astrodynx.coe2rv

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astrodynx.coe2rv#

astrodynx.coe2rv(p, e, incl, raan, argp, true_anom, mu=1)[source]#

Transfer classical orbital elements to position and velocity vectors.

Parameters:

  • p (ArrayLike) – Semiparameter of the orbit.

  • e (ArrayLike) – Eccentricity of the orbit; shape broadcast-compatible with p.

  • incl (ArrayLike) – Inclination of the orbit; shape broadcast-compatible with p and e.

  • raan (ArrayLike) – Right ascension of the ascending node; shape broadcast-compatible with p, e, and incl.

  • argp (ArrayLike) – Argument of periapsis; shape broadcast-compatible with p, e, incl, and raan.

  • true_anom (ArrayLike) – True anomaly; shape broadcast-compatible with p, e, incl, raan, and argp.

  • mu (ArrayLike) – Gravitational parameter of the central body; shape broadcast-compatible with p, e, incl, raan, argp, and true_anom.

Return type:

tuple[Array, Array]

Returns:

The position and velocity vectors of the object in the two-body system.

Notes

The position and velocity vectors are calculated using the following equations:

\[\begin{split} \begin{aligned} \boldsymbol{r} &= \boldsymbol{R}_z(-\Omega) \boldsymbol{R}_x(-i) \boldsymbol{R}_z(-\omega) \boldsymbol{r}_{pf} \\ \boldsymbol{v} &= \boldsymbol{R}_z(-\Omega) \boldsymbol{R}_x(-i) \boldsymbol{R}_z(-\omega) \boldsymbol{v}_{pf} \end{aligned} \end{split}\]
where \(\boldsymbol{R}_z\) and \(\boldsymbol{R}_x\) are the rotation matrices about the z-axis and x-axis. And, \boldsymbol{r}_{pf} and \boldsymbol{v}_{pf} are the position and velocity vectors in the perifocal frame:
\[\begin{split} \begin{aligned} \boldsymbol{r}_{pf} &= \frac{p}{1 + e \cos(f)} \begin{bmatrix} \cos(f) \\ \sin(f) \\ 0 \end{bmatrix} \\ \boldsymbol{v}_{pf} &= \sqrt{\frac{\mu}{p}} \begin{bmatrix} -\sin(f) \\ e + \cos(f) \\ 0 \end{bmatrix} \end{aligned} \end{split}\]
where \(p\) is the semiparameter, \(e\) is the eccentricity, \(f\) is the true anomaly, and \(\mu\) is the gravitational parameter.

References

Vallado, 2013, pp.119.

Examples

A simple example:

>>> import jax.numpy as jnp
>>> import astrodynx as adx
>>> p = 1.0
>>> e = 0.0
>>> incl = 0.0
>>> raan = 0.0
>>> argp = 0.0
>>> true_anom = 0.0
>>> mu = 1.0
>>> adx.coe2rv(p, e, incl, raan, argp, true_anom, mu)
(Array([1., 0., 0.], dtype=float32, weak_type=True), Array([0., 1., 0.], dtype=float32, weak_type=True))

With broadcasting, you can calculate the position and velocity vectors for multiple sets of orbital elements:

>>> mu = jnp.array([398600,398600.4418])
>>> p =jnp.array([16056.196688409433,11067.79])
>>> e = jnp.array([1.4,0.83285])
>>> incl = jnp.array([jnp.deg2rad(30),jnp.deg2rad(87.87)])
>>> raan = jnp.array([jnp.deg2rad(40),jnp.deg2rad(227.89)])
>>> argp = jnp.array([jnp.deg2rad(60),jnp.deg2rad(53.38)])
>>> true_anom = jnp.array([jnp.deg2rad(30),jnp.deg2rad(92.335)])
>>> pos_vec, vel_vec = adx.coe2rv(p, e, incl, raan, argp, true_anom, mu)
>>> assert jnp.allclose(pos_vec[0], jnp.array([-4039.8965, 4814.5605, 3628.625]))
>>> assert jnp.allclose(vel_vec[0], jnp.array([-10.385988, -4.771922, 1.7438745]))
>>> assert jnp.allclose(pos_vec[1], jnp.array([6525.3677, 6861.5317, 6449.117]))
>>> assert jnp.allclose(vel_vec[1], jnp.array([4.902279, 5.5331397, -1.9757109]))
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