astrodynx.true_anomaly

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astrodynx.true_anomaly#

astrodynx.true_anomaly(pos_vec, e_vec)[source]#

Returns the true anomaly of a two-body orbit.

Parameters:

  • pos_vec (ArrayLike) – (…, 3) position vector of the object in the two-body system.

  • e_vec (ArrayLike) – (…, 3) eccentricity vector of the object in the two-body system, which shape broadcast-compatible with pos_vec.

Return type:

Array

Returns:

The true anomaly of the orbit.

Notes

The true anomaly is calculated using equation:

\[ f = \arctan2(\|\boldsymbol{e}\times \boldsymbol{r}\|, \boldsymbol{e} \cdot \boldsymbol{r}) \]
where \(f\) is the true anomaly, \(\boldsymbol{e}\) is the eccentricity vector, and \(\boldsymbol{r}\) is the position vector.

References

Vallado, 2013, pp.118.

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