TidalPy.dynamics package

Submodules

TidalPy.dynamics.dual_dissipation module

TidalPy.dynamics.dual_dissipation.eccentricity_derivative(semi_major_axis: FloatArray, orbital_motion: FloatArray, eccentricity: FloatArray, mass_1: float, dU_dM_1: FloatArray, dU_dw_1: FloatArray, mass_2: float, dU_dM_2: FloatArray, dU_dw_2: FloatArray) → FloatArray[source]

Calculate the time derivative of the eccentricity for a dual dissipating system

See Boue and Efroimsky (2019, CMDA), Eq. 117

Parameters:

  • semi_major_axis (FloatArray) – Semi-major axis in [m]

  • orbital_motion (FloatArray) – Orbital mean motion [rad s-1]

  • eccentricity (FloatArray) – Orbital eccentricity

  • mass_1 (float) – Mass of body 1 in [kg]

  • dU_dM_1 (FloatArray) – Derivative of body 1’s tidal potential wrt mean anomaly

  • dU_dw_1 (FloatArray) – Derivative of body 1’s tidal potential wrt pericentre

  • mass_2 (float) – Mass of body 2 in [kg]

  • dU_dM_2 (FloatArray) – Derivative of body 2’s tidal potential wrt mean anomaly

  • dU_dw_2 (FloatArray) – Derivative of body 2’s tidal potential wrt pericentre

Returns:

de_dt – Time derivative of the eccentricity [s-1]

Return type:

FloatArray

TidalPy.dynamics.dual_dissipation.semi_major_axis_derivative(semi_major_axis: FloatArray, orbital_motion: FloatArray, mass_1: float, dU_dM_1: FloatArray, mass_2: float, dU_dM_2: FloatArray) → FloatArray[source]

Calculate the time derivative of the semi-major axis for a dual dissipating system

See Boue and Efroimsky (2019, CMDA), Eq. 116

Parameters:

  • semi_major_axis (FloatArray) – Semi-major axis in [m]

  • orbital_motion (FloatArray) – Orbital mean motion [rad s-1]

  • mass_1 (float) – Mass of body 1 in [kg]

  • dU_dM_1 (FloatArray) – Derivative of body 1’s tidal potential wrt mean anomaly

  • mass_2 (float) – Mass of body 2 in [kg]

  • dU_dM_2 (FloatArray) – Derivative of body 2’s tidal potential wrt mean anomaly

Returns:

da_dt – Time derivative of the semi-major axis [m s-1]

Return type:

FloatArray

TidalPy.dynamics.dual_dissipation.semia_eccen_derivatives(semi_major_axis: FloatArray, orbital_motion: FloatArray, eccentricity: FloatArray, mass_1: float, dU_dM_1: FloatArray, dU_dw_1: FloatArray, mass_2: float, dU_dM_2: FloatArray, dU_dw_2: FloatArray) → Tuple[FloatArray, FloatArray][source]

Calculate the time derivatives of semi-major axis and eccentricity for a dual dissipating system

See Boue and Efroimsky (2019, CMDA), Eqs. 116 and 117

Parameters:

  • semi_major_axis (FloatArray) – Semi-major axis in [m]

  • orbital_motion (FloatArray) – Orbital mean motion [rad s-1]

  • eccentricity (FloatArray) – Orbital eccentricity

  • mass_1 (float) – Mass of body 1 in [kg]

  • dU_dM_1 (FloatArray) – Derivative of body 1’s tidal potential wrt mean anomaly

  • dU_dw_1 (FloatArray) – Derivative of body 1’s tidal potential wrt pericentre

  • mass_2 (float) – Mass of body 2 in [kg]

  • dU_dM_2 (FloatArray) – Derivative of body 2’s tidal potential wrt mean anomaly

  • dU_dw_2 (FloatArray) – Derivative of body 2’s tidal potential wrt pericentre

Returns:

  • da_dt (FloatArray) – Time derivative of the semi-major axis [m s-1]

  • de_dt (FloatArray) – Time derivative of the eccentricity [s-1]

TidalPy.dynamics.single_dissipation module

TidalPy.dynamics.single_dissipation.eccentricity_derivative(semi_major_axis: FloatArray, orbital_motion: FloatArray, eccentricity: FloatArray, mass_1: float, dU_dM_1: FloatArray, dU_dw_1: FloatArray, mass_2: float) → FloatArray[source]

Calculate the time derivative of the eccentricity for a single-body dissipating system

See Boue and Efroimsky (2019, CMDA), Eq. 117

Parameters:

  • semi_major_axis (FloatArray) – Semi-major axis in [m]

  • orbital_motion (FloatArray) – Orbital mean motion [rad s-1]

  • eccentricity (FloatArray) – Orbital eccentricity

  • mass_1 (float) – Mass of body 1 in [kg]

  • dU_dM_1 (FloatArray) – Derivative of body 1’s tidal potential wrt mean anomaly

  • dU_dw_1 (FloatArray) – Derivative of body 1’s tidal potential wrt pericentre

  • mass_2 (float) – Mass of body 2 in [kg]

Returns:

de_dt – Time derivative of the eccentricity [s-1]

Return type:

FloatArray

TidalPy.dynamics.single_dissipation.semi_major_axis_derivative(semi_major_axis: FloatArray, orbital_motion: FloatArray, mass_1: float, dU_dM_1: FloatArray, mass_2: float) → FloatArray[source]

Calculate the time derivative of the semi-major axis for a signle-body dissipating system

See Boue and Efroimsky (2019, CMDA), Eq. 116

Parameters:

  • semi_major_axis (FloatArray) – Semi-major axis in [m]

  • orbital_motion (FloatArray) – Orbital mean motion [rad s-1]

  • mass_1 (float) – Mass of body 1 in [kg]

  • dU_dM_1 (FloatArray) – Derivative of body 1’s tidal potential wrt mean anomaly

  • mass_2 (float) – Mass of body 2 in [kg]

Returns:

da_dt – Time derivative of the semi-major axis [m s-1]

Return type:

FloatArray

TidalPy.dynamics.single_dissipation.semia_eccen_derivatives(semi_major_axis: FloatArray, orbital_motion: FloatArray, eccentricity: FloatArray, mass_1: float, dU_dM_1: FloatArray, dU_dw_1: FloatArray, mass_2: float) → Tuple[FloatArray, FloatArray][source]

Calculate the time derivatives of semi-major axis and eccentricity for a single-body dissipating system

See Boue and Efroimsky (2019, CMDA), Eqs. 116 and 117

Parameters:

  • semi_major_axis (FloatArray) – Semi-major axis in [m]

  • orbital_motion (FloatArray) – Orbital mean motion [rad s-1]

  • eccentricity (FloatArray) – Orbital eccentricity

  • mass_1 (float) – Mass of body 1 in [kg]

  • dU_dM_1 (FloatArray) – Derivative of body 1’s tidal potential wrt mean anomaly

  • dU_dw_1 (FloatArray) – Derivative of body 1’s tidal potential wrt pericentre

  • mass_2 (float) – Mass of body 2 in [kg]

Returns:

  • da_dt (FloatArray) – Time derivative of the semi-major axis [m s-1]

  • de_dt (FloatArray) – Time derivative of the eccentricity [s-1]

TidalPy.dynamics.single_dissipation.spin_rate_derivative(dU_dO: FloatArray, moment_of_inertia: float, host_mass: float) → FloatArray[source]

Calculate the time derivative of the spin frequency for a single-body or single or dual dissipation system

See Ferraz-Mello et. al. (2008)

Parameters:

  • dU_dO (FloatArray) – Partial derivative of the tidal potential wrt the target planet’s orbital node

  • moment_of_inertia (float) – Planet’s moment of inertia in [kg m2]

  • host_mass (float) – Mass of the tidal host [kg]

Returns:

dspin_dt – Change of spin frequency in [rad s-2]

Return type:

np.ndarray