astrodynx.twobody.pass_perigee

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astrodynx.twobody.pass_perigee#

astrodynx.twobody.pass_perigee(r1, v1, r2, mu=1)[source]#

Returns True if the orbit passes through perigee between two points.

Parameters:

  • r1 (ArrayLike) – (3,) The position vector at the first point.

  • v1 (ArrayLike) – (3,) The velocity vector at the first point.

  • r2 (ArrayLike) – (3,) The position vector at the second point.

  • mu (DTypeLike) – (optional) The gravitational parameter.

Return type:

Array

Returns:

True if the orbit passes through perigee between the two points, False otherwise.

Notes

Let’s define

\[ \boldsymbol{b}_1 = (\boldsymbol{r}_1 \times \boldsymbol{r}_2) \cdot (\boldsymbol{r}_1 \times \boldsymbol{e}) > 0 \]
and
\[ \boldsymbol{b}_2 = (\boldsymbol{r}_1 \times \boldsymbol{r}_2) \cdot (\boldsymbol{e} \times \boldsymbol{r}_2) > 0 \]
where \(\boldsymbol{e}\) is the eccentricity vector. Then, the orbit passes through perigee if:
\[ \boldsymbol{b}_1 \land \boldsymbol{b}_2 = \text{is_short_way}(\boldsymbol{r}_1, \boldsymbol{v}_1, \boldsymbol{r}_2) \]

Examples

A simple example:

>>> import jax.numpy as jnp
>>> import astrodynx as adx
>>> r1 = jnp.array([1.0, 0.0, 0.0])
>>> v1 = jnp.array([0.0, 1.0, 0.0])
>>> r2 = jnp.array([0.0, 1.0, 0.0])
>>> adx.twobody.pass_perigee(r1, v1, r2)
Array(False, dtype=bool)
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