orbix.kepler

Kepler equation solvers: exact core + grid/fixed-e shortcuts.

Submodules

• orbix.kepler.core
• orbix.kepler.shortcuts

Functions

E_solve(M, e)	Vectorized orvara solver for eccentric anomaly.
diff_solve_trig(M, e)	Solve Kepler's equation, returning (sinE, cosE) with exact gradients.
solve_trig(M, e)	Wrapper around E_solve_trig that returns only (sinE, cosE).
get_grid_solver([level, jit, kind, E, trig, n_e, n_M])	Helper function to get a grid-based solver and cache it.

Package Contents

orbix.kepler.E_solve(M, e)

Vectorized orvara solver for eccentric anomaly.

Parameters:

• M (jnp.ndarray) – Mean anomaly. Shape: (n,).

• e (float) – Eccentricity.

Returns:

Eccentric anomaly. Shape: (n,).

Return type:

E (jnp.ndarray)

The solver contract is 0 <= e < 1; e >= 1 or e < 0 silently produces NaN or garbage (unchecked to keep the hot path branch-free).

orbix.kepler.diff_solve_trig(M, e)

Solve Kepler’s equation, returning (sinE, cosE) with exact gradients.

Drop-in replacement for solve_trig() that supports reverse-mode autodiff (jax.grad, jax.vjp). Gradients come from the Implicit Function Theorem on M = E - e*sin(E), computed from (sinE, cosE, e) alone (no extra trig calls, no iterative re-solves).

Parameters:

• M (jnp.ndarray) – Mean anomaly. Shape: (n,).

• e (float) – Eccentricity.

Returns:

Sine of the eccentric anomaly. Shape: (n,). cosE (jnp.ndarray): Cosine of the eccentric anomaly. Shape: (n,).

Return type:

sinE (jnp.ndarray)

The solver contract is 0 <= e < 1; e >= 1 or e < 0 silently produces NaN or garbage (unchecked to keep the hot path branch-free).

orbix.kepler.solve_trig(M, e)

Wrapper around E_solve_trig that returns only (sinE, cosE).

Parameters:

• M (jnp.ndarray) – Mean anomaly. Shape: (n,).

• e (float) – Eccentricity.

Returns:

Sine of the eccentric anomaly. Shape: (n,). cosE (jnp.ndarray): Cosine of the eccentric anomaly. Shape: (n,).

Return type:

sinE (jnp.ndarray)

The solver contract is 0 <= e < 1; e >= 1 or e < 0 silently produces NaN or garbage (unchecked to keep the hot path branch-free).

orbix.kepler.get_grid_solver(level='scalar', jit=False, kind='bilinear', E=True, trig=True, n_e=512, n_M=2048)

Helper function to get a grid-based solver and cache it.

Parameters:

• level –

  How the solver should be batching things.

  • ”scalar” means the inputs will be a single (M, e) pair and the output will be a single E, sinE, cosE value.

  • ”planet” will vectorize over times first and then over orbits.

    • M: (n_orbits, n_times)

    • e: (n_orbits,)

• jit – Whether to jit the solver.

• kind – The kind of solver to use, either “linear” or “bilinear”.

• E – Whether to compute the eccentric anomaly.

• trig – Whether to compute the sine and cosine of the eccentric anomaly.

• n_e – The number of eccentricity steps in the grid.

• n_M – The number of mean anomaly steps in the grid.