Orbit Element Types

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The orbital elements are six independent parameters that describe the shape and orientation of a Spacecraft's orbit. The orbital element systems available in FreeFlyer are described below. The ElementConvert function can be used to convert orbital elements between the different systems.

 

FreeFlyer supports the following orbit element types, described on this page:

 

Cartesian

Keplerian

Spherical

Spherical (Latitude, Longitude)

Nonsingular Keplerian

Equinoctial

Modified Equinoctial

Brouwer-Lyddane Mean

J2 Brouwer-Lyddane

NORAD

 

The diagram below illustrates the orbital element systems that are available for each central body in FreeFlyer. Note that the Spherical (Latitude, Longitude), Brouwer-Lyddane Mean, J2 Brouwer-Lyddane, and NORAD elements are intended for use only when the Spacecraft's central body is Earth.

 

 

Cartesian


The Cartesian element set defines the position and velocity of a Spacecraft with respect to the origin of an inertial rectangular coordinate system. Positions and velocities are expressed by their components along the three principal axes of the MJ2000 Earth Equator reference frame.

 

Element

Description

X

Position along the X-axis

Y

Position along the Y-axis

Z

Position along the Z-axis

VX

Velocity along the X-axis

VY

Velocity along the Y-axis

VZ

Velocity along the Y-axis

 

// Assign values to the Cartesian orbital elements with respect to the MJ2000 Earth Equator frame

Spacecraft1.X = -3410.673;

Spacecraft1.Y = 5950.957;

Spacecraft1.Z = -1788.627;

Spacecraft1.VX = 1.893;

Spacecraft1.VY = -1.071;

Spacecraft1.VZ = -7.176;

 

You can also set and get a Spacecraft's or CelestialObject's Cartesian state with respect to other reference frames using the methods:

 

Spacecraft.SetCartesianState() and Spacecraft.GetCartesianState()

CelestialObject.SetCartesianState() and CelestialObject.GetCartesianStateAtEpoch()

 

 

Keplerian


 

Element

Description

A

Semi-major axis

E

Eccentricity

I

Inclination

RAAN

Right Ascension of the Ascending Node

W

Argument of Periapsis

TA

True Anomaly

 

// Assign values to the Keplerian orbital elements with respect to the MJ2000 Earth Equator frame

Spacecraft1.A = 7088.42;

Spacecraft1.E = 5.17E-08;

Spacecraft1.I = 98.22;

Spacecraft1.RAAN = 301.97;

Spacecraft1.W = 310.24;

Spacecraft1.TA = 244.52;

 

You can also set and get a Spacecraft's or CelestialObject's Keplerian state with respect to other reference frames using the methods:

 

Spacecraft.SetKeplerianState() and Spacecraft.GetKeplerianState()

CelestialObject.SetKeplerianState() and CelestialObject.GetKeplerianStateAtEpoch()

 

 

Spherical


Spherical orbital elements referenced to the MJ2000 Earth Equator reference frame.

 

Element

Description

Radius

Magnitude of the position vector

RA

Right Ascension

DEC

Declination

Vi

Magnitude of the velocity vector

Azimuth

Velocity azimuth angle

VFPA

Vertical Flight Path Angle

 

// Assign values to the Spherical orbital elements

Spacecraft1.SphericalRadius = 7088.42;

Spacecraft1.RA = 119.81;

Spacecraft1.DEC = -14.61;

Spacecraft1.Vi = 7.498;

Spacecraft1.SphericalAzimuth = 188.50;

Spacecraft1.VerticalFPA = 90.00;

 

 

Spherical (Latitude, Longitude)


This element set is intended for use only when the Spacecraft's central body is Earth.

 

Element

Description

Radius

Magnitude of the position vector

Latitude

Geodetic latitude of the spacecraft's subsatellite point

Longitude

Longitude of the spacecraft's subsatellite point

Vi

Magnitude of the velocity vector

Azimuth

Velocity azimuth angle

HFPA

Horizontal Flight Path Angle

 

// Assign values to the Spherical Latitude/Longitude orbital elements

Spacecraft1.LatLongRadius = 7088.42;

Spacecraft1.Latitude = -14.72;

Spacecraft1.Longitude = 64.13;

Spacecraft1.LatLongVi = 7.58;

Spacecraft1.LatLongAzimuth = 192.29;

Spacecraft1.HorizontalFPA = 0;

 

 

Nonsingular Keplerian


 

Element

Description

A

Semi-major axis

e1

E cos(RAAN + W)

e2

E sin(RAAN + W)

e3

sin(I/2) sin(RAAN)

e4

sin(I/2) cos(RAAN)

e5

RAAN + W + MA

 

// Assign values to the Nonsingular Keplerian orbital elements

Spacecraft1.NonSingularA = 7070.81;

Spacecraft1.NonSingularE1 = 0.00181;

Spacecraft1.NonSingularE2 = -0.00170;

Spacecraft1.NonSingularE3 = -0.641;

Spacecraft1.NonSingularE4 = 0.400;

Spacecraft1.NonSingularE5 = 136.72;

 

 

Equinoctial


 

Direct Equinoctial Reference Frame

Direct Equinoctial Reference Frame

 

Note: The equinoctial reference frame in FreeFlyer is the direct (prograde) equinoctial reference frame. This element set has a singularity at an inclination of 180 degrees.

 

Element

Description

A

Keplerian semi-major axis

h

E sin(RAAN + W)

k

E cos(RAAN + W)

p

tan(I/2) sin(RAAN)

q

tan(I/2) cos(RAAN)

Longitude

Mean Longitude: RAAN + W + MA

 

// Assign values to the Equinoctial orbital elements

Spacecraft1.EquinoctialA = 7070.81;

Spacecraft1.EquinoctialH = 0.00237;

Spacecraft1.EquinoctialK = 0.000731;

Spacecraft1.EquinoctialP = -0.735;

Spacecraft1.EquinoctialQ = 0.458;

Spacecraft1.EquinoctialLongitude = 4.412;

 

 

Modified Equinoctial


 

Element

Description

p

A(1 - E2)

f

E cos(RAAN + W)

g

E sin(RAAN + W)

h

tan(I/2) cos(RAAN)

k

tan(I/2) sin(RAAN)

L

True Longitude: RAAN + W + TA

 

// Assign values to the Modified Equinoctial orbital elements

Spacecraft1.ModifiedEquinoctialP = 7070.766;

Spacecraft1.ModifiedEquinoctialF = 0.00180;

Spacecraft1.ModifiedEquinoctialG = -0.00170;

Spacecraft1.ModifiedEquinoctialH = 0.610;

Spacecraft1.ModifiedEquinoctialK = -0.980;

Spacecraft1.ModifiedEquinoctialL = 136.64;

 

 

Brouwer-Lyddane Mean


This element set is intended for use only when the Spacecraft's central body is Earth.

 

Element

Description

A

Mean semi-major axis

E

Mean eccentricity

I

Mean inclination

RAAN

Mean Right Ascension of the Ascending Node

W

Mean Argument of Periapsis

MA

Mean Anomaly

 

// Assign values to the Brouwer-Lyddane Mean orbital elements

Spacecraft1.BL_A = 7088.42;

Spacecraft1.BL_E = 5.17E-08;

Spacecraft1.BL_I = 98.22;

Spacecraft1.BL_RAAN = 301.97;

Spacecraft1.BL_W = 310.24;

Spacecraft1.BL_MA = 244.52;

 

 

J2 Brouwer-Lyddane


This element set is intended for use only when the Spacecraft's central body is Earth.

 

Element

Description

A

J2 Mean semi-major axis

E

J2 Mean eccentricity

I

J2 Mean inclination

RAAN

J2 Mean Right Ascension of the Ascending Node

W

J2 Mean Argument of Periapsis

MA

J2 Mean Anomaly

 

// Assign values to the J2 Brouwer-Lyddane Mean orbital elements

Spacecraft1.BLJ2A = 7088.42;

Spacecraft1.BLJ2E = 5.17E-08;

Spacecraft1.BLJ2I = 98.22;

Spacecraft1.BLJ2RAAN = 301.97;

Spacecraft1.BLJ2W = 310.24;

Spacecraft1.BLJ2MA = 244.52;

 

 

Norad


This element set is intended for use only when the Spacecraft's central body is Earth.

 

Element

Description

I

Mean inclination

RAAN

Mean Right Ascension of the Ascending Node

E

Mean Eccentricity

W

Mean Argument of Perigee

MA

Mean Anomaly

N

Mean Motion

 

// Assign values to the Norad orbital elements

Spacecraft1.NoradI = 98.25;

Spacecraft1.NoradRAAN = 302.04;

Spacecraft1.NoradE = 0.00264;

Spacecraft1.NoradW = 357.18;

Spacecraft1.NoradMA = 197.55;

Spacecraft1.NoradMeanMotion = 14.61;

 

 

See Also


Orbit Reference Frames

Central Body

ElementConvert