orbix.equations.orbit ===================== .. py:module:: orbix.equations.orbit .. autoapi-nested-parse:: Common equations for orbital mechanics. Attributes ---------- .. autoapisummary:: orbix.equations.orbit.two_pi_G orbix.equations.orbit._TOL_E orbix.equations.orbit._TOL_N orbix.equations.orbit._ARC_EPS Functions --------- .. autoapisummary:: orbix.equations.orbit.period_a orbix.equations.orbit.period_n orbix.equations.orbit.mean_motion orbix.equations.orbit.period_to_sma orbix.equations.orbit.semi_amplitude orbix.equations.orbit.semi_amplitude_reduced orbix.equations.orbit.mean_anomaly_t0 orbix.equations.orbit.mean_anomaly_tp orbix.equations.orbit.AB_matrices orbix.equations.orbit.AB_matrices_reduced orbix.equations.orbit.thiele_innes_constants orbix.equations.orbit.thiele_innes_constants_reduced orbix.equations.orbit._safe_norm orbix.equations.orbit.state_vector_to_keplerian Module Contents --------------- .. py:data:: two_pi_G .. py:function:: period_a(a, mu) Orbital period from semi-major axis and standard gravitational parameter. :param a: Array Semi-major axis :param mu: Array Standard gravitational parameter :returns: Array Orbital period :rtype: T .. py:function:: period_n(n) Orbital period from mean motion. :param n: Array Mean motion :returns: Array Orbital period :rtype: T .. py:function:: mean_motion(a, mu) Mean motion from semi-major axis and standard gravitational parameter. :param a: Array Semi-major axis :param mu: Array Standard gravitational parameter :returns: Array Mean motion :rtype: n .. py:function:: period_to_sma(T, Ms) Semi-major axis from orbital period via Kepler's third law. :param T: Orbital period (days). Scalar or array. :param Ms: Stellar mass (kg). Scalar or array. :returns: Semi-major axis (AU). Scalar or array. :rtype: a .. py:function:: semi_amplitude(T, Ms, Mp, e, i) Semi-amplitude of the radial velocity curve from base quantities. :param T: Array Orbital period :param Ms: Array Mass of the star :param Mp: Array Mass of the planet :param e: Array Eccentricity :param i: Array Inclination :returns: Array Semi-amplitude of the radial velocity curve :rtype: K .. py:function:: semi_amplitude_reduced(T, Ms, minimum_mass, sqrt_one_minus_e2) Semi-amplitude of the radial velocity curve from pre-calculated quantities. :param T: Array Orbital period :param Ms: Array Mass of the star :param minimum_mass: Array Mass of the planet multiplied by sin(i) :param sqrt_one_minus_e2: Array Square root of (1 - eccentricity^2) :returns: Array Semi-amplitude of the radial velocity curve :rtype: K .. py:function:: mean_anomaly_t0(t, n, M0, t0) Mean anomaly at time t (can be vector) from epoch. Requires that all units are consistent and does NOT clip the mean anomaly to the range [0, 2pi). :param t: Array Time :param n: Array Mean motion :param M0: Array Mean anomaly at epoch :param t0: Array Epoch :returns: Array Mean anomaly at time t :rtype: M .. py:function:: mean_anomaly_tp(t, n, tp) Mean anomaly at time t (can be vector) from periapsis passage. :param t: Array Time :param n: Array Mean motion :param tp: Array Time of periapsis passage :returns: Array Mean anomaly at time t :rtype: M .. py:function:: AB_matrices(a, e, i, W, w) Compute the A and B matrices for a given set of orbital elements. In keplertools Dmitry defines these as: "inertial frame components of perifocal frame unit vectors scaled by orbit semi-major and semi-minor axes." and I wouldn't dare disagree with him on this. :param a: Array Semi-major axis :param e: Array Eccentricity :param i: Array Inclination :param W: Array Longitude of the ascending node :param w: Array Argument of periapsis :returns: jnp.ndarray A matrix B: jnp.ndarray B matrix :rtype: A .. py:function:: AB_matrices_reduced(a, sqrt_one_minus_e2, sini, cosi, sinW, cosW, sinw, cosw) Compute the A and B matrices from the trig values of the orbital elements. :param a: Semi-major axis :param sqrt_one_minus_e2: Square root of (1 - eccentricity^2) :param sini: Sine of the inclination :param cosi: Cosine of the inclination :param sinW: Sine of the longitude of the ascending node :param cosW: Cosine of the longitude of the ascending node :param sinw: Sine of the argument of periapsis :param cosw: Cosine of the argument of periapsis :returns: jnp.ndarray A matrix B: jnp.ndarray B matrix :rtype: A .. py:function:: thiele_innes_constants(W, i, w) Compute the Thiele-Innes constants from the orbital angles. :param W: Longitude of the ascending node :param i: Inclination :param w: Argument of periapsis :returns: A constant B: B constant F: F constant G: G constant :rtype: A .. py:function:: thiele_innes_constants_reduced(sinW, cosW, sinw, cosw, sinwcosi, coswcosi) Compute the Thiele-Innes constants from the orbital angles. :param sinW: Sine of the longitude of the ascending node :param cosW: Cosine of the longitude of the ascending node :param sinw: Sine of the argument of periapsis :param cosw: Cosine of the argument of periapsis :param sinwcosi: Sine of the argument of periapsis times cosine of the inclination :param coswcosi: Cosine of the argument of periapsis times cosine of the inclination :returns: A constant B: B constant F: F constant G: G constant :rtype: A .. py:data:: _TOL_E :value: 1e-09 .. py:data:: _TOL_N :value: 1e-09 .. py:data:: _ARC_EPS :value: 1e-07 .. py:function:: _safe_norm(x) Vector norm with a finite (zero) gradient at ``x == 0``. ``jnp.linalg.norm`` has a NaN gradient at exactly the zero vector (``x / norm(x)`` is ``0 / 0`` there). This computes the same value but evaluates the norm on a nonzero stand-in whenever ``x`` is zero, so the local derivative is finite; the ``jnp.where`` then zeroes the corresponding cotangent, giving a well-defined (zero) gradient. .. py:function:: state_vector_to_keplerian(r, v, mu) Convert state vectors (r, v) to Keplerian elements using JAX. Robust implementation handling edge cases (circular, equatorial, and non-bound orbits) using ``jnp.where`` for JIT compatibility. Unit-agnostic: ``r``, ``v``, and ``mu`` must be expressed in one consistent unit system (e.g. meters / m/s / m^3 s^-2, or the AU / day units used elsewhere in this library); the function does not enforce or convert any particular convention, and ``a`` is returned in the same length unit as ``r``. :param r: Stellar-centric position vector ``(3,)``. :param v: Stellar-centric velocity vector ``(3,)``. :param mu: Gravitational parameter ``G * M_total``. :returns: ``(a, e, i, W, w, M)`` -- semi-major axis (same length unit as ``r``), eccentricity, inclination [rad], longitude of ascending node [rad], argument of periapsis [rad], mean anomaly [rad]. :rtype: tuple