jnkepler.keplerian package

Submodules

jnkepler.keplerian.jacobian module

jnkepler.keplerian.jacobian.det_jkep2D_am(params)[source]

Analytic Jacobian determinant for the transformation (a, e, omega, M) → (x, z, vx, vz) in the 2D Kepler problem.

Parameters:

params (dict) – Orbital-element parameters.

Returns:

Analytic Jacobian determinant.

Return type:

float

jnkepler.keplerian.jacobian.det_jkep2D_pm(params)[source]

Analytic Jacobian determinant for the transformation (P, e, omega, M) → (x, z, vx, vz) in the 2D Kepler problem.

Parameters:

params (dict) – Orbital-element parameters.

Returns:

Analytic Jacobian determinant.

Return type:

float

jnkepler.keplerian.jacobian.det_jkep_am(params)[source]

Analytic Jacobian determinant for the transformation (a, e, i, Omega, omega, M) → (x, y, z, vx, vy, vz).

Parameters:

params (dict) – Orbital-element parameters.

Returns:

Analytic Jacobian determinant.

Return type:

float

jnkepler.keplerian.jacobian.det_jkep_atau(params)[source]

Analytic Jacobian determinant for the transformation (a, e, i, Omega, omega, tau) → (x, y, z, vx, vy, vz).

Parameters:

params (dict) – Orbital-element parameters.

Returns:

Analytic Jacobian determinant.

Return type:

float

jnkepler.keplerian.jacobian.det_jkep_pm(params)[source]

Analytic Jacobian determinant for the transformation (P, e, i, Omega, omega, M) → (x, y, z, vx, vy, vz).

Parameters:

params (dict) – Orbital-element parameters.

Returns:

Analytic Jacobian determinant.

Return type:

float

jnkepler.keplerian.jacobian.det_jkep_ptau(params)[source]

Analytic Jacobian determinant for the transformation (P, e, i, Omega, omega, tau) → (x, y, z, vx, vy, vz).

Parameters:

params (dict) – Orbital-element parameters.

Returns:

Analytic Jacobian determinant.

Return type:

float

jnkepler.keplerian.jacobian.slogdet_jkep2D_jax(params, keys)[source]

Compute the Jacobian determinant for the mapping from orbital elements to Cartesian state vectors in the 2D Kepler problem using JAX autodiff

Parameters:

  • params (dict) – Dictionary of orbital-element parameters.

  • keys (list[str]) – Parameter names with respect to which the Jacobian is computed. Only these parameters are differentiated. Typical choices correspond to combinations such as (a, ecc, omega, M), (period, ecc, omega, M).

Returns:

(sign, log_abs_det) from jnp.linalg.slogdet, where the Jacobian

is taken with respect to the flattened state vector (x, v).

Return type:

tuple

jnkepler.keplerian.jacobian.slogdet_jkep_jax(params, keys)[source]

Compute the Jacobian determinant for the mapping from orbital elements to Cartesian state vectors in the 3D Kepler problem using JAX autodiff

Parameters:

  • params (dict) – Dictionary of orbital-element parameters.

  • keys (list[str]) – Parameter names with respect to which the Jacobian is computed. Only these parameters are differentiated. Typical choices correspond to combinations such as (a, ecc, inc, lnode, omega, M), (a, ecc, inc, lnode, omega, tau), (period, ecc, inc, lnode, omega, M).

Returns:

(sign, log_abs_det) from jnp.linalg.slogdet, where the Jacobian

is taken with respect to the flattened state vector (x, v).

Return type:

tuple

jnkepler.keplerian.orbit module

jnkepler.keplerian.orbit.elements_to_xv(t, params)[source]

Convert orbital elements to Cartesian state vectors.

Parameters:

  • t (array_like) – Times (days) at which positions and velocities are evaluated.

  • params (dict) –

    Dictionary containing per-orbit orbital elements:

    • period : orbital period (days)

    • ecc : eccentricity

    • inc : inclination (radian)

    • omega : argument of periastron (radian)

    • lnode : longitude of ascending node (radian)

    • tau : time of periastron passage (days)

    • mass : total mass (solar masses)

Returns:

Cartesian position and velocity vectors:

  • x : array of shape (T, N, 3) if multiple orbits, or (T, 3) if a single orbit. Units: AU.

  • v : array of shape (T, N, 3) or (T, 3). Units: AU/day.

Return type:

dict

jnkepler.keplerian.orbit.elements_to_xv_scaled(t, params)[source]

Convert orbital elements to state vectors scaled by semi-major axis a.

Parameters:

  • t (array_like) – Times (days) at which positions and velocities are evaluated.

  • params (dict) –

    Dictionary containing per-orbit orbital elements:

    • period : orbital period (days)

    • ecc : eccentricity

    • inc : inclination (radian)

    • omega : argument of periastron (radian)

    • lnode : longitude of ascending node (radian)

    • tau : time of periastron passage (days)

Returns:

Cartesian position and velocity vectors divided by a:

  • x : array of shape (T, N, 3) or (T, 3). Dimensionless.

  • v : array of shape (T, N, 3) or (T, 3). Units: 1/day.

Return type:

dict

jnkepler.keplerian.orbit.radial_velocity_shape(t, params)[source]

Compute cos(omega+f) + e*cos(omega)

Parameters:

  • t – times at which RVs are computed

  • porb – period

  • ecc – eccentricity

  • omega – argument of periastron

  • tau – time of periastron passage

Returns:

radial velocities

Return type:

array

jnkepler.keplerian.orbit.radial_velocity_shape_multi(t, params)[source]

Vectorized over leading axis of each leaf in params_all (dict-of-arrays).

jnkepler.keplerian.orbit.tic_to_tau(tic, period, ecc, omega)[source]

Compute time of periastron passage from time of inferior conjunction tic

Parameters:

  • tic – time of inferior conjunction where omega + f = pi/2

  • period – orbital period

  • ecc – eccentricity

  • omega – argument of periastron

Returns:

time of periastron passage

Return type:

float

jnkepler.keplerian.orbit.xv_to_elements(x, v, mass, t_ref=None)[source]

Convert Cartesian state vectors to orbital elements.

Parameters:

  • x – array_like Cartesian position vector(s) in AU, shape (3,) or (N, 3).

  • v – array_like Cartesian velocity vector(s) in AU/day, shape (3,) or (N, 3).

  • mass – float or array_like Total mass (solar masses).

  • t_ref – float or array_like, optional Reference epoch (days). If provided, the time of periastron passage (tau) is computed as tau = t_ref - M/n.

Returns:

dict
Orbital elements:

  • a : semi-major axis (AU)

  • period : orbital period (days)

  • ecc : eccentricity

  • inc : inclination (radian)

  • omega : argument of periastron (radian)

  • lnode : longitude of ascending node (radian)

  • M : mean anomaly at t_ref (radian)

  • tau : time of periastron passage (days), if t_ref is given

  • mass : total mass (solar masses)

Each value is a scalar if a single orbit is given, or a 1-D array of length N for multiple orbits.

Module contents