Kepler

Functions for solving Kepler’s equation.

This is a fork of squishyplanet/engine/kepler.py, which itself is a fork of jaxoplanet/src/jaxoplanet/core/kepler.py, many thanks to the original authors

jorbit.utils.kepler.M_from_f(f, ecc)

Compute the mean anomaly from the true anomaly and eccentricity.

Parameters:

• f (float) – True anomaly in radians.

• ecc (float) – Eccentricity.

Returns:

Mean anomaly in radians.

Return type:

float

jorbit.utils.kepler.kepler(M, ecc)

Solve Kepler’s equation to compute the true anomaly.

This implementation is based on that within jaxoplanet, many thanks to the authors.

Parameters:

• M (float) – Mean anomaly

• ecc (float) – Eccentricity

Returns:

True anomaly in radians

Return type:

float

jorbit.utils.kepler.keplerian_propagate(x0, v0, t0, times, gm)

Propagate a Keplerian orbit to new times.

Parameters:

• x0 (Array) – Initial position (1, 3), ecliptic frame.

• v0 (Array) – Initial velocity (1, 3), ecliptic frame.

• t0 (float) – Initial time (scalar, JD TDB).

• times (Array) – Target times (N,), JD TDB.

• gm (float) – Gravitational parameter (GM) in AU^3/day^2.

Returns:

Positions (N, 3) and velocities (N, 3) in ecliptic frame.

Return type:

tuple[Array, Array]