-element classical set (semi-major axis, eccentricity, inclination, right ascension of the ascending node, argument of perigee, and mean anomaly).

$$a, e, i, \Omega, \omega, M$$

$$1 \times km,$$
$$1 \times NonDim,$$
$$4 \times degrees$$

1.3.112.4.57.5.12

Provisional

LDBARV

Modified spherical 6-element set (Earth longitude +E°, declination +N°, inertial flight path angle measured from the radial direction to inertial velocity direction (e.g. 90° for circular orbit), inertial azimuth angle measured from local North to projection of inertial velocity in local horizontal plane, radius magnitude, and velocity magnitude)

$$\lambda, \delta, \beta, A, r, v$$

$$4 \times degrees,$$
$$1 \times km,$$
$$1 \times \frac{km}{s}$$

1.3.112.4.57.5.13

Provisional

ONSTATION

A geosynchronous on-station-tailored set of orbital elements consisting of semi-major axis, x and y components of the eccentricity vector, x and y components of the inclination vector, and true longitude.

$$a, e_x, e_y, i_x, i_y, \lambda$$

$$km,$$
$$4 \times NonDim,$$
$$1 \times degrees$$

1.3.112.4.57.5.14

Provisional

POINCARE

Canonical counterpart of equinoctial 6-element set. See David A. Vallado, Fundamentals of Astrodynamics and Applications, 4th Ed., Microcosm Press and Springer, ISBN 978-1881883180.

$$(\lambda_M=M+\omega+\Omega), g_p, h_p, L_p, G_p, H_p$$

$$1 \times degrees,$$
$$2 \times \frac{km}{s^{0.5}},$$
$$1 \times \frac{km^2}{s},$$
$$2 \times \frac{km}{s^{0.5}}$$

1.3.112.4.57.5.15

Provisional

EQUINOCTIAL

Equinoctial elements (Broucke and Cefola, 1972) are popular because they do not suffer from the singularity problems that classical and other elements do. This standardized equinoctial seven-element set is adopted from the definition contained in David A. Vallado, Fundamentals of Astrodynamics and Applications, 4th Ed., Microcosm Press and Springer, ISBN 978-1881883180. The first six equinoctial elements have a singularity for exact 180º inclinations, which is overcome by the addition of a seventh element which specifies the retrograde factor [$$f_r$$ = ±1, where $$f_r$$ = 1 denotes direct orbits (inclination<=90°), -1 for retrograde orbits (inclination>90°)]. Note that some centers switch the retrograde factor (-1) only for exact retrograde orbits (switching the singularity for that case to an inclination of 0º), while others switch this retrograde factor to (-1) for any/all retrograde orbits.

$$[a, a_f, a_g, L=(M+\omega+f_r\Omega), \chi, \psi, f_r$$

$$1 \times km,$$
$$2 \times NonDim,$$
$$1 \times degrees,$$
$$2 \times NonDim,$$
$$1 \times (\pm1)$$

1.3.112.4.57.5.8