# ijk2keplerian

Keplerian orbit elements using position and velocity vectors

Since R2019a

## Syntax

``[a,ecc,incl,RAAN,argp,nu,truelon,arglat,lonper] = ijk2keplerian(r_ijk, v_ijk)``

## Description

example

````[a,ecc,incl,RAAN,argp,nu,truelon,arglat,lonper] = ijk2keplerian(r_ijk, v_ijk)` calculates Keplerian orbit elements for given position and velocity vectors in the geocentric equatorial coordinate system.```

## Examples

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Convert the geocentric equatorial coordinate system (IJK) position and velocity to Keplerian orbital elements.

```r_ijk = [-2981784 5207055 3161595]; v_ijk = [-3384 -4887 4843]; [a, ecc, incl, RAAN, argp, nu, truelon, arglat, lonper] =... ijk2keplerian(r_ijk, v_ijk)```
```a = 6.7845e+06 ecc = 9.1950e-04 incl = 51.7528 RAAN = 95.2570 argp = 106.4005 nu = 290.0096 truelon = NaN arglat = NaN lonper = NaN```

## Input Arguments

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Geocentric equatorial position components, specified as a 3-by-1 array, in meters.

Data Types: `double`

Geocentric equatorial velocity components, specified as a 3-by-1 array, in m/s.

Data Types: `double`

## Output Arguments

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Semimajor axis (half of the longest diameter) of the orbit, returned as a scalar, in meters.

Data Types: `double`

Orbit eccentricity (deviation of orbital curve from circular), returned as a scalar.

Data Types: `double`

Inclination (tilt angle) of the orbit, in degrees.

Data Types: `double`

Angle in the equatorial plane from the x-axis to the location of the ascending node (point at which the satellite crosses the equator from south to north), in degrees.

Data Types: `double`

Angle between the CubeSat ascending node and periapsis (closest point of orbit to Earth), in degrees.

Data Types: `double`

Angle between periapsis and current position of CubeSat, in degrees.

Data Types: `double`

Angle between the x-axis and CubeSat position vector, in degrees.

Data Types: `double`

Angle between the ascending node and the CubeSat position vector, in degrees.

Data Types: `double`

Angle between the x-axis and the eccentricity vector, in degrees.

Data Types: `double`

## References

[1] Vallado, D. A. Fundamentals of Astrodynamics and Applications. alg. 5. McGraw-Hill, 1997.

## Version History

Introduced in R2019a