Convert Keplerian Orbital Elements to a State Vector

Convert orbital elements to a state vector, or a state vector back to orbital elements.
Updated 12 Dec 2013

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Most readily available Keplerian orbital element conversion utilities do not address circular or parabolic orbits. This set of routines will address the complete spectrum of orbits from a circular equatorial orbit to a retrograde hyperbolic orbit without error. All functionality is vectorized for computational efficiency.

Example Function Call One:
>> [r_ECI v_ECEF] = orb2rv(p,e,i,O,o,nu);

p = semilatus rectum (km) [1 x N]
e = Eccentricity [1 x N]
i = Inclination (rad) [1 x N]
O = Right Ascension of the Ascending Node (rad) [1 x N]
o = Argument of Perigee (rad) [1 x N]
nu = True Anomaly (rad) [1 x N]

Example Function Call Two:
>>[a,e,i,O,o,nu] = rv2orb(r_ECI,v_ECI)

r = Position State Vector in km (ECI) [3 x N]
v = Velocity State Vector in km/s (ECI) [3 x N]

For those orbits which are equatorial or circular, the following full form function calls are necessary:

Convert state vector to full set of orbital elements:
>>[a,e,i,O,o,nu,truLon,argLat,lonPer,p] = rv2orb(r_ECI,v_ECI);

Convert full set of orbital elements back to a state vector:
>>[r_ECI,v_ECI] = orb2rv(p,e,i,O,o,nu,truLon,argLat,lonPer);

truLon = True Longitude (rad) [1 x N]
argLat = Argument of Latitude (rad) [1 x N]

Cite As

Darin Koblick (2024). Convert Keplerian Orbital Elements to a State Vector (, MATLAB Central File Exchange. Retrieved .

MATLAB Release Compatibility
Created with R2010b
Compatible with any release
Platform Compatibility
Windows macOS Linux

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Version Published Release Notes

Updated outputs for orbital parameters when state vector is circular and equatorial.