astrodynx.semimajor_axis

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astrodynx.semimajor_axis#

astrodynx.semimajor_axis(r_mag, v_mag, mu=1)[source]#

Returns the semimajor axis of a two-body orbit.

Parameters:

  • r_mag (ArrayLike) – Norm of the object’s position vector in the two-body system.

  • v_mag (ArrayLike) – Norm of the object’s velocity vector in the two-body system, which shape broadcast-compatible with r.

  • mu (ArrayLike) – Gravitational parameter of the central body; shape broadcast-compatible with r and v.

Return type:

ArrayLike

Returns:

The semimajor axis of the orbit.

Notes

The semimajor axis is calculated using equation (3.16):

\[ a = \left( \frac{2}{r} - \frac{v^2}{\mu} \right)^{-1} \]
where \(a\) is the semimajor axis, \(r\) is the norm of the position vector, \(v\) is the norm of the velocity vector, and \(\mu\) is the gravitational parameter.

References

Battin, 1999, pp.116.

Examples

A simple example of calculating the semimajor axis with a position vector norm of 1.0, velocity vector norm of 1.0, and gravitational parameter of 1.0:

>>> import jax.numpy as jnp
>>> import astrodynx as adx
>>> r = 1.0
>>> v = 1.0
>>> mu = 1.0
>>> adx.semimajor_axis(r, v, mu)
1.0

With broadcasting, you can calculate the semimajor axis for multiple position and velocity vectors:

>>> r = jnp.array([1.0, 2.0])
>>> v = jnp.array([1.0, 2.0])
>>> mu = jnp.array([1.0, 2.0])
>>> adx.semimajor_axis(r, v, mu)
Array([ 1., -1.], dtype=float32)
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