astrodynx.gravity.j2_acc

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astrodynx.gravity.j2_acc#

astrodynx.gravity.j2_acc(t, x, args={'J2': 0.0, 'R_eq': 1.0, 'mu': 1.0})[source]#

Returns the acceleration due to J2 perturbation.

Parameters:

  • t (DTypeLike) – The time.

  • x (ArrayLike) – (N,) The state vector, where the first 3 elements are the position vector.

  • args (PyTree[Any]) – Static arguments.

Return type:

ArrayLike

Returns:

The acceleration due to J2 perturbation.

Notes

The acceleration due to J2 perturbation is defined as:

\[\begin{split} \begin{align*} a_x &= -\frac{3}{2} \frac{\mu J_2 R_{eq}^2}{r^5} x \left( 1 - 5 \frac{z^2}{r^2} \right) \\ a_y &= -\frac{3}{2} \frac{\mu J_2 R_{eq}^2}{r^5} y \left( 1 - 5 \frac{z^2}{r^2} \right) \\ a_z &= -\frac{3}{2} \frac{\mu J_2 R_{eq}^2}{r^5} z \left( 3 - 5 \frac{z^2}{r^2} \right) \end{align*} \end{split}\]
where \(\boldsymbol{a}\) is the acceleration, \(\mu\) is the gravitational parameter, \(J_2\) is the second zonal harmonic, \(R_{eq}\) is the equatorial radius, and \(\boldsymbol{r} = [x, y, z]\) is the position vector.

References

Vallado, 2013, pp.594.

Examples

>>> import jax.numpy as jnp
>>> import astrodynx as adx
>>> t = 0.0
>>> x = jnp.array([1.0, -1.0, 1.0, 0.0, 0.0, 0.0])
>>> args = {"mu": 1.0, "J2": 1e-3, "R_eq": 1.0}
>>> expected = jnp.array([ 6.4150023e-05, -6.4150023e-05, -1.2830009e-04])
>>> actual = adx.gravity.j2_acc(t, x, args)
>>> jnp.allclose(expected, actual)
Array(True, dtype=bool)
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