TidalPy.tides.potential package

Submodules

TidalPy.tides.potential.nsr_med_eccen_gen_obliquity module

TidalPy.tides.potential.nsr_med_eccen_gen_obliquity.tidal_potential(radius: FloatArray, longitude: FloatArray, colatitude: FloatArray, time: FloatArray, orbital_frequency: FloatArray, rotation_frequency: FloatArray, eccentricity: FloatArray, obliquity: FloatArray, host_mass: float, semi_major_axis: FloatArray, use_static: bool = False) → TidalPotentialModeOutput

Tidal gravitational potential assuming moderate eccentricity, any obliquity, and non-synchronous rotation

This version that allows for moderate obliquity is about 1.75 to 2x slower than the non-obliquity version found in:

TidalPy.tides.potential.nsr_med_eccen_no_obliquity.py

Parameters:

• radius (FloatArray) – Radius of the world [m]

• longitude (FloatArray) – Longitude [radians]

• colatitude (FloatArray) – Co-latitude [radians]

• time (FloatArray) – Time (orbit position) [s]

• orbital_frequency (FloatArray) – Orbital mean motion of the world [rads s-1]

• rotation_frequency (FloatArray) – Rotation rate of the planet [rad s-1]

• eccentricity (FloatArray) – Eccentricity of the orbit

• obliquity (FloatArray) – Obliquity of the planet relative to the orbital plane [rads]

• host_mass (float) – Mass of tide-raising world

• semi_major_axis (FloatArray) – Orbital semi-major axis [m]

• use_static (bool = False) – Use the static portion of the potential equation (no time dependence in these terms)

Returns:

• tidal_frequencies (Dict[str, FloatArray]) – Tidal frequencies, abs(modes) [radians s-1]

• tidal_modes (Dict[str, FloatArray]) – Tidal frequency modes [radians s-1]

• potential_tuple_by_mode (PotentialTupleModeOutput) – Storage for the tidal potential and its derivatives.

  potentialFloatArray

  Tidal Potential

  potential_partial_thetaFloatArray

  Partial Derivative of the Tidal Potential wrt colatitude.

  potential_partial_phiFloatArray

  Partial Derivative of the Tidal Potential wrt longitude.

  potential_partial2_theta2FloatArray

  2nd Partial Derivative of the Tidal Potential wrt colatitude.

  potential_partial2_phi2FloatArray

  2nd Partial Derivative of the Tidal Potential wrt longitude.

  potential_partial2_theta_phiFloatArray

  2nd Partial Derivative of the Tidal Potential wrt colatitude and longitude.

See also

TidalPy.tides.potential.nsr_med_eccen_no_obliquity.py

TidalPy.tides.potential.nsr_med_eccen_med_obliquity module

TidalPy.tides.potential.nsr_med_eccen_med_obliquity.tidal_potential(radius: FloatArray, longitude: FloatArray, colatitude: FloatArray, time: FloatArray, orbital_frequency: FloatArray, rotation_frequency: FloatArray, eccentricity: FloatArray, obliquity: FloatArray, host_mass: float, semi_major_axis: FloatArray, use_static: bool = False) → TidalPotentialModeOutput

Tidal gravitational potential assuming moderate eccentricity, moderate obliquity, and non-synchronous rotation

This version that allows for moderate obliquity is about 1.75 to 2x slower than the non-obliquity version found in:

TidalPy.tides.potential.nsr_med_eccen_no_obliquity.py

Parameters:

• radius (FloatArray) – Radius of the world [m]

• longitude (FloatArray) – Longitude [radians]

• colatitude (FloatArray) – Co-latitude [radians]

• time (FloatArray) – Time (orbit position) [s]

• orbital_frequency (FloatArray) – Orbital mean motion of the world [rads s-1]

• rotation_frequency (FloatArray) – Rotation rate of the planet [rad s-1]

• eccentricity (FloatArray) – Eccentricity of the orbit

• obliquity (FloatArray) – Obliquity of the planet relative to the orbital plane [rads]

• host_mass (float) – Mass of tide-raising world

• semi_major_axis (FloatArray) – Orbital semi-major axis [m]

• use_static (bool = False) – Use the static portion of the potential equation (no time dependence in these terms)

Returns:

• tidal_frequencies (Dict[str, FloatArray]) – Tidal frequencies, abs(modes) [radians s-1]

• tidal_modes (Dict[str, FloatArray]) – Tidal frequency modes [radians s-1]

• potential_tuple_by_mode (PotentialTupleModeOutput) – Storage for the tidal potential and its derivatives.

  potentialFloatArray

  Tidal Potential

  potential_partial_thetaFloatArray

  Partial Derivative of the Tidal Potential wrt colatitude.

  potential_partial_phiFloatArray

  Partial Derivative of the Tidal Potential wrt longitude.

  potential_partial2_theta2FloatArray

  2nd Partial Derivative of the Tidal Potential wrt colatitude.

  potential_partial2_phi2FloatArray

  2nd Partial Derivative of the Tidal Potential wrt longitude.

  potential_partial2_theta_phiFloatArray

  2nd Partial Derivative of the Tidal Potential wrt colatitude and longitude.

See also

TidalPy.tides.potential.nsr_med_eccen_no_obliquity.py

TidalPy.tides.potential.nsr_med_eccen_no_obliquity module

TidalPy.tides.potential.nsr_med_eccen_no_obliquity.tidal_potential(radius: FloatArray, longitude: FloatArray, colatitude: FloatArray, time: FloatArray, orbital_frequency: FloatArray, rotation_frequency: FloatArray, eccentricity: FloatArray, host_mass: float, semi_major_axis: FloatArray, use_static: bool = False) → TidalPotentialModeOutput

Tidal gravitational potential assuming moderate eccentricity, no obliquity, and non-synchronous rotation

Parameters:

• radius (FloatArray) – Radius of the world [m]

• longitude (FloatArray) – Longitude [radians]

• colatitude (FloatArray) – Co-latitude [radians]

• time (FloatArray) – Time (orbit position) [s]

• orbital_frequency (FloatArray) – Orbital mean motion of the world [rads s-1]

• rotation_frequency (FloatArray) – Rotation rate of the planet [rad s-1]

• eccentricity (FloatArray) – Eccentricity of the orbit

• host_mass (float) – Mass of tide-raising world

• semi_major_axis (FloatArray) – Orbital semi-major axis [m]

• use_static (bool = False) – Use the static portion of the potential equation (no time dependence in these terms)

Returns:

• tidal_frequencies (Dict[str, FloatArray]) – Tidal frequencies, abs(modes) [radians s-1]

• tidal_modes (Dict[str, FloatArray]) – Tidal frequency modes [radians s-1]

• potential_tuple_by_mode (PotentialTupleModeOutput) – Storage for the tidal potential and its derivatives.

  potentialFloatArray

  Tidal Potential

  potential_partial_thetaFloatArray

  Partial Derivative of the Tidal Potential wrt colatitude.

  potential_partial_phiFloatArray

  Partial Derivative of the Tidal Potential wrt longitude.

  potential_partial2_theta2FloatArray

  2nd Partial Derivative of the Tidal Potential wrt colatitude.

  potential_partial2_phi2FloatArray

  2nd Partial Derivative of the Tidal Potential wrt longitude.

  potential_partial2_theta_phiFloatArray

  2nd Partial Derivative of the Tidal Potential wrt colatitude and longitude.

See also

TidalPy.tides.potential.nsr_med_eccen_med_obliquity.py

TidalPy.tides.potential.nsr_modes_low_eccen_gen_obliquity module

TidalPy.tides.potential.nsr_modes_low_eccen_gen_obliquity.tidal_potential(radius: FloatArray, longitude: FloatArray, colatitude: FloatArray, time: FloatArray, orbital_frequency: FloatArray, rotation_frequency: FloatArray, eccentricity: FloatArray, obliquity: FloatArray, host_mass: float, semi_major_axis: FloatArray, use_static: bool = False) → TidalPotentialModeOutput

Tidal gravitational potential assuming moderate eccentricity, any obliquity, and non-synchronous rotation

This function will keep the subcomponents of the potential separate for each tidal mode so that they may

be collapsed later on (e.g., after combining with different frequency response at each mode).

This version, which allows for obliquity, is about 2.5 times slower than the version that does not.

TidalPy.tides.potential.nsr_modes_med_eccen_no_obliquity.py

Parameters:

• radius (FloatArray) – Radius of the world [m]

• longitude (FloatArray) – Longitude [radians]

• colatitude (FloatArray) – Co-latitude [radians]

• time (FloatArray) – Time (orbit position) [s]

• orbital_frequency (FloatArray) – Orbital mean motion of the world [rads s-1]

• rotation_frequency (FloatArray) – Rotation rate of the planet [rad s-1]

• eccentricity (FloatArray) – Eccentricity of the orbit

• obliquity (FloatArray) – Obliquity of the planet relative to the orbital plane [rads]

• host_mass (float) – Mass of tide-raising world

• semi_major_axis (FloatArray) – Orbital semi-major axis [m]

• use_static (bool = False) – Use the static portion of the potential equation (no time dependence in these terms)

Returns:

• tidal_frequencies (Dict[str, FloatArray]) – Tidal frequencies, abs(modes) [radians s-1]

• tidal_modes (Dict[str, FloatArray]) – Tidal frequency modes [radians s-1]

• potential_tuple_by_mode (PotentialTupleModeOutput) – Storage for the tidal potential and its derivatives.

  potentialFloatArray

  Tidal Potential

  potential_partial_thetaFloatArray

  Partial Derivative of the Tidal Potential wrt colatitude.

  potential_partial_phiFloatArray

  Partial Derivative of the Tidal Potential wrt longitude.

  potential_partial2_theta2FloatArray

  2nd Partial Derivative of the Tidal Potential wrt colatitude.

  potential_partial2_phi2FloatArray

  2nd Partial Derivative of the Tidal Potential wrt longitude.

  potential_partial2_theta_phiFloatArray

  2nd Partial Derivative of the Tidal Potential wrt colatitude and longitude.

See also

TidalPy.tides.potential.nsr_modes_med_eccen_no_obliquity.py

TidalPy.tides.potential.nsr_modes_med_eccen_gen_obliquity module

TidalPy.tides.potential.nsr_modes_med_eccen_gen_obliquity.tidal_potential(radius: FloatArray, longitude: FloatArray, colatitude: FloatArray, time: FloatArray, orbital_frequency: FloatArray, rotation_frequency: FloatArray, eccentricity: FloatArray, obliquity: FloatArray, host_mass: float, semi_major_axis: FloatArray, use_static: bool = False) → TidalPotentialModeOutput

Tidal gravitational potential assuming moderate eccentricity, any obliquity, and non-synchronous rotation

This function will keep the subcomponents of the potential separate for each tidal mode so that they may

be collapsed later on (e.g., after combining with different frequency response at each mode).

This version, which allows for obliquity, is about 2.5 times slower than the version that does not.

TidalPy.tides.potential.nsr_modes_med_eccen_no_obliquity.py

Parameters:

• radius (FloatArray) – Radius of the world [m]

• longitude (FloatArray) – Longitude [radians]

• colatitude (FloatArray) – Co-latitude [radians]

• time (FloatArray) – Time (orbit position) [s]

• orbital_frequency (FloatArray) – Orbital mean motion of the world [rads s-1]

• rotation_frequency (FloatArray) – Rotation rate of the planet [rad s-1]

• eccentricity (FloatArray) – Eccentricity of the orbit

• obliquity (FloatArray) – Obliquity of the planet relative to the orbital plane [rads]

• host_mass (float) – Mass of tide-raising world

• semi_major_axis (FloatArray) – Orbital semi-major axis [m]

• use_static (bool = False) – Use the static portion of the potential equation (no time dependence in these terms)

Returns:

• tidal_frequencies (Dict[str, FloatArray]) – Tidal frequencies, abs(modes) [radians s-1]

• tidal_modes (Dict[str, FloatArray]) – Tidal frequency modes [radians s-1]

• potential_tuple_by_mode (PotentialTupleModeOutput) – Storage for the tidal potential and its derivatives.

  potentialFloatArray

  Tidal Potential

  potential_partial_thetaFloatArray

  Partial Derivative of the Tidal Potential wrt colatitude.

  potential_partial_phiFloatArray

  Partial Derivative of the Tidal Potential wrt longitude.

  potential_partial2_theta2FloatArray

  2nd Partial Derivative of the Tidal Potential wrt colatitude.

  potential_partial2_phi2FloatArray

  2nd Partial Derivative of the Tidal Potential wrt longitude.

  potential_partial2_theta_phiFloatArray

  2nd Partial Derivative of the Tidal Potential wrt colatitude and longitude.

See also

TidalPy.tides.potential.nsr_modes_med_eccen_no_obliquity.py

TidalPy.tides.potential.nsr_modes_med_eccen_med_obliquity module

TidalPy.tides.potential.nsr_modes_med_eccen_med_obliquity.tidal_potential(radius: FloatArray, longitude: FloatArray, colatitude: FloatArray, time: FloatArray, orbital_frequency: FloatArray, rotation_frequency: FloatArray, eccentricity: FloatArray, obliquity: FloatArray, host_mass: float, semi_major_axis: FloatArray, use_static: bool = False) → TidalPotentialModeOutput

Tidal gravitational potential assuming moderate eccentricity, moderate obliquity, and non-synchronous rotation

This function will keep the subcomponents of the potential separate for each tidal mode so that they may

be collapsed later on (e.g., after combining with different frequency response at each mode).

This version, which allows for obliquity, is about 2.5 times slower than the version that does not.

TidalPy.tides.potential.nsr_modes_med_eccen_no_obliquity.py

Parameters:

• radius (FloatArray) – Radius of the world [m]

• longitude (FloatArray) – Longitude [radians]

• colatitude (FloatArray) – Co-latitude [radians]

• time (FloatArray) – Time (orbit position) [s]

• orbital_frequency (FloatArray) – Orbital mean motion of the world [rads s-1]

• rotation_frequency (FloatArray) – Rotation rate of the planet [rad s-1]

• eccentricity (FloatArray) – Eccentricity of the orbit

• obliquity (FloatArray) – Obliquity of the planet relative to the orbital plane [rads]

• host_mass (float) – Mass of tide-raising world

• semi_major_axis (FloatArray) – Orbital semi-major axis [m]

• use_static (bool = False) – Use the static portion of the potential equation (no time dependence in these terms)

Returns:

• tidal_frequencies (Dict[str, FloatArray]) – Tidal frequencies, abs(modes) [radians s-1]

• tidal_modes (Dict[str, FloatArray]) – Tidal frequency modes [radians s-1]

• potential_tuple_by_mode (PotentialTupleModeOutput) – Storage for the tidal potential and its derivatives.

  potentialFloatArray

  Tidal Potential

  potential_partial_thetaFloatArray

  Partial Derivative of the Tidal Potential wrt colatitude.

  potential_partial_phiFloatArray

  Partial Derivative of the Tidal Potential wrt longitude.

  potential_partial2_theta2FloatArray

  2nd Partial Derivative of the Tidal Potential wrt colatitude.

  potential_partial2_phi2FloatArray

  2nd Partial Derivative of the Tidal Potential wrt longitude.

  potential_partial2_theta_phiFloatArray

  2nd Partial Derivative of the Tidal Potential wrt colatitude and longitude.

See also

TidalPy.tides.potential.nsr_modes_med_eccen_no_obliquity.py

TidalPy.tides.potential.nsr_modes_med_eccen_no_obliquity module

TidalPy.tides.potential.nsr_modes_med_eccen_no_obliquity.tidal_potential(radius: FloatArray, longitude: FloatArray, colatitude: FloatArray, time: FloatArray, orbital_frequency: FloatArray, rotation_frequency: FloatArray, eccentricity: FloatArray, host_mass: float, semi_major_axis: FloatArray, use_static: bool = False) → TidalPotentialModeOutput

Tidal gravitational potential assuming moderate eccentricity, no obliquity, and non-synchronous rotation

This function will keep the subcomponents of the potential separate for each tidal mode so that they may

be collapsed later on (e.g., after combining with different frequency response at each mode).

Parameters:

• radius (FloatArray) – Radius of the world [m]

• longitude (FloatArray) – Longitude [radians]

• colatitude (FloatArray) – Co-latitude [radians]

• time (FloatArray) – Time (orbit position) [s]

• orbital_frequency (FloatArray) – Orbital mean motion of the world [rads s-1]

• rotation_frequency (FloatArray) – Rotation rate of the planet [rad s-1]

• eccentricity (FloatArray) – Eccentricity of the orbit

• host_mass (float) – Mass of tide-raising world

• semi_major_axis (FloatArray) – Orbital semi-major axis [m]

• use_static (bool = False) – Use the static portion of the potential equation (no time dependence in these terms)

Returns:

• tidal_frequencies (Dict[str, FloatArray]) – Tidal frequencies, abs(modes) [radians s-1]

• tidal_modes (Dict[str, FloatArray]) – Tidal frequency modes [radians s-1]

• potential_tuple_by_mode (PotentialTupleModeOutput) – Storage for the tidal potential and its derivatives.

  potentialFloatArray

  Tidal Potential

  potential_partial_thetaFloatArray

  Partial Derivative of the Tidal Potential wrt colatitude.

  potential_partial_phiFloatArray

  Partial Derivative of the Tidal Potential wrt longitude.

  potential_partial2_theta2FloatArray

  2nd Partial Derivative of the Tidal Potential wrt colatitude.

  potential_partial2_phi2FloatArray

  2nd Partial Derivative of the Tidal Potential wrt longitude.

  potential_partial2_theta_phiFloatArray

  2nd Partial Derivative of the Tidal Potential wrt colatitude and longitude.

See also

TidalPy.tides.potential.nsr_modes_med_eccen_med_obliquity.py

TidalPy.tides.potential.synchronous_low_e module

TidalPy.tides.potential.synchronous_low_e.tidal_potential(radius: FloatArray, longitude: FloatArray, colatitude: FloatArray, time: FloatArray, orbital_frequency: FloatArray, eccentricity: FloatArray, host_mass: float, semi_major_axis: FloatArray) → TidalPotentialModeOutput

Tidal gravitational potential assuming low eccentricity, no obliquity, and synchronous rotation

Parameters:

• radius (FloatArray) – Radius of the world [m]

• longitude (FloatArray) – Longitude [radians]

• colatitude (FloatArray) – Co-latitude [radians]

• time (FloatArray) – Time (orbit position) [s]

• orbital_frequency (FloatArray) – Orbital mean motion of the world [rads s-1]

• eccentricity (FloatArray) – Eccentricity of the orbit

• host_mass (float) – Mass of tide-raising world

• semi_major_axis (FloatArray) – Orbital semi-major axis [m]

Returns:

• tidal_frequencies (Dict[str, FloatArray]) – Tidal frequencies, abs(modes) [radians s-1]

• tidal_modes (Dict[str, FloatArray]) – Tidal frequency modes [radians s-1]

• potential_tuple_by_mode (PotentialTupleModeOutput) – Storage for the tidal potential and its derivatives.

  potentialFloatArray

  Tidal Potential

  potential_partial_thetaFloatArray

  Partial Derivative of the Tidal Potential wrt colatitude.

  potential_partial_phiFloatArray

  Partial Derivative of the Tidal Potential wrt longitude.

  potential_partial2_theta2FloatArray

  2nd Partial Derivative of the Tidal Potential wrt colatitude.

  potential_partial2_phi2FloatArray

  2nd Partial Derivative of the Tidal Potential wrt longitude.

  potential_partial2_theta_phiFloatArray

  2nd Partial Derivative of the Tidal Potential wrt colatitude and longitude.